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<div>The paper "Dynamic Routing Between Capsules" was written by three researchers at Google Brain: Sara Sabour, Nicholas Frosst, and Geoffrey E. Hinton. This paper was published and presented at the 31st Conference on Neural Information Processing Systems (NIPS 2017) in Long Beach, California. The same three researchers recently published a highly related paper "[https://openreview.net/pdf?id=HJWLfGWRb Matrix Capsules with EM Routing]" for ICLR 2018.<br />
<br />
=Motivation=<br />
<br />
Ever since AlexNet eclipsed the performance of competing architectures in the 2012 ImageNet challenge, convolutional neural networks have maintained their dominance in computer vision applications. Despite the recent successes and innovations brought about by convolutional neural networks, some assumptions made in these networks are perhaps unwarranted and deficient. Using a novel neural network architecture, the authors create CapsuleNets, a network that they claim is able to learn image representations in a more robust, human-like manner. With only a 3 layer capsule network, they achieved near state-of-the-art results on MNIST.<br />
<br />
The activities of the neurons within an active capsule represent the various properties of a particular entity that is present in the image. These properties can include many different types of instantiation parameter such as pose (position, size, orientation), deformation, velocity, albedo, hue, texture, etc. One very special property is the existence of the instantiated entity in the image. An obvious way to represent existence is by using a separate logistic unit whose output is the probability that the entity exists. This paper explores an interesting alternative which is to use the overall length of the vector of instantiation parameters to represent the existence of the entity and to force the orientation of the vector to represent the properties of the entity. The length of the vector output of a capsule cannot exceed 1 because of an application of a non-linearity that leaves the orientation of the vector unchanged but scales down its magnitude.<br />
<br />
The fact that the output of a capsule is a vector makes it possible to use a powerful dynamic routing mechanism to ensure that the output of the capsule gets sent to an appropriate parent in the layer above. Initially, the output is routed to all possible parents but is scaled down by coupling coefficients that sum to 1. For each possible parent, the capsule computes a “prediction vector” by multiplying its own output by a weight matrix. If this prediction vector has a large scalar product with the output of a possible parent, there is top-down feedback which increases the coupling coefficient for that parent and decreasing it for other parents. This increases the contribution that the capsule makes to that parent thus further increasing the scalar product of the capsule’s prediction with the parent’s output. This type of “routing-by-agreement” should be far more effective than the very primitive form of routing implemented by max-pooling, which allows neurons in one layer to ignore all but the most active feature detector in a local pool in the layer below. The authors demonstrate that our dynamic routing mechanism is an effective way to implement the “explaining away” that is needed for segmenting highly overlapping objects<br />
<br />
==Adversarial Examples==<br />
<br />
First discussed by Christian Szegedy et. al. in late 2013, adversarial examples have been heavily discussed by the deep learning community as a potential security threat to AI learning. Adversarial examples are defined as inputs that an attacker creates intentionally fool a machine learning model. An example of an adversarial example is shown below: <br />
<br />
[[File:adversarial_img_1.png |center]]<br />
To the human eye, the image appears to be a panda both before and after noise is injected into the image, whereas the trained ConvNet model discerns the noisy image as a Gibbon with almost 100% certainty. The fact that the network is unable to classify the above image as a panda after the epsilon perturbation leads to many potential security risks in AI dependent systems such as self-driving vehicles. Although various methods have been suggested to combat adversarial examples, robust defenses are hard to construct due to the inherent difficulties in constructing theoretical models for the adversarial example crafting process. However, beyond the fact that these examples may serve as a security threat, it emphasizes that these convolutional neural networks do not learn image classification/object detection patterns the same way that a human would. Rather than identifying the core features of a panda such as its eyes, mouth, nose, and the gradient changes in its black/white fur, the convolutional neural network seems to be learning image representations in a completely different manner. Deep learning researchers often attempt to model neural networks after human learning, and it is clear that further steps must be taken to robustify ConvNets against targeted noise perturbations.<br />
<br />
==Drawbacks of CNNs==<br />
Hinton claims that the key fault with traditional CNNs lies within the pooling function. Although pooling builds translational invariance into the network, it fails to preserve spatial relationships between objects. When we pool, we effectively reduce a <math>k \cdot k</math> kernel of convolved cells into a scalar input. This results in a desired local invariance without inhibiting the network's ability to detect features but causes valuable spatial information to be lost.<br />
<br />
Also, in CNNs, higher-level features combine lower-level features as a weighted sum: activations of a previous layer multiplied by the current layer's weight, then passed to another activation function. In this process, pose relationship between simpler features is not part of the higher-level feature.<br />
<br />
In the example below, the network is able to detect the similar features (eyes, mouth, nose, etc) within both images, but fails to recognize that one image is a human face, while the other is a Picasso-esque due to the CNN's inability to encode spatial relationships after multiple pooling layers.<br />
In deep learning, the activation level of a neuron is often interpreted as the likelihood of detecting a specific feature. CNNs are good at detecting features but less effective at exploring the spatial relationships among features (perspective, size, orientation). <br />
<br />
[[File:Equivariance Face.png |center]]<br />
<br />
Here, the CNN could wrongly activate the neuron for the face detection. Without realizing the mismatch in spatial orientation and size, the activation for the face detection will be too high.<br />
<br />
Conversely, we hope that a CNN can recognize that both of the following pictures contain a kitten. Unfortunately, when we feed the two images into a ResNet50 architecture, only the first image is correctly classified, while the second image is predicted to be a guinea pig.<br />
<br />
<br />
[[File:kitten.jpeg |center]]<br />
<br />
<br />
[[File:kitten-rotated-180.jpg |center]]<br />
<br />
For a more in depth discussion on the problems with ConvNets, please listen to Geoffrey Hinton's talk "What is wrong with convolutional neural nets?" given at MIT during the Brain & Cognitive Sciences - Fall Colloquium Series (December 4, 2014).<br />
<br />
==Intuition for Capsules==<br />
Human vision ignores irrelevant details by using a carefully determined sequence of fixation points to ensure that only a tiny fraction of the optic array is ever processed at the highest resolution. Hinton argues that our brains reason visual information by deconstructing it into a hierarchical representation which we then match to familiar patterns and relationships from memory. The key difference between this understanding and the functionality of CNNs is that recognition of an object should not depend on the angle from which it is viewed. <br />
<br />
To enforce rotational and translational equivariance, Capsule Networks store and preserve hierarchical pose relationships between objects. The core idea behind capsule theory is the explicit numerical representations of relative relationships between different objects within an image. Building these relationships into the Capsule Networks model, the network is able to recognize newly seen objects as a rotated view of a previously seen object. For example, the below image shows the Statue of Liberty under five different angles. If a person had only seen the Statue of Liberty from one angle, they would be able to ascertain that all five pictures below contain the same object (just from a different angle).<br />
<br />
[[File:Rotational Invariance.jpeg |center]]<br />
<br />
Building on this idea of hierarchical representation of spatial relationships between key entities within an image, the authors introduce Capsule Networks. Unlike traditional CNNs, Capsule Networks are better equipped to classify correctly under rotational invariance. Furthermore, the authors managed to achieve state of the art results on MNIST using a fraction of the training samples that alternative state of the art networks requires.<br />
<br />
=Background, Notation, and Definitions=<br />
<br />
==What is a Capsule==<br />
"Each capsule learns to recognize an implicitly defined visual entity over a limited domain of viewing conditions and deformations and it outputs both the probability that the entity is present within its limited domain and a set of “instantiation parameters” that may include the precise pose, lighting, and deformation of the visual entity relative to an implicitly defined canonical version of that entity. When the capsule is working properly, the probability of the visual entity being present is locally invariant — it does not change as the entity moves over the manifold of possible appearances within the limited domain covered by the capsule. The instantiation parameters, however, are “equivariant” — as the viewing conditions change and the entity moves over the appearance manifold, the instantiation parameters change by a corresponding amount because they are representing the intrinsic coordinates of the entity on the appearance manifold."<br />
<br />
In essence, capsules store object properties in a vector form; probability of detection is encoded as the vector's length, while spatial properties are encoded as the individual vector components. Thus, when a feature is present but the image captures it under a different angle, the probability of detection remains unchanged.<br />
<br />
A brief overview/understanding of capsules can be found in other papers from the author. To quote from [https://openreview.net/pdf?id=HJWLfGWRb this paper]:<br />
<br />
<blockquote><br />
A capsule network consists of several layers of capsules. The set of capsules in layer L is denoted<br />
as <math>\Omega_L</math>. Each capsule has a 4x4 pose matrix, <math>M</math>, and an activation probability, <math>a</math>. These are like the<br />
activities in a standard neural net: they depend on the current input and are not stored. In between<br />
each capsule i in layer L and each capsule j in layer L + 1 is a 4x4 trainable transformation matrix,<br />
<math>W_{ij}</math> . These <math>W_{ij}</math>'s (and two learned biases per capsule) are the only stored parameters and they<br />
are learned discriminatively. The pose matrix of capsule i is transformed by <math>W_{ij}</math> to cast a vote<br />
<math>V_{ij} = M_iW_{ij}</math> for the pose matrix of capsule j. The poses and activations of all the capsules in layer<br />
L + 1 are calculated by using a non-linear routing procedure which gets as input <math>V_{ij}</math> and <math>a_i</math> for all<br />
<math>i \in \Omega_L, j \in \Omega_{L+1}</math><br />
</blockquote><br />
<math></math><br />
<br />
==Notation==<br />
<br />
We want the length of the output vector of a capsule to represent the probability that the entity represented by the capsule is present in the current input. The paper performs a non-linear squashing operation to ensure that vector length falls between 0 and 1, with shorter vectors (less likely to exist entities) being shrunk towards 0. <br />
<br />
\begin{align} \mathbf{v}_j &= \frac{||\mathbf{s}_j||^2}{1+ ||\mathbf{s}_j||^2} \frac{\mathbf{s}_j}{||\mathbf{s}_j||} \end{align}<br />
<br />
where <math>\mathbf{v}_j</math> is the vector output of capsule <math>j</math> and <math>s_j</math> is its total input.<br />
<br />
For all but the first layer of capsules, the total input to a capsule <math>s_j</math> is a weighted sum over all “prediction vectors” <math>\hat{\mathbf{u}}_{j|i}</math> from the capsules in the layer below and is produced by multiplying the output <math>\mathbf{u}i</math> of a capsule in the layer below by a weight matrix <math>\mathbf{W}ij</math><br />
<br />
\begin{align}<br />
\mathbf{s}_j = \sum_i c_{ij}\hat{\mathbf{u}}_{j|i}, ~\hspace{0.5em} \hat{\mathbf{u}}_{j|i}= \mathbf{W}_{ij}\mathbf{u}_i<br />
\end{align}<br />
where the <math>c_{ij}</math> are coupling coefficients that are determined by the iterative dynamic routing process.<br />
<br />
The coupling coefficients between capsule <math>i</math> and all the capsules in the layer above sum to 1 and are determined by a “routing softmax” whose initial logits <math>b_{ij}</math> are the log prior probabilities that capsule <math>i</math> should be coupled to capsule <math>j</math>.<br />
<br />
\begin{align}<br />
c_{ij} = \frac{\exp(b_{ij})}{\sum_k \exp(b_{ik})}<br />
\end{align}<br />
<br />
=Network Training and Dynamic Routing=<br />
<br />
==Understanding Capsules==<br />
The notation can get somewhat confusing, so I will provide intuition behind the computational steps within a capsule. The following image is taken from naturomic's talk on Capsule Networks.<br />
<br />
[[File:CapsuleNets.jpeg|center|800px]]<br />
<br />
The above image illustrates the key mathematical operations happening within a capsule (and compares them to the structure of a neuron). Although the operations are rather straightforward, it's crucial to note that the capsule computes an affine transformation onto each input vector. The length of the input vectors <math>\mathbf{u}_{i}</math> represent the probability of entity <math>i</math> existing in a lower level. This vector is then reoriented with an affine transform using <math>\mathbf{W}_{ij}</math> matrices that encode spatial relationships between entity <math>\mathbf{u}_{i}</math> and other lower level features.<br />
<br />
We illustrate the intuition behind vector-to-vector matrix multiplication within capsules using the following example: if vectors <math>\mathbf{u}_{1}</math>, <math>\mathbf{u}_{2}</math>, and <math>\mathbf{u}_{3}</math> represent detection of eyes, nose, and mouth respectively, then after multiplication with trained weight matrices <math>\mathbf{W}_{ij}</math> (where j denotes existence of a face), we should get a general idea of the general location of the higher level feature (face), similar to the image below.<br />
<br />
[[File:Predictions.jpeg |center]]<br />
<br />
==Dynamic Routing==<br />
A capsule <math>i</math> in a lower-level layer needs to decide how to send its output vector to higher-level capsules <math>j</math>. This decision is made with probability proportional to <math>c_{ij}</math>. If there are <math>K</math> capsules in the level that capsule <math>i</math> routes to, then we know the following properties about <math>c_{ij}</math>: <math>\sum_{j=1}^M c_{ij} = 1, c_{ij} \geq 0</math><br />
<br />
In essence, the <math>\{c_{ij}\}_{j=1}^M</math> denotes a discrete probability distribution with respect to capsule <math>i</math>'s output location. Lower level capsules decide which higher level capsules to send vectors into by adjusting the corresponding routing weights <math>\{c_{ij}\}_{j=1}^M</math>. After a few iterations in training, numerous vectors will have already been sent to all higher level capsules. Based on the similarity between the current vector being routed and all vectors already sent into the higher level capsules, we decide which capsule to send the current vector into.<br />
[[File:Dynamic Routing.png|center|900px]]<br />
<br />
From the image above, we notice that a cluster of points similar to the current vector has already been routed into capsule K, while most points in capsule J are highly dissimilar. It thus makes more sense to route the current observations into capsule K; we adjust the corresponding weights upward during training.<br />
<br />
These weights are determined through the dynamic routing procedure:<br />
<br />
<br />
[[File:Routing Algo.png|900px]]<br />
<br />
Note that the convergence of this routing procedure has been questioned. Although it is empirically shown that this procedure converges, the convergence has not been proven.<br />
<br />
Although dynamic routing is not the only manner in which we can encode relationships between capsules, the premise of the paper is to demonstrate the capabilities of capsules under a simple implementation. Since the paper was released in 2017, numerous alternative routing implementations have been released including an EM matrix routing algorithm by the same authors (ICLR 2018).<br />
<br />
=Architecture=<br />
The capsule network architecture given by the authors has 11.36 million trainable parameters. The paper itself is not very detailed on exact implementation of each architectural layer, and hence it leaves some degree of ambiguity on coding various aspects of the original network. The capsule network has 6 overall layers, with the first three layers denoting components of the encoder, and the last 3 denoting components of the decoder.<br />
<br />
==Loss Function==<br />
[[File:Loss Function.png|900px]]<br />
<br />
The cost function looks very complicated, but can be broken down into intuitive components. Before diving into the equation, remember that the length of the vector denotes the probability of object existence. The left side of the equation denotes loss when the network classifies an observation correctly; the term becomes zero when the classification is incorrect. To compute loss when the network correctly classifies the label, we subtract the vector norm from a fixed quantity <math>m^+ := 0.9</math>. On the other hand, when the network classifies a label incorrectly, we penalize the loss based on the network's confidence in the incorrect label; we compute the loss by subtracting <math>m^- := 0.1</math> from the vector norm.<br />
<br />
A graphical representation of loss function values under varying vector norms is given below.<br />
[[File:Loss function chart.png|900px]]<br />
<br />
==Encoder Layers==<br />
All experiments within this paper were conducted on the MNIST dataset, and thus the architecture is built to classify the corresponding dataset. For more complex datasets, the experiments were less promising. <br />
<br />
[[File:Architecture.png|center|900px]]<br />
<br />
The encoder layer takes in a 28x28 MNIST image and learns a 16 dimensional representation of instantiation parameters.<br />
<br />
'''Layer 1: Convolution''': <br />
This layer is a standard convolution layer. Using kernels with size 9x9x1, a stride of 1, and a ReLU activation function, we detect the 2D features within the network.<br />
<br />
'''Layer 2: PrimaryCaps''': <br />
We represent the low level features detected during convolution as 32 primary capsules. Each capsule applies eight convolutional kernels with stride 2 to the output of the convolution layer and feeds the corresponding transformed tensors into the DigiCaps layer.<br />
<br />
'''Layer 3: DigiCaps''': <br />
This layer contains 10 digit capsules, one for each digit. As explained in the dynamic routing procedure, each input vector from the PrimaryCaps layer has its own corresponding weight matrix <math>W_{ij}</math>. Using the routing coefficients <math>c_{ij}</math> and temporary coefficients <math>b_{ij}</math>, we train the DigiCaps layer to output a ten 16 dimensional vectors. The length of the <math>i^{th}</math> vector in this layer corresponds to the probability of detection of digit <math>i</math>.<br />
<br />
==Decoder Layers==<br />
The decoder layer aims to train the capsules to extract meaningful features for image detection/classification. During training, it takes the 16 layer instantiation vector of the correct (not predicted) DigiCaps layer, and attempts to recreate the 28x28 MNIST image as best as possible. Setting the loss function as reconstruction error (Euclidean distance between the reconstructed image and original image), we tune the capsules to encode features that are meaningful within the actual image.<br />
<br />
[[File:Decoder.png|center|900px]]<br />
<br />
The layer consists of three fully connected layers, and transforms a 16x1 vector from the encoder layer into a 28x28 image.<br />
<br />
In addition to the digicaps loss function, we add reconstruction error as a form of regularization. During training, everything but the activity vector of the correct digit capsule is masked, and then this activity vector is used to reconstruct the input image. We minimize the Euclidean distance between the outputs of the logistic units and the pixel intensities of the original and reconstructed images. We scale down this reconstruction loss by 0.0005 so that it does not dominate the margin loss during training. As illustrated below, reconstructions from the 16D output of the CapsNet are robust while keeping only important details.<br />
<br />
[[File:Reconstruction.png|center|900px]]<br />
<br />
=MNIST Experimental Results=<br />
<br />
==Accuracy==<br />
The paper tests on the MNIST dataset with 60K training examples, and 10K testing. Wan et al. [2013] achieves 0.21% test error with ensembling and augmenting the data with rotation and scaling. They achieve 0.39% without them. As shown in Table 1, the authors manage to achieve 0.25% test error with only a 3 layer network; the previous state of the art only beat this number with very deep networks. This example shows the importance of routing and reconstruction regularizer, which boosts the performance. On the other hand, while the accuracies are very high, the number of parameters is much smaller compared to the baseline model.<br />
<br />
[[File:Accuracies.png|center|900px]]<br />
<br />
==What Capsules Represent for MNIST==<br />
The following figure shows the digit representation under capsules. Each row shows the reconstruction when one of the 16 dimensions in the DigitCaps representation is tweaked by intervals of 0.05 in the range [−0.25, 0.25]. By tweaking the values, we notice how the reconstruction changes, and thus get a sense for what each dimension is representing. The authors found that some dimensions represent global properties of the digits, while other represent localized properties. <br />
[[File:CapsuleReps.png|center|900px]]<br />
<br />
One example the authors provide is: different dimensions are used for the length of the ascender of a 6 and the size of the loop. The variations include stroke thickness, skew and width, as well as digit-specific variations. The authors are able to show dimension representations using a decoder network by feeding a perturbed vector.<br />
<br />
==Robustness of CapsNet==<br />
The authors conclude that DigitCaps capsules learn more robust representations for each digit class than traditional CNNs. The trained CapsNet becomes moderately robust to small affine transformations in the test data.<br />
<br />
To compare the robustness of CapsNet to affine transformations against traditional CNNs, both models (CapsNet and a traditional CNN with MaxPooling and DropOut) were trained on a padded and translated MNIST training set, in which each example is an MNIST digit placed randomly on a black background of 40 × 40 pixels. The networks were then tested on the [http://www.cs.toronto.edu/~tijmen/affNIST/ affNIST] dataset (MNIST digits with random affine transformation). An under-trained CapsNet which achieved 99.23% accuracy on the MNIST test set achieved a corresponding 79% accuracy on the affnist test set. A traditional CNN achieved similar accuracy (99.22%) on the mnist test set, but only 66% on the affnist test set.<br />
<br />
=MultiMNIST & Other Experiments=<br />
<br />
==MultiMNIST==<br />
To evaluate the performance of the model on highly overlapping digits, the authors generate a 'MultiMNIST' dataset. In MultiMNIST, images are two overlaid MNIST digits of the same set(train or test) but different classes. The results indicate a classification error rate of 5%. Additionally, CapsNet can be used to segment the image into the two digits that compose it. Moreover, the model is able to deal with the overlaps and reconstruct digits correctly since each digit capsule can learn the style from the votes of PrimaryCapsules layer (Figure 5).<br />
<br />
There are some additional steps to generating the MultiMNIST dataset.<br />
<br />
1. Both images are shifted by up to 4 pixels in each direction resulting in a 36 × 36 image. Bounding boxes of digits in MNIST overlap by approximately 80%, so this is used to make both digits identifiable (since there is no RGB difference learnable by the network to separate the digits)<br />
<br />
2. The label becomes a vector of two numbers, representing the original digit and the randomly generated (and overlaid) digit.<br />
<br />
<br />
<br />
[[File:CapsuleNets MultiMNIST.PNG|600px|thumb|center|Figure 5: Sample reconstructions of a CapsNet with 3 routing iterations on MultiMNIST test dataset.<br />
The two reconstructed digits are overlayed in green and red as the lower image. The upper image<br />
shows the input image. L:(l1; l2) represents the label for the two digits in the image and R:(r1; r2)<br />
represents the two digits used for reconstruction. The two right most columns show two examples<br />
with wrong classification reconstructed from the label and from the prediction (P). In the (2; 8)<br />
example the model confuses 8 with a 7 and in (4; 9) it confuses 9 with 0. The other columns have<br />
correct classifications and show that the model accounts for all the pixels while being able to assign<br />
one pixel to two digits in extremely difficult scenarios (column 1 − 4). Note that in dataset generation<br />
the pixel values are clipped at 1. The two columns with the (*) mark show reconstructions from a<br />
digit that is neither the label nor the prediction. These columns suggest that the model is not just<br />
finding the best fit for all the digits in the image including the ones that do not exist. Therefore in case<br />
of (5; 0) it cannot reconstruct a 7 because it knows that there is a 5 and 0 that fit best and account for<br />
all the pixels. Also, in the case of (8; 1) the loop of 8 has not triggered 0 because it is already accounted<br />
for by 8. Therefore it will not assign one pixel to two digits if one of them does not have any other<br />
support.]]<br />
<br />
==Other datasets==<br />
The authors also tested the proposed capsule model on CIFAR10 dataset and achieved an error rate of 10.6%. The model tested was an ensemble of 7 models. Each of the models in the ensemble had the same architecture as the model used for MNIST (apart from 3 additional channels and 64 different types of primary capsules being used). These 7 models were trained on 24x24 patches of the training images for 3 iterations. During experimentation, the authors also found out that adding an additional none-of-the-above category helped improved the overall performance. The error rate achieved is comparable to the error rate achieved by a standard CNN model. According to the authors, one of the reasons for low performance is the fact that background in CIFAR-10 images are too varied for it to be adequately modeled by reasonably sized capsule net.<br />
<br />
The proposed model was also evaluated using a small subset of SVHN dataset. The network trained was much smaller and trained using only 73257 training images. The network still managed to achieve an error rate of 4.3% on the test set.<br />
<br />
=Critique=<br />
Although the network performs incredibly favorable in the author's experiments, it has a long way to go on more complex datasets. On CIFAR 10, the network achieved subpar results, and the experimental results seem to be worse when the problem becomes more complex. This is anticipated, since these networks are still in their early stage; later innovations might come in the upcoming decades/years. It could also be wise to apply the model to other datasets with larger sizes to make the functionality more acceptable. MNIST dataset has simple patterns and even if the model wanted to be presented with only one dataset, it was better not to be MNIST dataset especially in this case that the focus is on human-eye detection and numbers are not that regular in real-life experiences.<br />
<br />
Hinton talks about CapsuleNets revolutionizing areas such as self-driving, but such groundbreaking innovations are far away from CIFAR10, and even further from MNIST. Only time can tell if CapsNets will live up to their hype.<br />
<br />
Moreover, there is no underlying intuition provided on the main point of the paper which is that capsule nets preserve relations between extracted features from the proposed architecture. An explanation on the intuition behind this idea will go a long way in arguing against CNN networks.<br />
<br />
Capsules inherently segment images and learn a lower dimensional embedding in a new manner, which makes them likely to perform well on segmentation and computer vision tasks once further research is done. <br />
<br />
Additionally, these networks are more interpretable than CNNs, and have strong theoretical reasoning for why they could work. Naturally, it would be hard for a new architecture to beat the heavily researched/modified CNNs.<br />
<br />
* ([https://openreview.net/forum?id=HJWLfGWRb]) it's not fully clear how effective it can be performed / how scalable it is. Evaluation is performed on a small dataset for shape recognition. The approach will need to be tested on larger, more challenging datasets.<br />
<br />
=Future Work=<br />
The same authors [N. F. Geoffrey E Hinton, Sara Sabour] presented another paper "MATRIX CAPSULES WITH EM ROUTING" in ICLR 2018, which achieved better results than the work presented in this paper. They presented a new multi-layered capsule network architecture, implemented an EM routing procedure, and introduced "Coordinate Addition". This new type reduced number of errors by 45%, and performed better than standard CNN on white box adversarial attacks. Capsule architectures are gaining interest because of their ability to achieve equivariance of parts, and employ a new form of pooling called "routing" (as opposed to max pooling) which groups parts that make similar predictions of the whole to which they belong, rather than relying on spatial co-locality.<br />
Moreover, the authors hint towards trying to change the curvature and sensitivities to various factors by introducing new form of loss function. It may improve the performance of the model for more complicated data set which is one of the model's drawback.<br />
<br />
Moreover, as mentioned in critiques, a good future work for this group would be making the model more robust to the dataset and achieve acceptable performance on datasets with more regularly seen images in real life experiences.<br />
<br />
=References=<br />
#N. F. Geoffrey E Hinton, Sara Sabour. Matrix capsules with em routing. In International Conference on Learning Representations, 2018.<br />
#S. Sabour, N. Frosst, and G. E. Hinton, “Dynamic routing between capsules,” arXiv preprint arXiv:1710.09829v2, 2017<br />
# Hinton, G. E., Krizhevsky, A. and Wang, S. D. (2011), Transforming Auto-encoders <br />
#Geoffrey Hinton's talk: What is wrong with convolutional neural nets? - Talk given at MIT. Brain & Cognitive Sciences - Fall Colloquium Series. [https://www.youtube.com/watch?v=rTawFwUvnLE ]<br />
#Understanding Hinton’s Capsule Networks - Max Pechyonkin's series [https://medium.com/ai%C2%B3-theory-practice-business/understanding-hintons-capsule-networks-part-i-intuition-b4b559d1159b]<br />
#Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg SCorrado, Andy Davis, Jeffrey Dean, Matthieu Devin, et al. Tensorflow: Large-scale machinelearning on heterogeneous distributed systems.arXiv preprint arXiv:1603.04467, 2016.<br />
#Jimmy Ba, Volodymyr Mnih, and Koray Kavukcuoglu. Multiple object recognition with visualattention.arXiv preprint arXiv:1412.7755, 2014.<br />
#Jia-Ren Chang and Yong-Sheng Chen. Batch-normalized maxout network in network.arXiv preprintarXiv:1511.02583, 2015.<br />
#Dan C Cire ̧san, Ueli Meier, Jonathan Masci, Luca M Gambardella, and Jürgen Schmidhuber. High-performance neural networks for visual object classification.arXiv preprint arXiv:1102.0183,2011.<br />
#Ian J Goodfellow, Yaroslav Bulatov, Julian Ibarz, Sacha Arnoud, and Vinay Shet. Multi-digit numberrecognition from street view imagery using deep convolutional neural networks.arXiv preprintarXiv:1312.6082, 2013.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Reinforcement_Learning_in_Continuous_Action_Spaces_a_Case_Study_in_the_Game_of_Simulated_Curling&diff=42142Deep Reinforcement Learning in Continuous Action Spaces a Case Study in the Game of Simulated Curling2018-11-30T22:47:10Z<p>R82zhang: [T] /* AlphaGo Lee */</p>
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<div>This page provides a summary and critique of the paper '''Deep Reinforcement Learning in Continuous Action Spaces: a Case Study in the Game of Simulated Curling''' [[http://proceedings.mlr.press/v80/lee18b/lee18b.pdf Online Source]], published in ICML 2018. The source code for this paper is available [https://github.com/leekwoon/KR-DL-UCT here]<br />
<br />
= Introduction and Motivation =<br />
<br />
In recent years, Reinforcement Learning methods have been applied to many different games, such as chess and checkers. More recently, the use of CNN's has allowed neural networks to out-perform humans in many difficult games, such as Go. However, many of these cases involve a discrete state or action space; the number of actions a player can take and/or the number of possible game states are finite. Deep CNNs for large, non-convex continuous action spaces are not directly applicable. To solve this issue, we conduct a policy search with an efficient stochastic continuous action search on top of policy samples generated from a deep CNN. Our deep CNN still discretizes the state space and the action space. However, in<br />
the stochastic continuous action search, we lift the restriction of the deterministic discretization and conduct a local search procedure in a physical simulator with continuous action samples. In this way, the benefits of both deep neural networks and physical simulators can be realized.<br />
<br />
Interacting with the real world (e.g.; a scenario that involves moving physical objects) typically involves working with a continuous action space. It is thus important to develop strategies for dealing with continuous action spaces. Deep neural networks that are designed to succeed in finite action spaces are not necessarily suitable for continuous action space problems. This is due to the fact that deterministic discretization of a continuous action space causes strong biases in policy evaluation and improvement. <br />
<br />
This paper introduces a method to allow learning with continuous action spaces. A CNN is used to perform learning on a discretion state and action spaces, and then a continuous action search is performed on these discrete results.<br />
<br />
Curling is chosen as a domain to test the network on. Curling was chosen due to its large action space, potential for complicated strategies, and need for precise interactions.<br />
<br />
== Curling ==<br />
<br />
Curling is a sport played by two teams on a long sheet of ice. Roughly, the goal is for each time to slide rocks closer to the target on the other end of the sheet than the other team. The next sections will provide a background on the game play, and potential challenges/concerns for learning algorithms. A terminology section follows.<br />
<br />
=== Game play ===<br />
<br />
A game of curling is divided into ends. In each end, players from both teams alternate throwing (sliding) eight rocks to the other end of the ice sheet, known as the house. Rocks must land in a certain area in order to stay in play, and must touch or be inside concentric rings (12ft diameter and smaller) in order to score points. At the end of each end, the team with rocks closest to the center of the house scores points.<br />
<br />
When throwing a rock, the curling can spin the rock. This allows the rock to 'curl' its path towards the house and can allow rocks to travel around other rocks. Team members are also able to sweep the ice in front of a moving rock in order to decrease friction, which allows for fine-tuning of distance (though the physics of sweeping are not implemented in the simulation used).<br />
<br />
Curling offers many possible high-level actions, which are directed by a team member to the throwing member. An example set of these includes:<br />
<br />
* Draw: Throw a rock to a target location<br />
* Freeze: Draw a rock up against another rock<br />
* Takeout: Knock another rock out of the house. Can be combined with different ricochet directions<br />
* Guard: Place a rock in front of another, to block other rocks (ex: takeouts)<br />
<br />
=== Challenges for AI ===<br />
<br />
Curling offers many challenges for curling based on its physics and rules. This section lists a few concerns.<br />
<br />
The effect of changing actions can be highly nonlinear and discontinuous. This can be seen when considering that a 1-cm deviation in a path can make the difference between a high-speed collision, or lack of collision.<br />
<br />
Curling will require both offensive and defensive strategies. For example, consider the fact that the last team to throw a rock each end only needs to place that rock closer than the opposing team's rocks to score a point and invalidate any opposing rocks in the house. The opposing team should thus be considering how to prevent this from happening, in addition to scoring points themselves.<br />
<br />
Curling also has a concept known as 'the hammer'. The hammer belongs to the team which throws the last rock each end, providing an advantage, and is given to the team that does not score points each end. It could very well be a good strategy to try not to win a single point in an end (if already ahead in points, etc), as this would give the advantage to the opposing team.<br />
<br />
Finally, curling has a rule known as the 'Free Guard Zone'. This applies to the first 4 rocks thrown (2 from each team). If they land short of the house, but still in play, then the rocks are not allowed to be removed (via collisions) until all of the first 4 rocks have been thrown.<br />
<br />
=== Terminology ===<br />
<br />
* End: A round of the game<br />
* House: The end of the sheet of ice, which contains<br />
* Hammer: The team that throws the last rock of an end 'has the hammer'<br />
* Hog Line: thick line that is drawn in front of the house, orthogonal to the length of the ice sheet. Rocks must pass this line to remain in play.<br />
* Back Line: think line drawn just behind the house. Rocks that pass this line are removed from play.<br />
<br />
<br />
== Related Work ==<br />
<br />
=== AlphaGo Lee ===<br />
<br />
AlphaGo Lee (Silver et al., 2016, [5]) refers to an algorithm used to play the game Go, which was able to defeat international champion Lee Sedol. <br />
<br />
<br />
Go game:<br />
* Start with 19x19 empty board<br />
* One player takes black stones and the other take white stones<br />
* Two players take turns to put stones on the board<br />
* Once the stone has been placed, the stones cannot be moved anymore<br />
* Rules:<br />
1. If one connected part is completely surrounded by the opponent's stones, remove it from the board<br />
<br />
2. Ko rule: Forbids a board play to repeat a board position<br />
* End when there are no valuable moves. <br />
* Count the territory of both players. The objective of the game is to capture more territory than your opponent. The player with black stone plays first. However, the black player needs to give 7.5 points to whites points (called Komi) as a tradeoff. There are some variations on how much points the player with the black stone should give based on different rules in different Asia countries.<br />
* This game used to be a huge challenge to artificial intelligence due to two reasons. One is the search space is extremely large. It is estimated to be on the order of 10^172, which is more than the number of atoms in the universe, and it is much larger than the game states in Chess 10^47. Another reason is there was no good heuristic function for evaluating a situation in Go. So the traditional alpha-beta pruning algorithm will not have good performance due to the poor heuristic function. For Alpha go lee, the CNN plays a role like a good heuristic function, which results on the huge performance improvement of the AI.<br />
[[File:go.JPG|700px|center]]<br />
<br />
Two neural networks were trained on the moves of human experts, to act as both a policy network and a value network. A Monte Carlo Tree Search algorithm was used for policy improvement.<br />
<br />
The AlphaGo Lee policy network predicts the best move given a board configuration. It has a CNN architecture with 13 hidden layers, and it is trained using expert game play data and improved through self-play.<br />
<br />
The value network evaluates the probability of winning given a board configuration. It consists of a CNN with 14 hidden layers, and it is trained using self-play data from the policy network. <br />
<br />
Finally, the two networks are combined using Monte-Carlo Tree Search, which performs a look-ahead search to select the actions for gameplay.<br />
<br />
The use of both policy and value networks are reflected in this paper's work.<br />
<br />
=== AlphaGo Zero ===<br />
<br />
AlphaGo Zero (Silver et al., 2017, [6]) is an improvement on the AlphaGo Lee algorithm. AlphaGo Zero uses a unified neural network in place of the separate policy and value networks and is trained on self-play, without the need of expert training.<br />
Previous versions of AlphaGo initially trained on thousands of human amateur and professional games to learn how to play Go. AlphaGo Zero skips this step and learns to play simply by playing games against itself, starting from completely random play. In doing so, it quickly surpassed human level of play and defeated the previously published champion-defeating version of AlphaGo by 100 games to 0.<br />
It is able to do this by using a novel form of reinforcement learning, in which AlphaGo Zero becomes its own teacher. The system starts off with a neural network that knows nothing about the game of Go. It then plays games against itself, by combining this neural network with a powerful search algorithm. As it plays, the neural network is tuned and updated to predict moves, as well as the eventual winner of the games.<br />
<br />
This updated neural network is then recombined with the search algorithm to create a new, stronger version of AlphaGo Zero, and the process begins again. In each iteration, the performance of the system improves by a small amount, and the quality of the self-play games increases, leading to more and more accurate neural networks and ever stronger versions of AlphaGo Zero.<br />
<br />
This technique is more powerful than previous versions of AlphaGo because it is no longer constrained by the limits of human knowledge. Instead, it is able to learn tabula rasa from the strongest player in the world: AlphaGo itself.<br />
<br />
Other differences from the previous AlphaGo iterations are as follows. AlphaGo Zero only uses the black and white stones from the Go board as its input, whereas previous versions of AlphaGo included a small number of hand-engineered features. It uses one neural network rather than two. Earlier versions of AlphaGo used a “policy network” to select the next move to play and a ”value network” to predict the winner of the game from each position. These are combined in AlphaGo Zero, allowing it to be trained and evaluated more efficiently. AlphaGo Zero does not use “rollouts” - fast, random games used by other Go programs to predict which player will win from the current board position. Instead, it relies on its high quality neural networks to evaluate positions. All of these differences help improve the performance of the system and make it more general. But it is the algorithmic change that makes the system much more powerful and efficient.<br />
<br />
The unification of networks and self-play are also reflected in this paper.<br />
<br />
=== Curling Algorithms ===<br />
<br />
Some past algorithms have been proposed to deal with continuous action spaces. For example, (Yammamoto et al, 2015, [7]) use game tree search methods in a discretized space. The value of an action is taken as the average of nearby values, with respect to some knowledge of execution uncertainty.<br />
<br />
=== Monte Carlo Tree Search ===<br />
<br />
Monte Carlo Tree Search algorithms have been applied to continuous action spaces. These algorithms, to be discussed in further detail, balance exploration of different states, with knowledge of paths of execution through past games. An MCTS called <math>KR-UCT</math> which is able to find effective selections and use kernel regression (KR) and kernel density estimation(KDE) to estimate rewards using neighborhood information has been applied to continuous action space by researchers. <br />
<br />
With bandit problem, scholars used hierarchical optimistic optimization(HOO) to create a cover tree and divide the action space into small ranges at different depths, where the most promising node will create fine granularity estimates.<br />
<br />
=== Curling Physics and Simulation ===<br />
<br />
Several references in the paper refer to the study and simulation of curling physics. Scholars have analyzed friction coefficients between curling stones and ice. While modelling the changes in friction on ice is not possible, a fixed friction coefficient was predefined in the simulation. The behavior of the stones was also modeled. Important parameters are trained from professional players. The authors used the same parameters in this paper.<br />
<br />
== General Background of Algorithms ==<br />
<br />
=== Policy and Value Functions ===<br />
<br />
A policy function is trained to provide the best action to take, given a current state. Policy iteration is an algorithm used to improve a policy over time. This is done by alternating between policy evaluation and policy improvement.<br />
<br />
POLICY IMPROVEMENT: LEARNING ACTION POLICY<br />
<br />
Action policy <math> p_{\sigma}(a|s) </math> outputs a probability distribution over all eligible moves <math> a </math>. Here <math> \sigma </math> denotes the weights of a neural network that approximates the policy. <math>s</math> denotes the set of states and <math>a</math> denotes the set of actions taken in the environment. The policy is a function that returns a action given the state at which the agent is present. The policy gradient reinforcement learning can be used to train action policy. It is updated by stochastic gradient ascent in the direction that maximizes the expected outcome at each time step t,<br />
\[ \Delta \rho \propto \frac{\partial p_{\rho}(a_t|s_t)}{\partial \rho} r(s_t) \]<br />
where <math> r(s_t) </math> is the return.<br />
<br />
POLICY EVALUATION: LEARNING VALUE FUNCTIONS<br />
<br />
A value function is trained to estimate the value of a value of being in a certain state with parameter <math> \theta </math>. It is trained based on records of state-action-reward sets <math> (s, r(s)) </math> by using stochastic gradient de- scent to minimize the mean squared error (MSE) between the predicted regression value and the corresponding outcome,<br />
\[ \Delta \theta \propto \frac{\partial v_{\theta}(s)}{\partial \theta}(r(s)-v_{\theta}(s)) \]<br />
<br />
=== Monte Carlo Tree Search ===<br />
<br />
Monte Carlo Tree Search (MCTS) is a search algorithm used for finite-horizon tasks (ex: in curling, only 16 moves, or throw stones, are taken each end).<br />
<br />
MCTS is a tree search algorithm similar to minimax. However, MCTS is probabilistic and does not need to explore a full game tree or even a tree reduced with alpha-beta pruning. This makes it tractable for games such as GO, and curling.<br />
<br />
Nodes of the tree are game states, and branches represent actions. Each node stores statistics on how many times it has been visited by the MCTS, as well as the number of wins encountered by playouts from that position. A node has been considered 'visited' if a full playout has started from that node. A node is considered 'expanded' if all its children have been visited.<br />
<br />
MCTS begins with the '''selection''' phase, which involves traversing known states/actions. This involves expanding the tree by beginning at the root node, and selecting the child/score with the highest 'score'. From each successive node, a path down to a root node is explored in a similar fashion.<br />
<br />
The next phase, '''expansion''', begins when the algorithm reaches a node where not all children have been visited (ie: the node has not been fully expanded). In the expansion phase, children of the node are visited, and '''simulations''' run from their states.<br />
<br />
Once the new child is expanded, '''simulation''' takes place. This refers to a full playout of the game from the point of the current node, and can involve many strategies, such as randomly taken moves, the use of heuristics, etc.<br />
<br />
The final phase is '''update''' or '''back-propagation''' (unrelated to the neural network algorithm). In this phase, the result of the '''simulation''' (ie: win/lose) is update in the statistics of all parent nodes.<br />
<br />
A selection function known as Upper Confidence Bound (UCT) can be used for selecting which node to select. The formula for this equation is shown below [[https://www.baeldung.com/java-monte-carlo-tree-search source]]. Note that the first term essentially acts as an average score of games played from a certain node. The second term, meanwhile, will grow when sibling nodes are expanded. This means that unexplored nodes will gradually increase their UCT score, and be selected in the future.<br />
<br />
<math> \frac{w_i}{n_i} + c \sqrt{\frac{\ln t}{n_i}} </math><br />
<br />
In which<br />
<br />
* <math> w_i = </math> number of wins after <math> i</math>th move<br />
* <math> n_i = </math> number of simulations after <math> i</math>th move<br />
* <math> c = </math> exploration parameter (theoritically eqal to <math> \sqrt{2}</math>)<br />
* <math> t = </math> total number of simulations for the parent node<br />
<br />
<br />
Sources: 2,3,4<br />
<br />
[[File:MCTS_Diagram.jpg | 500px|center]]<br />
<br />
=== Kernel Regression ===<br />
<br />
Kernel regression is a form of weighted averaging which uses a kernel function as a weight to estimate the conditional expectation of a random variable. Given two items of data, '''x''', each of which has a value '''y''' associated with them, and a choice of Kernel '''K''', the kernel functions outputs a weighting factor. An estimate of the value of a new, unseen point, is then calculated as the weighted average of values of surrounding points.<br />
<br />
A typical kernel is a Gaussian kernel, shown below. The formula for calculating estimated value is shown below as well (sources: Lee et al.).<br />
<br />
[[File:gaussian_kernel.png | 400 px]]<br />
<br />
[[File:kernel_regression.png | 250 px]]<br />
<br />
The denominator of the conditional expectation is related to kernel density estimation, which is defined as <math display="inline">W(x)=\sum_{i=0}^n K(x,x_i)</math>.<br />
<br />
In this case, the combination of the two-act to weigh scores of samples closest to '''x''' more strongly.<br />
<br />
= Methods =<br />
<br />
== Variable Definitions ==<br />
<br />
The following variables are used often in the paper:<br />
<br />
* <math>s</math>: A state in the game, as described below as the input to the network.<br />
* <math>s_t</math>: The state at a certain time-step of the game. Time-steps refer to full turns in the game<br />
* <math>a_t</math>: The action taken in state <math>s_t</math><br />
* <math>A_t</math>: The actions taken for sibling nodes related to <math>a_t</math> in MCTS<br />
* <math>n_{a_t}</math>: The number of visits to node a in MCTS<br />
* <math>v_{a_t}</math>: The MCTS value estimate of a node<br />
<br />
== Network Design ==<br />
<br />
The authors design a CNN called the 'policy-value' network. The network consists of a common network structure, which is then split into 'policy' and 'value' outputs. This network is trained to learn a probability distribution of actions to take, and expected rewards, given an input state.<br />
<br />
=== Shared Structure ===<br />
<br />
The network consists of 1 convolutional layer followed by 9 residual blocks, each block consisting of 2 convolutional layers with 32 3x3 filters. The structure of this network is shown below:<br />
<br />
<br />
[[File:curling_network_layers.png|600px|thumb|center|Figure 2. A detail description of our policy-value network. The shared network is composed of one convolutional layer and nine residual blocks. Each residual block (explained in b) has two convolutional layer with batch normalization (Ioffe & Szegedy, 2015[11]) followed by the addition of the input and the residual block. Each layer in the shared network uses 3x3 filters. The policy head<br />
has two more convolutional layers, while the value head has two fully connected layers on top of a convolutional layer. For the activation function of each convolutional layer, ReLU (Nair & Hinton[12]) is used.]]<br />
<br />
<br />
<br />
the input to this network is the following:<br />
* Location of stones<br />
* Order to tee (the center of the sheet)<br />
* A 32x32 grid of representation of the ice sheet, representing which stones are present in each grid cell.<br />
<br />
The authors do not describe how the stone-based information is added to the 32x32 grid as input to the network.<br />
<br />
=== Policy Network ===<br />
<br />
The policy head is created by adding 2 convolutional layers with 2 (two) 3x3 filters to the main body of the network. The output of the policy head is a distribution of probabilities of the actions to select the best shot out of a 32x32x2 set of actions. The actions represent target locations in the grid and spin direction of the stone.<br />
<br />
[[File:policy-value-net.PNG | 700px]]<br />
<br />
=== Value Network ===<br />
<br />
The valve head is created by adding a convolution layer with 1 3x3 filter, and dense layers of 256 and 17 units, to the shared network. The 17 output units represent a probability of scores in the range of [-8,8], which are the possible scores at each end of a curling game.<br />
<br />
== Continuous Action Search ==<br />
<br />
The policy head of the network only outputs actions from a discretized action space. For real-life interactions, and especially in curling, this will not suffice, as very fine adjustments to actions can make significant differences in outcomes.<br />
<br />
Actions in the continuous space are generated using an MCTS algorithm, with the following steps:<br />
<br />
=== Selection ===<br />
<br />
From a given state, the list of already-visited actions is denoted as A<sub>t</sub>. Scores and the number of visits to each node are estimated using the equations below (the first equation shows the expectation of the end value for one-end games). These are likely estimated rather than simply taken from the MCTS statistics to help account for the differences in a continuous action space.<br />
<br />
[[File:curling_kernel_equations.png | 400px]]<br />
<br />
The UCB formula is then used to select an action to expand.<br />
<br />
The actions that are taken in the simulator appear to be drawn from a Gaussian centered around <math>a_t</math>. This allows exploration in the continuous action space.<br />
<br />
=== Expansion ===<br />
<br />
The authors use a variant of regular UCT for expansion. In this case, they expand a new node only when existing nodes have been visited a certain number of times. The authors utilize a widening approach to overcome problems with standard UCT performing a shallow search when there is a large action space.<br />
<br />
=== Simulation ===<br />
<br />
Instead of simulating with a random game playout, the authors use the value network to estimate the likely score associated with a state. This speeds up simulation (assuming the network is well trained), as the game does not actually need to be simulated.<br />
<br />
=== Backpropogation ===<br />
<br />
Standard backpropagation is used, updating both the values and number of visits stored in the path of parent nodes.<br />
<br />
<br />
== Supervised Learning ==<br />
<br />
During supervised training, data is gathered from the program AyumuGAT'16 ([8]). This program is also based on both an MCTS algorithm, and a high-performance AI curling program. 400 000 state-action pairs were generated during this training.<br />
<br />
=== Policy Network ===<br />
<br />
The policy network was trained to learn the action taken in each state. Here, the likelihood of the taken action was set to be 1, and the likelihood of other actions to be 0.<br />
<br />
=== Value Network ===<br />
<br />
The value network was trained by 'd-depth simulations and bootstrapping of the prediction to handle the high variance in rewards resulting from a sequence of stochastic moves' (quote taken from paper). In this case, ''m'' state-action pairs were sampled from the training data. For each pair, <math>(s_t, a_t)</math>, a state d' steps ahead was generated, <math>s_{t+d}</math>. This process dealt with uncertainty by considering all actions in this rollout to have no uncertainty, and allowing uncertainty in the last action, ''a<sub>t+d-1</sub>''. The value network is used to predict the value for this state, <math>z_t</math>, and the value is used for learning the value at ''s<sub>t</sub>''.<br />
<br />
=== Policy-Value Network ===<br />
<br />
The policy-value network was trained to maximize the similarity of the predicted policy and value, and the actual policy and value from a state. The learning algorithm parameters are:<br />
<br />
* Algorithm: stochastic gradient descent<br />
* Batch size: 256<br />
* Momentum: 0.9<br />
* L2 regularization: 0.0001<br />
* Training time: ~100 epochs<br />
* Learning rate: initialized at 0.01, reduced twice<br />
<br />
A multi-task loss function was used. This takes the summation of the cross-entropy losses of each prediction:<br />
<br />
[[File:curling_loss_function.png | 300px]]<br />
<br />
== Self-Play Reinforcement Learning ==<br />
<br />
After initialization by supervised learning, the algorithm uses self-play to further train itself. During this training, the policy network learns probabilities from the MCTS process, while the value network learns from game outcomes.<br />
<br />
At a game state ''s<sub>t</sub>'':<br />
<br />
1) the algorithm outputs a prediction ''z<sub>t</sub>''. This is en estimate of game score probabilities. It is based on similar past actions, and computed using kernel regression.<br />
<br />
2) the algorithm outputs a prediction <math>\pi_t</math>, representing a probability distribution of actions. These are proportional to estimated visit counts from MCTS, based on kernel density estimation.<br />
<br />
It is not clear how these predictions are created. It would seem likely that the policy-value network generates these, but the wording of the paper suggests they are generated from MCTS statistics.<br />
<br />
The policy-value network is updated by sampling data <math>(s, \pi, z)</math> from recent history of self-play. The same loss function is used as before.<br />
<br />
It is not clear how the improved network is used, as MCTS seems to be the driving process at this point.<br />
<br />
== Long-Term Strategy Learning ==<br />
<br />
Finally, the authors implement a new strategy to augment their algorithm for long-term play. In this context, this refers to playing a game over many ends, where the strategy to win a single end may not be a good strategy to win a full game. For example, scoring one point in an end, while being one point ahead, gives the advantage to the other team in the next round (as they will throw the last stone). The other team could then use the advantage to score two points, taking the lead.<br />
<br />
The authors build a 'winning percentage' table. This table stores the percentage of games won, based on the number of ends left, and the difference in score (current team - opposing team). This can be computed iteratively and using the probability distribution estimation of one-end scores.<br />
<br />
== Final Algorithms ==<br />
<br />
The authors make use of the following versions of their algorithm:<br />
<br />
=== KR-DL ===<br />
<br />
''Kernel regression-deep learning'': This algorithm is trained only by supervised learning.<br />
<br />
=== KR-DRL ===<br />
<br />
''Kernel regression-deep reinforcement learning'': This algorithm is trained by supervised learning (ie: initialized as the KR-DL algorithm), and again on self-play. During self-play, each shot is selected after 400 MCTS simulations of k=20 randomly selected actions. Data for self-play was collected over a week on 5 GPUS and generated 5 million game positions. The policy-value network was continually updated using samples from the latest 1 million game positions.<br />
<br />
=== KR-DRL-MES ===<br />
<br />
''Kernel regression-deep reinforcement learning-multi-ends-strategy'': This algorithm makes use of the winning percentage table generated from self-play.<br />
<br />
= Testing and Results =<br />
The authors use data from the public program AyumuGAT’16 to test. Testing is done with a simulated curling program [9]. This simulator does not deal with changing ice conditions, or sweeping, but does deal with stone trajectories and collisions.<br />
<br />
== Comparison of KR-DL-UCT and DL-UCT ==<br />
<br />
The first test compares an algorithm trained with kernel regression with an algorithm trained without kernel regression, to show the contribution that kernel regression adds to the performance. Both algorithms have networks initialised with the supervised learning, and then trained with two different algorithms for self-play. KR-DL-UCT uses the algorithm described above. The authors do not go into detail on how DL-UCT selects shots, but state that a constant is set to allow exploration.<br />
<br />
As an evaluation, both algorithms play 2000 games against the DL-UCT algorithm, which is frozen after supervised training. 1000 games are played with the algorithm taking the first, and 100 taking the 2nd, shots. The games were two-end games. The figure below shows each algorithm's winning percentage given different amounts of training data. While the DL-UCT outperforms the supervised-training-only-DL-UCT algorithm, the KR-DL-UCT algorithm performs much better.<br />
<br />
<center>[[File:curling_KR_test.png | 400px]]</center><br />
<br />
== Matches ==<br />
<br />
Finally, to test the performance of their multiple algorithms, the authors run matches between their algorithms and other existing programs. Each algorithm plays 200 matches against each other program, 100 of which are played as the first-playing team, and 100 as the second-playing team. Only 1 program was able to out-perform the KR-DRL algorithm. The authors state that this program, ''JiritsukunGAT'17'' also uses a deep network and hand-crafted features. However, the KR-DRL-MES algorithm was still able to out-perform this. Figure 4 shows the Elo ratings of the different programs. Note that the programs in blue are those created by the authors. They also played some games between their KR-DRL-MES and notable<br />
programs. Table 1, shows the details of the match results. ''JiritsukunGAT'17'' shows a similar level of performance but KR-DRL-MES is still the winner.<br />
<br />
<br />
<br />
[[File:curling_ratings.png|600px|thumb|center|Figure 4. Elo rating and winning percentages of our models and GAT rankers. Each match has 200 games (each program plays 100 pre-ordered games), because the player which has the last shot (the hammer shot) in each end would have an advantage.]]<br />
<br />
<br />
[[File:ttt.png|600px|thumb|center|Table 1. The 8-end game results for KR-DRL-MES against other programs alternating the opening player each game. The matches are held by following the rules of the latest GAT competition.]]<br />
<br />
= Conclusion & Critique =<br />
<br />
The authors have presented a new framework which incorporates a deep neural network for learning game strategy with a kernel-based Monte Carlo tree search from a continuous space. Without the use of any hand-crafted feature, their policy-value network is successfully trained using supervised learning followed by reinforcement learning with a high-fidelity simulator for the Olympic sport of curling. Following are my critiques on the paper:<br />
<br />
== Strengths ==<br />
<br />
This algorithm out-performs other high-performance algorithms (including past competition champions).<br />
<br />
I think the paper does a decent job of comparing the performance of their algorithm to others. They are able to clearly show the benefits of many of their additions.<br />
<br />
The authors do seem to be able to adopt strategies similar to those used in Go and other games to the continuous action-space domain. In addition, the final strategy needs no hand-crafted features for learning.<br />
<br />
== Weaknesses ==<br />
<br />
Somtimes, I found this paper difficult to follow. One problem was that the algorithms were introduced first, and then how they were used was described. So when the paper stated that self-play shots were taken after 400 simulations, it seemed unclear what simulations were being run and at what stage of the algorithm (ex: MCTS simulations, simulations sped up by using the value network, full simulations on the curling simulator). In particular, both the MCTS statistics and the policy-value network could be used to estimate both action probabilities and state values, so it is difficult to tell which is used in which case. There was also no clear distinction between discrete-space actions and continuous-space actions.<br />
<br />
While I think the comparison of different algorithms was done well, I believe it still lacked significant details. There were one-off mentioned in the paper which would have been nice to see as results. These include the statement that having a policy-value network in place of two networks lead to better performance.<br />
<br />
At this point, the algorithms used still rely on initialization by a pre-made program.<br />
<br />
There was little theoretical development or justification done in this paper.<br />
<br />
While curling is an interesting choice for demonstrating the algorithm, the fact that the simulations used did not support many of the key points of curling (ice conditions, sweeping) seems very limited. Another game, such as pool, would likely have offered some of the same challenges but offered more high-fidelity simulations/training.<br />
<br />
While the spatial placements of stones were discretized in a grid, the curl of thrown stones was discretized to only +/-1. This seems like it may limit learning high- and low-spin moves. It should be noted that having zero spins is not commonly used, to the best of my knowledge.<br />
<br />
=References=<br />
# Lee, K., Kim, S., Choi, J. & Lee, S. "Deep Reinforcement Learning in Continuous Action Spaces: a Case Study in the Game of Simulated Curling." Proceedings of the 35th International Conference on Machine Learning, in PMLR 80:2937-2946 (2018)<br />
# https://www.baeldung.com/java-monte-carlo-tree-search<br />
# https://jeffbradberry.com/posts/2015/09/intro-to-monte-carlo-tree-search/<br />
# https://int8.io/monte-carlo-tree-search-beginners-guide/<br />
# https://en.wikipedia.org/wiki/Monte_Carlo_tree_search<br />
# Silver, D., Huang, A., Maddison, C., Guez, A., Sifre, L.,Van Den Driessche, G., Schrittwieser, J., Antonoglou, I.,Panneershelvam, V., Lanctot, M., Dieleman, S., Grewe,D., Nham, J., Kalchbrenner, N.,Sutskever, I., Lillicrap, T.,Leach, M., Kavukcuoglu, K., Graepel, T., and Hassabis,D. Mastering the game of go with deep neural networksand tree search. Nature, pp. 484–489, 2016.<br />
# Silver, D., Schrittwieser, J., Simonyan, K., Antonoglou,I., Huang, A., Guez, A., Hubert, T., Baker, L., Lai, M., Bolton, A., Chen, Y., Lillicrap, T., Hui, F., Sifre, L.,van den Driessche, G., Graepel, T., and Hassabis, D.Mastering the game of go without human knowledge.Nature, pp. 354–359, 2017.<br />
# Yamamoto, M., Kato, S., and Iizuka, H. Digital curling strategy based on game tree search. In Proceedings of the IEEE Conference on Computational Intelligence and Games, CIG, pp. 474–480, 2015.<br />
# Ohto, K. and Tanaka, T. A curling agent based on the montecarlo tree search considering the similarity of the best action among similar states. In Proceedings of Advances in Computer Games, ACG, pp. 151–164, 2017.<br />
# Ito, T. and Kitasei, Y. Proposal and implementation of digital curling. In Proceedings of the IEEE Conference on Computational Intelligence and Games, CIG, pp. 469–473, 2015.<br />
# Ioffe, S. and Szegedy, C. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In Proceedings of the International Conference on Machine Learning, ICML, pp. 448–456, 2015.<br />
# Nair, V. and Hinton, G. Rectified linear units improve restricted boltzmann machines.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=42134Annotating Object Instances with a Polygon RNN2018-11-30T22:32:35Z<p>R82zhang: [T]/* Critique */</p>
<hr />
<div>Summary of the CVPR '17 best [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf ''paper'']<br />
<br />
The presentation video of paper is available here[https://www.youtube.com/watch?v=S1UUR4FlJ84].<br />
<br />
= Background =<br />
<br />
If a snapshot of an image is given to a human, how will he/she describe a scene? He/she might identify that there is a car parked near the curb, or that the car is parked right beside a street light. This ability to decompose objects in scenes into separate entities is key to understanding what is around us and it helps to reason about the behavior of objects in the scene.<br />
<br />
Automating this process is a classic computer vision problem and is often termed "object detection". There are four distinct levels of detection (refer to Figure 1 for a visual cue):<br />
<br />
1. Classification + Localization: This is the most basic method that detects whether '''an''' object is either present or absent in the image and then identifies the position of the object within the image in the form of a bounding box overlayed on the image.<br />
<br />
2. Object Detection: The classic definition of object detection points to the detection and localization of '''multiple''' objects of interest in the image. The output of the detection is still a bounding box overlayed on the image at the position corresponding to the location of the objects in the image.<br />
<br />
3. Semantic Segmentation: This is a pixel level approach, i.e., each pixel in the image is assigned to a category label. Here, there is no difference between instances; this is to say that there are objects present from three distinct categories in the image, without tracking or reporting the number of appearances of each instance within a category. <br />
<br />
4. Instance Segmentation (''This paper performs this''): The goal is to not only to assign pixel-level categorical labels, but to identify each entity separately as sheep 1, sheep 2, sheep 3, grass, and so on.<br />
<br />
[[File:Figure_1.jpeg | 450px|thumb|center|Figure 1: Different levels of detection in an image.]]<br />
<br />
<br />
== Motivation ==<br />
<br />
Semantic segmentation helps us achieve a deeper understanding of images than image classification or object detection. Over and above this, instance segmentation is crucial in applications where multiple objects of the same category are to be tracked, especially in autonomous driving, mobile robotics, and medical image processing. This paper deals with a novel method to tackle the instance segmentation problem pertaining specifically to the field of autonomous driving, but shown to generalize well in other fields such as medical image processing.<br />
A polygon is natural form of annotation. Current instant segmentations annotated by humans use polygons because it is a special representation of the image which can use small number of vertices instead of various pixels and makes it easy to incorporate user modifications.<br />
<br />
[[File:polygon.png|600px|center]]<br />
<br />
== Goal ==<br />
<br />
Most of the recent approaches to on instance segmentation are based on deep neural networks and have demonstrated impressive performance. Given that these approaches require a lot of computational resources and that their performance depends on the amount of accessible training data, there has been an increase in the demand to label/annotate large-scale datasets. This is both expensive and time-consuming. <br />
<br />
{| class=wikitable width=700 align=center<br />
|Thus, the '''main goal''' of the paper is to enable '''semi-automatic''' annotation of object instances.<br />
|}<br />
<br />
Figure 2 demonstrates how the interface looks like for better clarity.<br />
<br />
Most of the datasets available pass through a stage where annotators manually outline the objects with a closed polygon. Polygons allow annotation of objects with a small number of clicks (30 - 40) compared to other methods. This approach works as the silhouette of an object is typically connected without holes. <br />
<br />
{| class=wikitable width=900 align=center<br />
|Thus, the authors suggest to adopt this same technique to annotate images using polygons, except they plan to automate the method and replace/reduce manual labeling. The '''intuition''' behind the success of this method is the '''sparse''' nature of these polygons that allow annotating of an object through a cluster of pixels rather than classification at the pixel-level.<br />
|}<br />
<br />
[[File:Annotating Object Instances Example.png | 450px|thumb|center|Figure 2: Given a bounding box, polygon outlining the the object instance inside the box is predicted. This approach is designed to facilitation annotation, and easily incorporates user corrections of points to improve the overall object’s polygon. ]]<br />
<br />
<br />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': In general, GrabCut is a method to separate the foreground and background of an image with minimal user interaction. Specifically, the user need only create a rectangular bounding box containing the foreground, and the algorithm will extract the object in the foreground. A major contribution of the paper is that labelling (of the object in the foreground) was not required, as the algorithm was able to identify where significant changes in colour pattern occurred. In this sense, it mimics automatic segmentation when combined with a Region Proposal Network. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 3: Illustration of GrabCut.]]<br />
<br />
2. '''GrabCut + CNN''': Scribbles have also been used to train CNNs for semantic image segmentation. <br />
<br />
3. '''Superpixels''': Superpixels in the form of small polygons where the color intensity within each superpixel is similar, to a certain threshold, have been used to provide a sparse representation of the large number of pixels in an image. However, the performance of this technique depends on the scale of the superpixels and hence sometimes merges small objects.<br />
<br />
[[File:Superpixel_idea.jpg | 450px|thumb|center|Figure 4: Illustration of the superpixel idea.]]<br />
<br />
= Model =<br />
<br />
As an '''input''' to the model, an annotator or perhaps another neural network provides a bounding box containing an object of interest and the model auto-generates a polygon outlining the object instance using a Recurrent Neural Network which they call: Polygon-RNN.<br />
<br />
The RNN model predicts the vertices of the polygon at each time step given a CNN representation of the image, the last two time steps, and the first vertex location. The location of the first vertex is defined differently and will be defined shortly. The information regarding the previous two-time steps helps the RNN create a polygon in a specific direction and the first vertex provides a cue for loop closure of the polygon edges.<br />
<br />
The polygon is parametrized as a sequence of 2D vertices and it is assumed that the polygon is closed. In addition, the polygon generation is fixed to follow a clockwise orientation since there are multiple ways to create a polygon given that it is cyclic structure. However, the starting point of the sequence is defined so that it can be any of the vertices of the polygon.<br />
<br />
== Architecture ==<br />
<br />
There are two primary networks at play: 1. CNN with skip connections, and 2. One-to-many type RNN.<br />
<br />
[[File:Figure_2_Neel.JPG | 800px|thumb|center|Figure 5: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type) ('''Note''': A possible point of confusion - the authors have only shown the layers of VGG16 architecture here that have the skip connections introduced).]]<br />
<br />
1. '''CNN with skip connections''':<br />
<br />
The authors have adopted the VGG16 feature extractor architecture with a few modifications pertaining to the preservation of features fused together in a tensor that can feed into the RNN (refer to Figure 5). Namely, the last max-pooling layer (''pool5'') present in the VGG16 CNN has been removed. The image fed into the CNN is pre-shrunk to a 224x224x3 tensor(3 being the Red, Green, and Blue channels). The image passes through 2 pooling layers and 2 convolutional layers. Since, the features extracted after each operation are to be preserved and fused later on, at each of these four steps, the idea is to have a tensor with a common width of 512; so the output tensor at pool2 is convolved with 4 3x3x128 filters and the output tensor at pool3 is convolved with 2 3x3x256 filters. The skip connections from the four layers allow the CNN to extract low-level edge and corner features (helps to follow the object's boundaries) as well as boundary/semantic information about the instances (helps to identify the object). Finally, a 3x3 convolution applied along with a ReLU non-linearity results in a 28x28x128 tensor that contains semantic information pertinent to the image frame and is taken as an input by the RNN.<br />
<br />
2. '''RNN - 2 Layer ConvLSTM'''<br />
<br />
The RNN is employed to capture information about the previous vertices in the time-series. Specifically, a Convolutional LSTM is used as a decoder. The ConvLSTM allows preservation of the spatial information in 2D received from CNN and reduces the number of parameters compared to a Fully Connected RNN. The polygon is modeled with a kernel size of 3x3 and 16 channels outputting a vertex at each time step. The ConvLSTM gets as input a tensor step t which<br />
concatenates 4 features: the CNN feature representation of the image, one-hot encoding of the previous predicted vertex and the vertex predicted<br />
from two time steps ago, as well as the one-hot encoding of the first predicted vertex. <br />
<br />
The Convolutional LSTM computes the hidden state <math display = "inline">h_t</math> given the input <math display = "inline">x_t</math> based on the following equations:<br />
<center><br />
<math display="block"><br />
\begin{pmatrix}<br />
i_t \\<br />
f_t \\<br />
o_t \\<br />
g_t \\<br />
\end{pmatrix}<br />
= W_h * h_{t-1} + W_x * x_t + b<br />
</math><br />
<br />
<math display="block"><br />
c_t = \sigma(f_t) \bigodot c_{t-1} + \sigma(i_t) \bigodot tanh(g_t)<br />
</math><br />
<br />
<math display="block"><br />
h_t = \sigma(o_t) \bigodot tanh(c_t)<br />
</math><br />
</center><br />
where <math display = "inline">i, f, o</math> denote the input, forget, and output gate, <math display = "inline">h</math> is the hidden state and <math display = "inline">c</math> is the cell state. Also, <math display = "inline">\sigma</math> denotes the sigmoid function, <math display = "inline">\bigodot</math> indicates an element-wise product and <math display = "inline">*</math> a convolution. <math display = "inline">W_h</math> denotes the hidden-to-state convolution kernel and <math display = "inline">W_x</math> the input-to-state convolution kernel.<br />
<br />
The authors have treated the vertex prediction task as a classification task in that the location of the vertices is through a one-hot representation of dimension DxD + 1 (D chosen to be 28 by the authors in tests). The one additional dimension is the storage cue for loop closure for the polygon. Given that, the one-hot representation of the two previously predicted vertices and the first vertex are taken in as an input, a clockwise (or for that reason any fixed direction) direction can be forced for the creation of the polygon. Coming back to the prediction of the first vertex, as polygon is a circle, any vertex of a polygon can be used as a starting point. Therefore the authors treat the starting point as special, and this is done through further modification of the CNN by adding two DxD layers with one branch predicting object instance boundaries while the other takes in this output as well as the image features to predict vertices of the polygon. The boundaries and vertices prediction are being treated as binary classification problem in each cell in the output grid. This CNN is trained separately. Here, <math display = "inline">y_t</math> denotes the one-hot encoding of the vertex and is the output at time step t.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN loss function. To avoid over-penalizing of mispredictions, non-zero probability mass are assigned to locations which are within a distance of 2 in D × D output grid.<br />
<br />
2. Instead of Stochastic Gradient Descent, Adam is used for optimization: batch size = 8, learning rate = 1e^-4 (learning rate decays after 10 epochs by a factor of 10) <br />
<br />
3. For the first vertex prediction, the modified CNN mentioned previously, is trained using a multi-task cost function.<br />
<br />
The reported time for training is one day on a Nvidia Titan-X GPU.<br />
<br />
The resolution of the polygon is 28 x 28, based on the downsampling factor and ConvLSTM resolution. They simplified the polygon by removing vertices on the grid line and the same vertices that fall in the same grid. They also randomly flipped images, enlarged original bounding boxes and randomly selected the starting vertex of the polygon notation as their data augmentation process.<br />
<br />
== Importance of Human Annotator in the Loop ==<br />
<br />
The model allows for the prediction at a given time step to be corrected and this corrected vertex is then fed into the next time step of the RNN, effectively rejecting the network predicted vertex. This has the simple effect of putting the model "back on the right track". Note that this is only possible due to the adoption of the RNN architecture i.e. the inherent nature of the RNN to accept previous outputs allows incorporation of the user's judgement. The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
== Evaluation Metrics ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. There are two metrics used for evaluation:<br />
<br />
1. '''IoU''': The standard Intersection over Union (IoU) measure is used for comparison. In add The calculation for IoU takes both the predicted and ground-truth object boundaries. The intersection (area contained in both boundaries at once) is divided by the union (the area contained by at least one, or both, of the boundaries). A low score of this metric would mean that there is little overlap between the boundaries, or large areas on non-overlap, and a score of 1.0 would indicate that the two boundaries contain the same area.<br />
<br />
2. '''Number of Clicks''': To evaluate the speed up factor, the checkerboard distance is used to measure the distance between the ground truth (GT) and the output of the Polygon RNN. A set of distance thresholds are set <math display = "inline">T &isin; [1,2,3,4]</math> and if the distance exceeds the particular threshold, the correction is made by an annotator to match the GT and the '''Number of Clicks''' is used to evaluate the speed up factor.<br />
<br />
== Baseline Techniques ==<br />
<br />
1. '''SharpMask''': a 50 layer ResNet considered as the state of the art annotation method.<br />
<br />
2. '''DeepMask''': a build-up on the 50 layer ResNet with an addition of another CNN.<br />
<br />
3. '''Dilation10''': another simple technique using purely convolutional operations.<br />
<br />
4. '''SquareBox''': a simple technique where an entire bounding box is labeled as an object<br />
<br />
== Quantitative Results ==<br />
<br />
We report the IoU metric in Table<br />
1. The Polygon RNN method outperforms the baselines in 6 out of the 8 categories and has a mean IoU greater than all of the baselines. Particularly, in the car, person, and rider categories, a 12%, 7%, and 6% higher performance than SharpMask is achieved.<br />
<br />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
In addition, with the help of the annotator, the speedup factor was 7.3 times with under 5 clicks which the authors claim is the main advantage of this method.<br />
<br />
[[File:Table_0_Neel.JPG | 800px|thumb|center|Table 2: IoU performance on Cityscapes data with annotator intervention.]]<br />
<br />
The method also works well with other datasets such as KITTI:<br />
<br />
[[File:Table_2_Neel.JPG | 800px|thumb|center|Table 3: IoU performance on KITTI data.]]<br />
<br />
== Effect of object size ==<br />
In Fig. 4, we see how our model performs w.r.t baselines on different instance sizes. For small instances, our model performs significantly better than the baselines. For larger objects, the baselines have an advantage due to the larger output resolution. <br />
<br />
[[File:IoU_vs_size_of_instance.PNG | 500px|thumb|center|Fig 4: IoU_vs_size_of_instance.]]<br />
<br />
== Qualitative Results ==<br />
<br />
In addition, most of the comparisons with human annotators show that the method is at par with human-level annotation.<br />
<br />
<gallery widths=500px heights=500px perrow=2 mode="packed"><br />
File:Figure_3_Neel.JPG|Figure 6: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 7: Qualitative results: comparison with human annotator.|alt=alt language<br />
</gallery><br />
<br />
=Conclusion=<br />
<br />
The important conclusions from this paper are:<br />
<br />
1. The paper presented a powerful generic annotation tool for modelling complex annotations as a simple polygon that works on different unseen datasets. <br />
<br />
2. Significant improvement in annotation time can be achieved with the Polygon-RNN method itself (speed-up factor of 4.74).<br />
<br />
3. However, the flexibility of having inputs from a human annotator helps increase the IoU for a certain range of clicks.<br />
<br />
4. The model architecture has a down-sampling factor of 16 and the final output resolution and accuracy is sensitive to object size.<br />
<br />
5. Another downside of the model architecture is that training time is increased due to the training of the CNN for the first vertex.<br />
<br />
=Critique=<br />
<br />
1. With the human annotator in the loop, the model speeds up the process of annotation by over 7 times which is perhaps a big cost and time cutting improvement for companies.<br />
<br />
2. Given that this model uses the VGG16 architecture compared to the 50 layer ResNet in SharpMask, this method is quite efficient.<br />
<br />
3. This paper requires training of an entire CNN for the first vertex and is inefficient in that sense as it introduces additional parameters adding to the computation time and resource demand.<br />
<br />
4. The baseline methods have an upper hand compared to this model when it comes to larger objects since the nature of the down-scaled structure adopted by this model.<br />
<br />
5. In terms of future work, elimination of the additional CNN for the first vertex as well as an enhanced architecture to remain insensitive to the size of the object to be annotated should be implemented.<br />
<br />
6. Compared to other models, the model was shown to not perform as well for larger objects (see table 3). This is likely due to the fact that vertex location determination is done in a highly compressed (28x28) representation compared to the input image(224x224). For larger objects, bounding boxes are larger. Each vertex represents many pixels. When up-converted back to the input image/bounding box size these may lead to errors especially when considering a very precise evaluation metric (intersection over union) is used. Potentially, the results can be improved by considering a higher resolution for the internal representation or one that scales with the size of the bounding.<br />
<br />
7. While the model outperforms the baseline for certain categories of object, it is surprising that it underperforms in categories such as 'bus' and 'train'. With human annotators in the loop, one would expect the model to outperform in all categories.<br />
<br />
8. One of the major contributions of this paper lies on the fact that this paper presents a method that does have an applicable value in the real world. In the paper, it does show that it can greatly reduce the human labeling efforts, and with human collaboration, this algorithm can help us tackle the image labeling problem much more efficiently. However, it does not provide the theoretical explanation that why would an RNN work better than a CNN in this case, a more in-depth analysis would make the paper better.<br />
<br />
=Code=<br />
# [https://github.com/AlexMa011/pytorch-polygon-rnn] (unofficial)<br />
# Code for an updated version of the model is available at [https://github.com/fidler-lab/polyrnn-pp] (official)</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946w18/Towards_Image_Understanding_From_Deep_Compression_Without_Decoding&diff=42128stat946w18/Towards Image Understanding From Deep Compression Without Decoding2018-11-30T22:14:23Z<p>R82zhang: [T] /* Critique */</p>
<hr />
<div>Paper Title: Towards Image Understanding from Deep Compression Without Decoding - ICLR 2018<br />
<br />
Presented By: Aravind Ravi<br />
<br />
== Introduction ==<br />
Recent advances in the deep neural network (DNN) based image compression methods have shown potential improvements in image quality, savings in storage and bandwidth reduction. These methods leverage common neural network architectures such as convolutional autoencoders or recurrent neural networks to compress and reconstruct RGB images and outperform classical techniques such as JPEG2000 and BPG on perceptual metrics such as structural similarity index (SSIM) and multi-scale structural similarity index (MS-SSIM).<br />
<br />
These approaches encode an image <math>x </math> to some feature map (compressed representation), which is subsequently quantized to a set of symbols <math>z </math>. These symbols are then losslessly compressed to a bitstream, from which a decoder reconstructs an image <math>{\hat{x}} </math>, of the same dimensions as <math>x </math>.<br />
<br />
Learned compression algorithms have an advantage over engineering compression algorithms in that they can be much more easily adapted to specific domains. For example, a learned compression algorithm might be able to learn good performance on compressing medical images, without specifically tuning the algorithm.<br />
<br />
In this paper, the authors explore the idea of applying the learned representations to perform inference without reconstructing the compressed image. Specifically, instead of reconstructing an RGB image from the compressed representation and feeding it to a network for inference, the paper proposes to use a modified network that bypasses reconstruction of the RGB image.<br />
<br />
The rationale behind this approach is that the neural network architectures commonly used for learned compression (in particular the encoders) are similar to the ones commonly used for inference, and learned image encoders are hence, in principle, capable of extracting features relevant for inference tasks. The encoder might learn features relevant for inference purely by training on the compression task, and can be forced to learn these features by training on the compression and inference tasks jointly<br />
<br />
The advantage of learning an encoder for image compression which produces compressed representation containing features relevant for inference is obvious in scenarios where images are transmitted (e.g. from a mobile device) before processing (e.g. in the cloud), as it saves reconstruction of the RGB image as well as part of the feature extraction and hence speeds up processing. A typical use case is a cloud photo storage application where every image is processed immediately upon upload for indexing and search purposes.<br />
<br />
Note: [https://en.wikipedia.org/wiki/Structural_similarity More Information on SSIM, MSSIM]<br />
<br />
== Intuition ==<br />
<br />
Compression techniques (something as common as zipping) are commonly used by us in day to day file handling tasks. Most often we use engineered compression techniques. Deep Neural Networks (DNNs) are nonlinear function approximators which act as feature extractors, extracting features from inputs (like images or sound files). These can be seen as learning based compression techniques as they can perform compression and they can be trained using back propagation as well. If image classification can be done on these compressed files, large image data sets like hyperspectral images and MRI images can be stored efficiently and the compressed files can be used directly by the DNNs for classification or reinforcement learning tasks.<br />
<br />
==Motivation and Contributions==<br />
The authors propose to perform image understanding tasks such as image classification and segmentation directly on DNN based compressed representations. Performing the image understanding tasks on the compressed representations/encoded feature maps has two advantages. <br />
# This method bypasses the process of decoding the image into the RGB space before classification<br />
# The authors show that it reduces the overall computational complexity up to 2 times<br />
<br />
=== Contributions of the Paper ===<br />
* A method to perform image classification and semantic segmentation from compressed representations. In large scale image understanding problems, learning from a compressed representation is definitely something that is interesting. <br />
* The proposed method offers classification accuracy similar to that achieved on decompressed images while reducing the computational complexity by 2 times.<br />
* Semantic segmentation has been shown to be as accurate as performance on decompressed images for moderate compression rates and higher accuracy for aggressive compression rates. In addition, this method achieves lower computational complexity.<br />
* Joint training for image compression and classification has been shown to improve the quality of the image and increase in accuracy of classification and segmentation<br />
<br />
==Related Work==<br />
<br />
The prior work has shown image classification from compressed images based on engineered codecs. Some of the works in this area are:<br />
<br />
* In video analysis domain: Action recognition (Yeo et al., 2008; Kantorov & Laptev, 2014)<br />
* Classification of compressed hyperspectral images (Hahn et al., 2014; Aghagolzadeh & Radha, 2015)<br />
* Discrete Cosine Transform based compression performed on images before feeding into a neural network, which shows an improvement in training speed by up to 10 times Fu & Guimaraes (2016)<br />
* Video analysis on compressed video (using engineered codecs) has also been studied in the past (Babu et al., 2016)<br />
* Criticism on document image analysis methods (Javed et al.2017)<br />
<br />
The authors propose a method that does inference on top of learned feature representation and hence has a direct relation to unsupervised feature learning using autoencoders.<br />
They also claim that so far there hasn't been any work using learned compressed representations for image classification and segmentation.<br />
<br />
==Learned Deeply Compressed Representations==<br />
<br />
The image compression task is performed based on a convolutional autoencoder architecture proposed by Theis et al. 2017 (shown in the figure below), and a variant of the training procedure described by Agustsson et. al 2017. <br />
<br />
[[File:AR_theisAutoencoder.png|600px|center]]<br />
<br />
Some points to better understand the architecture:<br />
<br />
1. Most convolutions are done in a convolved, lower-dimensional space to speed up computation<br />
<br />
2. Different activation functions are used. Blank arrows indicate the identity function (no additional linearity), while black arrows indicate leaky rectifications<br />
<br />
3. The “round” box simply rounds all elements in the tensor to the nearest integer<br />
<br />
4. The “subpix” block is just an upsampling /reconstruction block where the feature map’s coefficients are reshuffled after a convolution<br />
<br />
<br />
<br />
=== Compression Architecture ===<br />
<br />
The compression network is an autoencoder that takes an input image <math>x </math> and outputs <math>{\hat{x}} </math> as the approximation to the input. <br />
<br />
[[File:AR_Fig2a.png|300px|center]]<br />
<br />
The encoder has the following structure: It starts with 2 convolutional layers with spatial subsampling by a factor of 2, followed by 3 residual units, and a final convolutional layer with spatial subsampling by a factor of 2. This results in a <math>w/8</math> x <math>h/8</math> x <math>C</math> dimensional representation, where <math>w </math> and <math>h </math> are the spatial dimensions of <math>x </math>, and the number of channels C is a hyperparameter related to the rate <math>R </math>. This representation is then quantized to a discrete set of symbols, forming a compressed representation, <math>z </math>.<br />
<br />
To get the reconstruction <math>{\hat{x}} </math>, the compressed representation is fed into the decoder, which mirrors the encoder, but uses upsampling and deconvolutions instead of subsampling and convolutions.<br />
<br />
Quantizing the compressed representation imposes a distortion <math>D </math> on <math>{\hat{x}} </math> w.r.t. <math>x </math>, i.e., it increases the reconstruction error. This is traded for a decrease in entropy of the quantized compressed representation<br />
<math>z </math> which leads to a decrease of the length of the bitstream as measured by the rate <math>R </math>. Thus, to train the image compression network, the classical rate-distortion trade-off <math>D + \beta R</math> is minimized. As a metric for <math>D </math>, the mean squared error (MSE) between <math>x </math> and <math>{\hat{x}} </math> are used and <math>R</math> is estimated using<br />
<math>H(q)</math>. <math>H(q)</math> is the entropy of the probability distribution over the symbols and is estimated using a histogram of the probability distribution (as done by Agustsson et al., 2017). The trade-off between MSE and the entropy is controlled by adjusting <math>\beta </math>. For each <math>\beta </math> an operating point is derived where the images have a certain bit rate, as measured by bits per pixel (bpp), and corresponding MSE. To better control the bpp, a target entropy Ht is introduced by the authors to formulate the loss defined as:<br />
<br />
\begin{align}<br />
\mathcal{L_c} = \text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0)<br />
\end{align}<br />
<br />
Agustsson et. al 2017, proposed a method to overcome the issue of non-differentiability of the quantization step by proposing a differentiable approximation to the quantization. This method has been adapted to suit the current application in the paper.<br />
<br />
Three operating points at 0.0983 bpp (C=8), 0.330 bpp (C=16), and 0.635 bpp (C=32) are obtained empirically. All further experiments are performed with these three operating points and the results for the same are presented in the following sections.<br />
<br />
==Image Classification from Compressed Representations==<br />
<br />
=== Classification on RGB Images ===<br />
<br />
For the image classification task based on the RGB images, the authors use the ResNet-50 architecture. <br />
Further information on residual networks can be found in the following links: <br />
[https://youtu.be/K0uoBKBQ1gA ResNets Part-1]<br />
[https://youtu.be/GSsKdtoatm8 ResNets Part-2]<br />
<br />
The details of the architecture are presented in the table below:<br />
<br />
[[File:AR_Tab1.png|400px|center]]<br />
<br />
In this paper, the number of 14x14 (conv4_x) blocks have been modified to obtain a new architecture called ResNet-71. <br />
<br />
=== Classification on Compressed Representations ===<br />
<br />
For input images with spatial dimension 224x224, the encoder of the compression network outputs a compressed representation with dimensions 28x28xC, where C is the number of channels. To use this compressed representation as input to the classification network, a simple variant of the ResNet architecture is proposed. This variant is referred to as cResNet-k, where c stands for “compressed representation” and k is the<br />
number of convolutional layers in the network. These networks are constructed by simply “cutting off” the front of the regular (RGB) ResNet. The root-block of the network and the residual layers that have a larger spatial dimension than 28x28 are removed. To adjust the number of layers k, the ResNet architecture proposed by He et al. (2015) is used and the number of 14x14 (conv4 x) residual blocks are modified.<br />
<br />
In this way, three different architectures are derived:<br />
* cResNet-39 is ResNet-50 with the first 11 layers removed as described above, and this significantly reduces computational cost<br />
* cResNet-51<br />
* cResNet-72<br />
<br />
cResNet-51 and cResNet-72 are obtained by adding 14x14 residual blocks to match the computational cost of ResNet-50 and ResNet-71 respectively.<br />
<br />
The detailed description of all the network architectures are presented below:<br />
<br />
[[File:AR_Tab3.png|600px|center]]<br />
<br />
==Semantic Segmentation from Compressed Representations==<br />
<br />
For semantic segmentation, the ResNet based DeepLab architecture is adapted for the proposed application. The cResNet<br />
and ResNet image classification architectures are re-purposed with atrous<br />
convolutions, where the filters are upsampled instead of downsampling the feature maps. This is<br />
done to increase their receptive field and to prevent aggressive subsampling of the feature maps. For segmentation, the ResNet architecture is restructured such<br />
that the output feature map has 8 times smaller spatial dimension than the original RGB image (instead<br />
subsampling by a factor 32 times like for classification). When using the cResNets the output feature<br />
map has the same spatial dimensions as the input compressed representation (instead of subsampling<br />
4 times like for classification). This results in comparably sized feature maps for both the compressed<br />
representation and the reconstructed RGB images. Finally the last 1000-way classification layer of<br />
these classification architectures is replaced by an atrous spatial pyramid pooling (ASPP) with four<br />
parallel branches with rates {6, 12, 18, 24}, which provides the final pixel-wise classification.<br />
<br />
==Joint Training for Compression and Image Classification==<br />
<br />
The authors propose a joint training strategy to combine compression and classification tasks. To do this, the proposed method combines the compression network and the cResNet-51 architecture. The figure below shows the combined pipeline:<br />
<br />
[[File:AR_Fig2b.png|300px|center]]<br />
<br />
All parts, encoder, decoder, and inference network, are trained at the same time. The compressed representation is fed<br />
to the decoder to optimize for mean-squared reconstruction error and to a cResNet-51 network to<br />
optimize for classification using a cross-entropy loss. The combined loss function takes the form:<br />
<br />
\begin{align}<br />
\mathcal{L_c} = \gamma(\text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0))+l_{ce}(y,{\hat{y}})<br />
\end{align}<br />
<br />
where the loss terms for the compression network, <math> \mathcal{L_c} = \text{MSE}(x,{\hat{x}})+\beta\max({H(q)}-{H_t},0)</math>, are the same as in training for compression only. <math> l_{ce}</math> is the cross-entropy loss for classification.<br />
<math>\gamma </math> controls the trade-off between the compression loss and the classification loss.<br />
<br />
==Experiments and Results==<br />
<br />
=== Learned Deeply Compressed Representations Results ===<br />
<br />
All experiments have been performed on the ILSVRC2012 dataset.<br />
<br />
The metrics used to measure the compression quality are as follows: <br />
* PSNR (Peak Signal-to-Noise Ratio) is a standard measure, depending monotonically on mean squared error defined as: <br />
<br />
\begin{align}<br />
PSNR = 10(\log_{10}(255^2/MSE))<br />
\end{align}<br />
<br />
* SSIM (Structural Similarity Index) and MS-SSIM (Multi-Scale SSIM) are metrics proposed to measure the similarity of images as perceived by humans<br />
<br />
The figure below depicts the performance of the deep compression models vs. standard JPEG and JPEG2000. Higher values are better. The proposed technique outperforms the JPEG and JPEC2000 at the operating points used in this paper.<br />
<br />
[[File:AR_Fig8.png|600px|center]]<br />
<br />
The learned compressed representations are illustrated in the figure below. <br />
<br />
[[File:AR_Fig9.png|500px|center]]<br />
<br />
In the above figure, the original RGB-image is shown along with compressed versions of the RGB image which are reconstructed from the compressed representations. The 4 channels with the highest entropy are shown in the visualizations. These visualizations indicate how the networks compress an image, as the rate (bpp) gets lower the entropy cost of the network forces the<br />
compressed representation to use fewer quantization levels, as can clearly be seen. For the most aggressive compression, the channel maps use only 2 levels for the compressed representation.<br />
<br />
=== Classification on Compressed Representations ===<br />
<br />
All experiments have been performed on the ILSVRC2012 dataset. It consists of 1.28 million training images and 50k validation images. These images are distributed across 1000 diverse classes. For image classification, the top-1 classification accuracy and top-5 classification accuracy are reported on the validation set on 224x224 center crops for RGB images and 28x28 center crops for the compressed representation.<br />
<br />
==== Training Procedure ====<br />
<br />
The compression network is fixed while training the classification network, both when training with compressed representations and with reconstructed compressed RGB images. For the compressed representations, the output of the fixed encoder (the compressed representation) is provided input to the cResNets (decoder is not needed). When training on the reconstructed compressed RGB images, the output of the fixed encoder-decoder (RGB image) is provided as input to the ResNet. This is done for each operating point.<br />
<br />
Refer to Appendix A Section A4, of the paper for details on the hyperparameters and optimization used for training the network [1].<br />
<br />
==== Classification Results ====<br />
<br />
The tables below present the results of the classification at each operating point, both classifying from the compressed representation and the corresponding reconstructed compressed RGB images.<br />
<br />
[[File:AR_Tab2.png|400|center]]<br />
<br />
Figure below shows the validation curves for ResNet-50, cResNet-51, and cResNet-39. <br />
<br />
[[File:AR_Fig3.png|700|center]]<br />
<br />
For the 2 classification architectures with the same computational complexity (ResNet-50 and cResNet-51), the validation curves at the 0.635 bpp compression operating point almost coincide, with ResNet-50 performing slightly better. As the rate (bpp) gets smaller this performance gap gets smaller. The table above shows the<br />
classification results when the different architectures have converged. At the 0.635 bpp operating point, ResNet-50 only performs 0.5% better in top-5 accuracy than cResNet-51, while for the 0.0983 bpp operating point this difference is only 0.3%.<br />
Using the same pre-processing and the same learning rate schedule but starting from the original uncompressed RGB images yields 89.96% top-5 accuracy. The top-5 accuracy obtained from the compressed representation at the 0.635 bpp compression operating point, 87.85%, is even competitive<br />
with that obtained for the original images at a significantly lower storage cost. Specifically, at 0.635 bpp the ImageNet dataset requires 24.8 GB of storage space instead of 144 GB for the original version, a reduction by a factor 5.8 times.<br />
<br />
Notes on top-1 and top-5 accuracy:<br />
<br />
* Top-1 accuracy: This is the conventional accuracy metric used in machine learning. Wherein if the true label of the input to a model matches the highest probability class of the last layer of the output of CNN (predicted class probability), then the given input is correctly classified, else it is considered as incorrectly classified.<br />
* Top-5 accuracy: In this case, if any of the model's 5 highest classification probabilities match with the true label of the input, then this is considered as a correct classification, else it is an incorrect classification.<br />
<br />
===Semantic Segmentation Results===<br />
<br />
All experiments have been performed on the PASCAL VOC-2012 dataset for semantic segmentation. It has 20 object foreground classes and 1 background class. The dataset<br />
consists of 1464 training and 1449 validation images. In every image, each pixel is annotated with<br />
one of the 20 + 1 classes. The original dataset is furthermore augmented with extra annotations, so the final dataset has 10,582 images for training and 1449 images for validation.<br />
<br />
All performance is measured on pixel wise intersection-over-union (IoU) averaged over all the classes or mean-intersection-over-union (mIoU) on the validation set. <br />
<br />
[https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/ Details on IoU]<br />
<br />
==== Training Procedure ====<br />
The cResNet/ResNet networks are pre-trained on the ImageNet dataset using the procedure described earlier on the image classification task, the encoder and decoder is fixed as in the earlier scenario. The architectures are then adapted with dilated convolutions, cResNet-d/ResNet-d, and<br />
finetuned on the semantic segmentation task.<br />
<br />
Refer to Appendix A Section A5, of the paper for details on the hyperparameters and optimization used for training the network [1].<br />
<br />
==== Segmentation Results ====<br />
<br />
The table below shows the mIoU results for the segmentation task.<br />
<br />
[[File:AR_Tab2.png|450|center]]<br />
<br />
The figure below illustrates the segmentation results with respect to each compression operating point.<br />
<br />
[[File:AR_Fig4.png|700|center]]<br />
<br />
For semantic segmentation ResNet-50-d and cResNet-51-d perform equally well at the 0.635 bpp compression operating point. For the<br />
0.330 bpp operating point, segmentation from the compressed representation performs slightly better, 0.37%, and at the 0.0983 bpp operating point segmentation from the compressed representation<br />
performs considerably better than for the reconstructed compressed RGB images, by 1.65%.<br />
<br />
[[File:AR_Fig5.png|600px|center]]<br />
<br />
The above figure shows the predicted segmentation visually for both the cResNet-51-d and the ResNet-50-d<br />
architecture at each operating point. Along with the segmentation, it also shows the original uncompressed<br />
RGB image and the reconstructed compressed RGB image. These images highlight<br />
the challenging nature of these segmentation tasks, but they can nevertheless be performed using the<br />
compressed representation. They also clearly indicate that the compression affects the segmentation,<br />
as lowering the rate (bpp) progressively removes details in the image. Comparing the segmentation<br />
from the reconstructed RGB images to the segmentation from the compressed representation visually,<br />
the performance is similar.<br />
<br />
The figure below is another example of visual results of segmentation from compressed representation and reconstructed RGB<br />
images. The performance is visually similar for all operating points except for the 0.0983<br />
bpp operating point where the reconstructed RGB image fails to capture the back part of<br />
the train, while the compressed representation manages to capture that aspect of the image in the<br />
segmentation.<br />
<br />
[[File:AR_Fig10.png|600px|center]]<br />
<br />
=== Results on Computational Gains ===<br />
<br />
[[File:AR_Fig6.png|400px|center]]<br />
<br />
=====Computational Gains on Classification=====<br />
<br />
The figure on the left illustrates, the top-5 classification accuracy as a function of computational<br />
complexity for the 0.0983 bpp compression operating point.<br />
Looking at a fixed computational cost, the reconstructed compressed RGB images perform about 0.25% better. Looking at a fixed classification cost, inference from the compressed representation costs about 0.6 * 10^9 FLOPs more. However when accounting for the decoding cost at a fixed<br />
classification performance, inference from the reconstructed compressed RGB images costs 2.2*10^9 FLOPs more than inference from the compressed representation.<br />
<br />
=====Computational Gains on Segmentation=====<br />
<br />
In the figure on the right illustrates, the mIoU validation performance is shown as a function of computational complexity for<br />
the 0.0983 bpp compression operating point. <br />
Here, even without accounting for the decoding cost of the reconstructed images, the compressed representation<br />
performs better. At a fixed computational cost, segmentation from the compressed representation gives about 0.7% better mIoU. And at a fixed mIoU the computational cost is about 3.3*10^9 FLOPs<br />
lower for compressed representations. Accounting for the decoding costs this difference becomes 6.1*10^9 FLOPs. due to the nature of the dilated convolutions and the increased feature map size, the<br />
relative computational gains for segmentation are not as pronounced as for classification.<br />
<br />
===Joint Training for Compression and Image Classification===<br />
<br />
==== Training Procedure ====<br />
<br />
When doing joint training, the compression network and the classification networks are first initialized<br />
from a trained state obtained as described previously. After initialization, the networks are<br />
both finetuned jointly. For a detailed<br />
description of hyperparameters used and the training schedule see Appendix A8.<br />
<br />
To control that the change in classification accuracy is not only due to (1) a better compression<br />
operating point or (2) the fact that the cResNet is trained longer, the following is done. A new operating point is obtained by finetuning the compression network only using the schedule described<br />
above. The cResNet-51 is trained on top of this new operating point from scratch. Finally, the compression network is fixed at the new operating point, and the cResNet-51 is trained for 9 epochs. <br />
<br />
To obtain segmentation results, the jointly trained network is used. The operating point is fixed and the jointly finetuned classification network is adopted fro segmentation (cResNet-51-d).<br />
<br />
==== Joint Training Results ====<br />
<br />
[[File:AR_Fig7.png|400px|center]]<br />
<br />
It can be seen from the figure, that the classification and segmentation results “move<br />
up” from the baseline through fine tuning. When training jointly the improvement for classification are larger and<br />
a significant improvement for segmentation is achieved. For the 0.635 bpp operating point the classification performance is similar for training the network jointly and training<br />
the compression network only, but when using these operating points for segmentation the difference is considerable.<br />
<br />
The results presented by the authors suggest an improvement in classification by 2%, a performance gain which would<br />
require an additional 75% of the computational complexity of cResNet-51. The segmentation<br />
performance after training the networks jointly is 1.7% better in mIoU than training only<br />
the compression network.<br />
<br />
==Critique==<br />
<br />
The paper proposes how previous work in auto-encoders and image compression can be extended effectively to a novel task of a combined image compression and recognition task. The work has provided extensive experimental evaluation and evidence that suggests that learned compressed representations can be effective in classification and segmentation tasks. While maintaining the performance of the techniques to state of the art performance, the authors show that the proposed method can offer significant computational gains. The applications of this can be in<br />
multimedia communication, wireless transmission of images, video surveillance on the mobile edge, etc. With the advent of 5G and other new wireless technologies, this method offers capabilities that can be utilized to conserve wireless bandwidth, savings on storage while retaining the perceptual quality of images.<br />
The joint training of compression and classification network provides some added advantages and also shows that at aggressive compression rates the performance in classification and segmentation can be improved significantly.<br />
<br />
Another critique is the authors did not answer the question of why we want to do image understanding from a compressed space. From the intuitive sense, the learning algorithm could easily just learn from the original feature space, which obviously contains more information. The troubling part is that the author does not answer a more fundamental question of why learning from a compressed space would bring any benefit compared to learning directly from the original feature space.<br />
<br />
The authors mention that the complexity of the current approach is still high in comparison with methods like JPEG or JPEG2000. They also mention that this can be overcome when the networks are trained and run on GPU's. Although this has been seen as a drawback, with subsequent improvements in physical hardware and more specialized deep learning platforms, the limitation of the current approach can be overcome. While the authors did thorough experiments and gave extensive results on compressed representations and their advantages, the idea itself is not very novel.Finally, in the light of providing extensive experimental contributions,<br />
the authors have written a quite lengthy paper. There are parts of the paper where the ideas have been repeated frequently, and this could've been avoided leading to a more well-balanced length of the article.<br />
<br />
* ([[https://openreview.net/forum?id=HkXWCMbRW]]) As it is mentioned in the paper, solving a Vision problem directly from a compressed image, is not a novel method (e.g: DCT coefficients were used for both vision and audio data to solve a task without any decompression).<br />
<br />
==Conclusion==<br />
<br />
The paper proposes an inference task using compressed image representations without the need to decode for classification and semantic segmentation. The paper has successfully demonstrated through a set of rigorous experiments the approach<br />
for performing the intended tasks. The results show significant improvements in computational complexity while maintaining state of the art classification and segmentation performance. The authors also intend to explore other computer vision tasks based on using compressed representation as part of the future work. They also suggest that this could potentially lead to gaining a better understanding of the features/compressed representations learned by image compression networks leading to applications in unsupervised or semi-supervised learning.<br />
<br />
==References==<br />
# Torfason, R., Mentzer, F., Agustsson, E., Tschannen, M., Timofte, R., & Van Gool, L. (2018). Towards image understanding from deep compression without decoding. arXiv preprint arXiv:1803.06131.<br />
# Theis, L., Shi, W., Cunningham, A., & Huszár, F. (2017). Lossy image compression with compressive autoencoders. arXiv preprint arXiv:1703.00395.<br />
# Agustsson, E., Mentzer, F., Tschannen, M., Cavigelli, L., Timofte, R., Benini, L., & Gool, L. V. (2017). Soft-to-hard vector quantization for end-to-end learning compressible representations. In Advances in Neural Information Processing Systems (pp. 1141-1151).<br />
# He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 770-778).<br />
# Chen, L. C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2018). Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE transactions on pattern analysis and machine intelligence, 40(4), 834-848.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Hierarchical_Representations_for_Efficient_Architecture_Search&diff=42125Hierarchical Representations for Efficient Architecture Search2018-11-30T22:10:06Z<p>R82zhang: [T] /* Introduction neural Architecture search and hierarchical representation */</p>
<hr />
<div>Summary of the paper: [https://arxiv.org/abs/1711.00436 ''Hierarchical Representations for Efficient Architecture Search'']<br />
<br />
= Introduction =<br />
<br />
Deep Neural Networks (DNNs) have shown remarkable performance in several areas such as computer vision, natural language processing, among others; however, improvements over previous benchmarks have required extensive research and experimentation by domain experts. In DNNs, the composition of linear and nonlinear functions produce internal representations of data which are in most cases better than handcrafted ones; consequently, researchers using Deep Learning techniques have lately shifted their focus from working on input features to designing optimal DNN architectures. However, the quest for finding an optimal DNN architecture by combining layers and modules requires frequent trial and error experiments, a task that resembles the previous work on looking for handcrafted optimal features. As researchers aim to solve more difficult challenges the complexity of the resulting DNN is also increasing; therefore, some studies are introducing the use of automated techniques focused on searching for optimal architectures. The latest emerging field, Neural Architecture Search, is aimed to tackle exactly this problem. The goal of Neural Architecture Search is to try to transform the problem of designing a network into a search problem. For a search problem, it needs a clear definition of three things: the search space, the search strategy, and performance evaluation strategy. The search space is a high-level description of the architecture of the network. The search space needs to contain enough freedom such that the resulted model will have enough expressive power, but cannot be too broad thus makes the search process too computational consuming. The search strategy is how to efficiently search in the search space. The performance evaluation strategy is the methods that are used to evaluate the network. Here, the evaluation is more tricky because in order to evaluate a neural network, we need to train it first, and training takes time. So it is important to define a proxy task that can help us better evaluate a network. Here, this paper will tackle these problems with a new hierarchical representation.<br />
<br />
Lately, the use of algorithms for finding optimal DNN architectures has attracted the attention of researchers who have tackled the problem through four main groups of techniques. The first such method employs a supplementary network called a “Hypernet”, which generates ideal network weights given a random architecture. There are two main parts to generating an “optimal” architecture. First, we train the HyperNet. One training cycle consists of generating a random architecture from a sample space of allowed architectures and generating its predicted weights with the HyperNet. Then, the validation score of this proposed network is calculated, and the error is used to backpropagate through the HyperNet. In this manner, the HyperNet can learn to assign robustly optimal initial weights to a given architecture. At “test” time, we generate a random sample of architectures and predict initialized weights for each with our tuned HyperNet. We take the model with the highest validation score and train it as we would a regular architecture. We use this heuristic of “initial validation error” as the relative performance of networks typically stays constant throughout training. That is, if it starts of better, it will very likely end better. The second technique is Monte Carlo Tree Search (MCTS) which repeatedly narrows the search space by focusing on the most promising architectures previously seen. The third group of techniques use evolutionary algorithms where fitness criteria are applied to filter the initial population of DNN candidates, then new individuals are added to the population by selecting the best-performing ones and modifying them with one or several random mutations as in [https://arxiv.org/abs/1703.01041 [Real, 2017]]. The fourth and last group of techniques implement Reinforcement Learning where a policy based controller seeks to optimize the expected accuracy of new architectures based on rewards (accuracy) gained from previous proposals in the architecture space. From these four groups of techniques, Reinforcement Learning has offered the best experimental results; however, the paper we are summarizing implements evolutionary algorithms as its main approach.<br />
<br />
Despite the technique used to look for an optimal architecture, searching in the architecture space usually requires the training and evaluation of many DNN candidates; therefore, it demands huge computational resources and poses a significant limitation for practical applications. Consequently, most techniques narrow the search space with predefined heuristics, either at the beginning or dynamically during the searching process. In the paper we are summarizing, the authors reduce the number of feasible architectures by forcing a hierarchical structure between network components. In other words, each DNN suggested as a candidate is formed by combining basic building blocks to form small modules, then the same basic structures introduced on the building blocks are used to combine and stack networks on the upper levels of the hierarchy. This approach allows the searching algorithm to sample highly complex and modularized networks similar to Inception or ResNet.<br />
<br />
Despite some weaknesses regarding the efficiency of evolutionary algorithms, this study reveals that in fact, these techniques can generate architectures which show competitive performance when a narrowing strategy is imposed over the search space. Accordingly, the main contributions of this paper is a well-defined set of hierarchical representations which acts as the filtering criteria to pick DNN candidates and a novel evolutionary algorithm which produces image classifiers that achieve state of the art performance among similar evolutionary-based techniques.<br />
<br />
=Architecture representations=<br />
<br />
==Flat architecture representation==<br />
All the evaluated network architectures are directed acyclic graphs with only one source and one sink. Each node in the network represents a feature map and consequently, each directed edge represents an operation that takes the feature map in the departing node as input and outputs a feature map on the arriving node. Under the previous assumption, any given architecture in the narrowed search space is formally expressed as a graph assembled by a series of operations (edges) among a defined set of adjacent feature maps (nodes).<br />
<br />
[[File:flatarch.PNG | 650px|thumb|center|Flat architecture representation os neural networks]]<br />
<br />
Multiple primitive operations defined in [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Primitive_operations section 2.3] are used to form small networks defined as ''motifs'' by the authors. To combine the outputs of multiple primitive operations and guarantee a unique output per motif the authors introduce a merge operation which in practice works as a depthwise concatenation that does not require inputs with the same number of channels.<br />
<br />
Accordingly, these motifs can also be combined to form more complex motifs on a higher level in the hierarchy until the network is complex enough to perform competitively in challenging classification tasks.<br />
<br />
==Hierarchical architecture representation==<br />
<br />
The composition of more complex motifs based on simpler motifs at lower levels allows the authors to create a hierarchy-like representation of very complex DNN starting with only a few primitive operations as shown in Figure 1. In other words, an architecture with <math> L </math> levels has only primitive operations at its bottom and only one complex motif at its top. Any motif in between the bottom and top levels can be defined as the composition of motifs in lower levels of the hierarchy.<br />
<br />
Formally, the <math>m</math>-th motif in level <math>l</math>, <math>o_m^{(l)}</math>, is recursively defined as the composition of lower-level motifs <math>\textbf{o}^{(l-1)}</math> according to its network structure.<br />
<br />
<center><math> o_m^{(l)}=assemble(G_m^{(l)}, \textbf{o}^{(l-1)})</math></center><br />
<br />
[[File:hierarchicalrep.PNG | 700px|thumb|center|Figure 1. Hierarchical architecture representation]]<br />
<br />
In figure 1, the architecture of the full model (its flat structure) is shown in the top right corner. The input (source) is the bottom-most node. The output (sink) is the topmost node. The paper presents an alternative hierarchical view of the model shown on the left-hand side (before the assemble function). This view represents the same model in three layers. The first layer is a set of primitive operations only (bottom row, middle column). In all other layers component motifs (computational graphs) G are described by an adjacency matrix and a set of operations. The set of operations are from the previous layer. An example motif <math> G^{(2)}_{1}</math> in the second layer is shown in the bottom row (left and middle columns). There are three unique motifs in the second layer. These are shown in the middle layer of the top row. Note that the motifs in the previous layer become the operations in the next layer. The higher layer can use these motifs multiple times. Finally, the top level graph, which contains only one motif, <math> G^{(3)}_{1}</math>, is shown in the top row left column. Here, there are 4 nodes with 6 operations defined between them.<br />
<br />
==Primitive operations==<br />
<br />
The six primitive operations used as building blocks for connecting nodes in either flat or hierarchical representations are:<br />
* 1 × 1 convolution of C channels<br />
* 3 × 3 depthwise convolution<br />
* 3 × 3 separable convolution of C channels<br />
* 3 × 3 max-pooling<br />
* 3 × 3 average-pooling<br />
* Identity mapping<br />
<br />
The authors argue that convolution operations involving larger receptive fields can be obtained by the composition of lower-level motifs with smaller receptive fields. Accordingly, convolution operations considering a large number of channels can be generated by the depthwise concatenation of lower-level motifs. Batch normalization and ''ReLU'' activation function are applied after each convolution in the network. There is a seventh operation called null and is used in the adjacency matrix <math> G </math> to state explicitly that there are no operations between two nodes.<br />
<br />
<br />
Side note:<br />
<br />
Some explanations for different types for convolution:<br />
<br />
* Spatial convolution: Convolutions performed in spatial dimensions - width and height.<br />
* Depthwise convolution: Spatial convolution performed independently over each channel of an input.<br />
* 1x1 convolution: Convolution with the kernel of size 1x1<br />
<br />
[[File:convolutions.png | 350px|thumb|center]]<br />
<br />
=Evolutionary architecture search=<br />
<br />
Before moving forward we introduce the concept of genotypes in the context of the article. In this article, a genotype is a particular neural network architecture defined according to the components described in [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_representations section 2]. In order to make the NN architectures ''evolve'' the authors implemented a three stages process that includes establishing the permitted mutations, creating an initial population and make them compete in a tournament where only the best candidates will survive.<br />
<br />
==Mutation==<br />
<br />
One mutation over a specific architecture is a sequence of five changes in the following order:<br />
<br />
* Sample a level in the hierarchy, different than the basic level.<br />
* Sample a motif in that level.<br />
* Sample a successor node <math>(i)</math> in the motif.<br />
* Sample a predecessor node <math>(j)</math> in the motif.<br />
* Replace the current operation between nodes <math>i</math> and <math>j</math> from one of the available operations.<br />
<br />
The original operation between the nodes <math>i</math> and <math>j</math> in the graph is defined as <math> [G_{m}^{\left ( l \right )}] _{ij} = k </math>. Therefore, a mutation between the same pair of nodes is defined as <math> [G_{m}^{\left ( l \right )}] _{ij} = {k}' </math>.<br />
<br />
The allowed mutations include:<br />
# Change the basic primitive between the predecessor and successor nodes (ie. alter an existing edge): if <math>o_k^{(l-1)} \neq none</math> and <math>o_{k'}^{(l-1)} \neq none</math> and <math>o_{k'}^{(l-1)} \neq >o_k^{(l-1)}</math><br />
# Add a connection between two previously unconnected nodes. The connection between the node can have any of the six possible primitives: if <math>o_k^{(l-1)}=none</math> and <math>o_{k'}^{(l-1)} \neq none</math><br />
# Remove a connection between existing nodes: if <math>o_k^{(l-1)} \neq none</math> and <math>o_{k'}^{(l-1)} = none</math><br />
<br />
==Initialization==<br />
<br />
An initial population is required to start the evolutionary algorithm; therefore, the authors introduced a trivial genotype (candidate solution, the hierarchical architecture of the model) composed only of identity mapping operations. Then a large number of random mutations was run over the ''trivial genotype'' to simulate a diversification process. The authors argue that this diversification process generates a representative population in the search space and at the same time prevents the use of any handcrafted NN structures. Surprisingly, some of these random architectures show a performance comparable to the performance achieved by the architectures found later during the evolutionary search algorithm.<br />
<br />
==Search algorithms==<br />
<br />
Tournament selection and random search are the two search algorithms used by the authors. <br />
<br />
=== Tournament Selection ===<br />
In one iteration of the tournament selection algorithm, 5% of the entire population is randomly selected, trained, and evaluated against a validation set. Then the best performing genotype is picked to go through the mutation process and put back into the population. No genotype is ever removed from the population, but the selection criteria guarantee that only the best performing models will be selected to ''evolve'' through the mutation process.<br />
<br />
We define the pseudocode for tournament selection as follows:<br />
<br />
1. Choose k (the tournament size) individuals from the population at random<br />
<br />
2. Choose the best individual from the tournament with probability p<br />
<br />
3. Choose the second best individual with probability p*(1-p)<br />
<br />
4. Choose the third best individual with probability p*((1-p)^2)<br />
<br />
5. Continue until number of selected individuals equal the number we desire.<br />
<br />
Tournament selection is often chosen over alternative genetic algorithms due to the following benefits: it is efficient to code, works on parallel architectures and allows the selection pressure to be easily adjusted.<br />
<br />
=== Random Search ===<br />
In the random search algorithm every genotype from the initial population is trained and evaluated, then the best performing model is selected. In contrast to the tournament selection algorithm, the random search algorithm is much simpler and the training and evaluation process for every genotype can be run in parallel to reduce search time.<br />
<br />
==Implementation==<br />
<br />
To implement the tournament selection algorithm two auxiliary algorithms are introduced. The first is called the controller and directs the evolution process over the population, in other words, the controller repeatedly picks 5% of genotypes from the current population, send them to the tournament and then apply a random mutation over the best performing genotype from each group. <br />
<br />
[[File:asyncevoalgorithm1.PNG | 700px|thumb|center|Controller]]<br />
<br />
The second auxiliary algorithm is called the worker and is in charge of training and evaluating each genotype, a task that must be completed each time a new genotype is created and added to the population either by an initialization step or by an evolutionary step.<br />
<br />
[[File:asyncevoalgorithm2.PNG | 700px|thumb|center|Worker]]<br />
<br />
Both auxiliary algorithms work together asynchronously and communicate each other through a shared tabular memory file where genotypes and their corresponding fitness are recorded.<br />
<br />
=Experiments and results=<br />
<br />
==Experimental setup==<br />
<br />
Instead of a looking for a complete NN model, the search framework introduced in [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_representations section 2] is applied to look for the best performing architectures of a small neural network module called the convolutional cell. Using small modules as building blocks to form a larger and more complex model is an approach proved to be successful in previous cases such as the Inception architecture. Additionally, this approach allowed the authors to evaluate cell candidates efficiently and scale to larger and more complex models faster.<br />
<br />
In total three models were implemented as hosts for the experimental cells, the first two use the CIFAR-10 dataset and the third uses the ImageNet dataset. The search framework is implemented only in the first host model to look for the best performing cells ([https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_search_on_CIFAR-10 section 4.2]), once found, these cells were inserted into the second and third host models to evaluate overall performance on the respective datasets ([https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_evaluation_on_CIFAR-10_and_ImageNet section 4.3]).<br />
<br />
The terms training time step, initialization time step, and evolutionary time step will be used to describe some parts of the experiments. Be aware that these three terms have different meanings; however, each term will be properly defined when introduced.<br />
<br />
==Architecture search on CIFAR-10==<br />
<br />
The overall goal in this stage is to find the best performing cells. The search framework is run using the small CIFAR-10 depicted in Figure 2 as host model for the cells; therefore, during the searching process, only the cells change while the rest of the host model’s structure remains the same. In the context of the evolutionary search algorithm, a cell is also called a candidate or a genotype. Additionally, on every time step during the search process, the three cells in the model will share the same structure and consequently every time a new candidate architecture is evaluated the three cells will simultaneously adopt the new candidate’s architecture.<br />
<br />
[[File:smallcifar10.PNG | 350px|thumb|center|Figure 2. Small CIFAR-10 model]]<br />
<br />
To begin the architecture searching process an initial population of genotypes is required. Random mutations are applied over a trivial genotype to generate a candidate and grow the seminal population. This is called an initialization step and is repeated 200 times to produce an equivalent number of candidates. Creating these 200 candidates with random structures is equivalent to running a random search over a constrained architecture space. <br />
<br />
Then, the evolutionary search algorithm takes over and runs from timestep 201 up to time step 7000, these are called evolutionary timesteps. On each evolutionary time step, a group of genotypes equivalent to 5% of the current population is selected randomly and sent to the tournament for fitness computation. To perform a fitness evaluation each candidate cell is inserted into the three predefined positions within the small CIFAR-10 host model. Then for each candidate cell, the host model is trained with stochastic gradient descent during 5000 training steps and decreasing learning rate. Due to a small standard deviation of up to 0.2% found when evaluating the exact same model, the overall fitness is obtained as the average of four training-evaluation runs. Finally, a random mutation is applied over a copy of the best cell within the group to create a new genotype that is added to the current population.<br />
<br />
The fitness of each evaluated genotype is recorded in the shared tabular memory file to avoid recalculation in case the same genotype is selected again in a future evolutionary time step.<br />
<br />
The search framework is run for 7000-time steps (200 initialization time steps and the rest are evolutionary time steps) for each one of three different types of cell architecture, namely hierarchical representation, flat representation and flat representation with constrained parameters. <br />
<br />
* A cell that follows a hierarchical representation has NN connections at three different levels; at the bottom level it has only primitive operations, at the second level it contains motifs with four-nodes and at the third level it has only one motif with five-nodes.<br />
<br />
* A cell that follows a flat representation has 11 nodes with only primitive operations between them. These cells look similar to level 2 motifs but instead of having four nodes they have 11 and therefore many more pairs of nodes and operations.<br />
<br />
* For a cell that follows a flat representation with constrained parameters the total number of parameters used by its operations cannot be superior to the total number of parameters used by the cells that follow a hierarchical representation.<br />
<br />
Figure 3 shows the current fitness achieved by the best performing cell from each one of the three types of cells when plugged in the small CIFAR-10 model. Even though the fitness grows rapidly after the first 200 (initialization) time steps, it tends to plateau between 89% to 90%. Overall, cells that follow a flat representation without restriction in the number of parameters tend to perform better than those following a hierarchical structure. It could be due to the fact that the flat representation allows more flexibility when adding connections between nodes, especially between distant ones. Unfortunately, the authors do not describe the architecture of the best performing flat cell.<br />
<br />
[[File:currentfitness.PNG | 300px|thumb|center|Figure 3. Current fitness]]<br />
<br />
Figure 4 presents the maximum fitness reached by any cell seen by the search framework between each one of the three types of cells, the fitness at time step 200 is, therefore, equivalent to the best model obtained by a random search over 200 architectures from each type of cell.<br />
<br />
[[File:maxfitness.PNG | 300px|thumb|center|Figure 4. Maximum fitness]]<br />
<br />
The total number of parameters used by each genotype at any given time step is shown in Figure 5. It suggests that flat representations tend to add more connections over time and most likely those connections correspond to convolutional operations which in turn require more parameters than other primitive operations.<br />
<br />
[[File:numparameters.PNG | 300px|thumb|center|Figure 5. Number of parameters]]<br />
<br />
To run each time step (either initialization or evolutionary) in the search framework, it takes one hour for a GPU to perform four training and evaluation rounds for every single candidate. Therefore, the authors used 200 GPUs simultaneously to complete 7000-time steps in 35 hours. Considering the three types of cell (hierarchical, flat, and parameter-constrained flat), approximately 20000 GPU-hours could be required to replicate the experiment.<br />
<br />
==Architecture evaluation on CIFAR-10 and ImageNet==<br />
<br />
Once the evolutionary search finds the best-fitted cells those are plug into the two larger host models to evaluate their performance in those more complex architectures. The first large model (Figure 6) is targeted to image classification on the CIFAR-10 dataset and the second model (Figure 7) is focused on image classification on the ImageNet dataset. Although all the parameters in these two larger host models are trained from scratch including those within the cells, no changes in the cell’s architectures will happen since their structure was found to be optimal during the evolutionary search.<br />
<br />
The large CIFAR-10 model is trained with stochastic gradient descent during 80K training steps and decreasing learning rate. To account for the non-negligible standard deviation found when evaluating the exact same model, the percentage of error is determined as the average of five training-evaluation runs.<br />
<br />
[[File:largecifar10.PNG | 500px|thumb|center|Figure 6. Large CIFAR-10 model]]<br />
<br />
The ImageNet model is trained with stochastic gradient descent during 200K training steps and decreasing learning rate. For this model, neither standard deviation nor multiple training-evaluation runs were reported.<br />
<br />
[[File:imagenetmodel.PNG | 600px|thumb|center|Figure 7. ImageNet model]]<br />
<br />
In [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_search_on_CIFAR-10 section 4.2] three types of cells were described: hierarchical, flat, and parameter-constrained flat. For the hierarchical type of cells, the percentage of error in both large models is reported in Table 1 for four different cases: a cell with random architecture, the best-fitted cell from 200 random architectures, the best-fitted cell from 7000 random architectures, and the best-fitted cell after 7000 evolutionary steps. On the other hand, for the flat and parameter-constrained flat types of architecture, only some of the mentioned four cases are reported in Table 1.<br />
<br />
[[File:comparisoncells.PNG | 750px|thumb|center|Table 1. Comparison between types of cells and searching method]]<br />
<br />
According to the results in Table 1, for both large host models, the hierarchical cell found by the evolutionary search algorithm achieved the lowest errors with 3.75% in CIFAR-10, 20.3% top-1 error and 5.2% top-5 error in ImageNet. The errors reported in both datasets are calculated by using the trained large models on test sets of images never seen before during any of the previous stages. Even though the cell that follows a hierarchical representation achieved the lowest error, the ones showing the lowest standard deviations are those following a flat representation.<br />
<br />
The performance achieved by the large CIFAR-10 host model using the best cell is then compared against other classifiers in Table 2. As an additional improvement, the authors increased the number of channels in its first convolutional layer from 64 to 128. It is worth to note that this first convolutional layer is not part of the cell obtained during the evolutionary search process, instead, it is part of the original host model. The results are grouped into three categories depending on how the classifiers involved in the comparison were created, from top to bottom: handcrafted, reinforcement learning, and evolutionary algorithms.<br />
<br />
[[File:comparisonlargecifar10.PNG | 500px|thumb|center|Table 2. Comparison against other classifiers on CIFAR-10]]<br />
<br />
The classification error achieved by the ImageNet host model when using the best cell is also compared against some high performing image classifiers in the literature and the results are presented in Table 3. Although the classification error scored by the architecture introduced in this paper is not significantly lower than those obtained by state of the art classifiers, it shows outstanding results considering that it is not a hand engineered structure.<br />
<br />
[[File:comparisonimagenet.PNG | 500px|thumb|center|Table 3. Comparison against other classifiers on ImageNet]]<br />
<br />
A visualisation of the evolved hierarchical cell is shown below. The detailed visualisations of each motif can be seen in Appendix A of the paper. It can be noted that motif 4 directly links the input and output, and itself contains (among other operations) an identity mapping from input to output. Many other such 'skip connections' can be seen.<br />
<br />
[[File:WF_SecCont_03_hier_vis.png]]<br />
<br />
=Conclusion=<br />
<br />
A new evolutionary framework is introduced for searching neural network architectures over searching spaces defined by flat and hierarchical representations of a convolutional cell, which uses smaller operations instead of the larger ones as the building blocks. Experiments show that the proposed framework achieves competitive results against state of the art classifiers on the CIFAR-10 and ImageNet datasets.<br />
<br />
Also, compared to contemporary RL-based architecture search approaches, the proposed approach is generally faster with comparable performance.<br />
<br />
=Critique=<br />
<br />
While the method introduced in this paper achieves a lower error in comparison to other evolutionary methods, it is not significantly better than those obtained by handcrafted design or reinforcement learning. A more in-depth analysis considering the number of parameters and required computational resources would be necessary to accurately compare the listed methods.<br />
<br />
The paper does not provide enough reasons why the author chose specific two searching algorithms. Possibly more efficient searching are available, which can lead to better performance. Especially, when the performance of the algorithm is not significantly better than previous handcradted ones, this can be a possible technical improvements.<br />
<br />
In [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_evaluation_on_CIFAR-10_and_ImageNet section 4.3] it is not clear why the results for the four different cases that are reported for the hierarchical cells in Table 1 are not reported for the ones following a flat representation, considering that the flat cells showed a better performance during the evolutionary search. Recall that the four cases are: a cell with random architecture, the best-fitted cell from 200 random architectures, the best-fitted cell from 7000 random architectures, and the best-fitted cell after 7000 evolutionary steps.<br />
<br />
It seems contradictory that the flat type of cells who clearly performed better than the hierarchical ones during the architecture search ([https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_search_on_CIFAR-10 section 4.2]) are not the ones scoring the lowest error when evaluated on the two large host models ([https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Hierarchical_Representations_for_Efficient_Architecture_Search#Architecture_evaluation_on_CIFAR-10_and_ImageNet section 4.3]).<br />
<br />
= References =<br />
<br />
# Hanxiao Liu, Karen Simonyan, Oriol Vinyals, Chrisantha Fernando, Koray Kavukcuoglu, https://arxiv.org/abs/1711.00436.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/Autoregressive_Convolutional_Neural_Networks_for_Asynchronous_Time_Series&diff=42122stat946F18/Autoregressive Convolutional Neural Networks for Asynchronous Time Series2018-11-30T21:59:00Z<p>R82zhang: [T]/* Time series forecasting */</p>
<hr />
<div>This page is a summary of the paper "[http://proceedings.mlr.press/v80/binkowski18a/binkowski18a.pdf Autoregressive Convolutional Neural Networks for Asynchronous Time Series]" by Mikołaj Binkowski, Gautier Marti, Philippe Donnat. It was published at ICML in 2018. The code for this paper is provided [https://github.com/mbinkowski/nntimeseries here].<br />
<br />
=Introduction=<br />
In this paper, the authors propose a deep convolutional network architecture called Significance-Offset Convolutional Neural Network for regression of multivariate asynchronous time series. The model is inspired by standard autoregressive (AR) models and gating systems used in recurrent neural networks. The model is evaluated on various time series data including:<br />
# Hedge fund proprietary dataset of over 2 million quotes for a credit derivative index, <br />
# An artificially generated noisy auto-regressive series, <br />
# A UCI household electricity consumption dataset. <br />
<br />
This paper focused on time series that have multivariate and noisy signals, especially financial data. Financial time series is challenging to predict due to their low signal-to-noise ratio and heavy-tailed distributions. For example, the same signal (e.g. price of a stock) is obtained from different sources (e.g. financial news, an investment bank, financial analyst etc.) asynchronously. Each source may have a different bias or noise. ([[Media: Junyi1.png|Figure 1]]) The investment bank with more clients can update their information more precisely than the investment bank with fewer clients, which means the significance of each past observations may depend on other factors that change in time. Therefore, the traditional econometric models such as AR, VAR (Vector Autoregressive Model), VARMA (Vector Autoregressive Moving Average Model) [1] might not be sufficient. However, their relatively good performance could allow us to combine such linear econometric models with deep neural networks that can learn highly nonlinear relationships. This model is inspired by the gating mechanism which is successful in RNNs and Highway Networks.<br />
<br />
Time series forecasting is focused on modeling the predictors of future values of time series given their past. As in many cases the relationship between past and future observations is not deterministic, this amounts to expressing the conditional probability distribution as a function of the past observations: The time series forecasting problem can be expressed as a conditional probability distribution below,<br />
<div style="text-align: center;"><math>p(X_{t+d}|X_t,X_{t-1},...) = f(X_t,X_{t-1},...)</math></div><br />
This forecasting problem has been approached almost independently by econometrics and machine learning communities. In this paper, the authors focus on modeling the predictors of future values of time series given their past values. <br />
<br />
The reasons that financial time series are particularly challenging:<br />
* Low signal-to-noise ratio and heavy-tailed distributions.<br />
* Being observed different sources (e.g. financial news, analysts, portfolio managers in hedge funds, market-makers in investment banks) in asynchronous moments of time. Each of these sources may have a different bias and noise with respect to the original signal that needs to be recovered.<br />
* Data sources are usually strongly correlated and lead-lag relationships are possible (e.g. a market-maker with more clients can update its view more frequently and precisely than one with fewer clients). <br />
* The significance of each of the available past observations might be dependent on some other factors that can change in time. Hence, the traditional econometric models such as AR, VAR, VARMA might not be sufficient.<br />
<br />
The predictability of financial dataset still remains an open problem and is discussed in various publications [2].<br />
<br />
[[File:Junyi1.png | 500px|thumb|center|Figure 1: Quotes from four different market participants (sources) for the same credit default swaps (CDS) throughout one day. Each trader displays from time to time the prices for which he offers to buy (bid) and sell (ask) the underlying CDS. The filled area marks the difference between the best sell and buy offers (spread) at each time.]]<br />
<br />
The paper also provides empirical evidence that their model which combines linear models with deep learning models could perform better than just DL models like CNN, LSTMs and Phased LSTMs.<br />
<br />
=Related Work=<br />
===Time series forecasting===<br />
From recent proceedings in main machine learning venues i.e. ICML, NIPS, AISTATS, UAI, we can notice that time series are often forecasted using Gaussian processes[3,4], especially for irregularly sampled time series[5]. Though still largely independent, combined models have started to appear, for example, the Gaussian Copula Process Volatility model[6]. For this paper, the authors use coupling AR models and neural networks to achieve such combined models.<br />
<br />
Although deep neural networks have been applied into many fields and produced satisfactory results, there still is little literature on deep learning for time series forecasting. More recently, the papers include Sirignano (2016)[7] that used 4-layer perceptrons in modeling price change distributions in Limit Order Books and Borovykh et al. (2017)[8] who applied more recent WaveNet architecture to several short univariate and bivariate time-series (including financial ones). Heaton et al. (2016)[9] claimed to use autoencoders with a single hidden layer to compress multivariate financial data. Neil et al. (2016)[10] presented augmentation of LSTM architecture suitable for asynchronous series, which stimulates learning dependencies of different frequencies through the time gate. The LSTM architecture has three "gates", the input gate, the forget gate, and the update gate. It performs well in practice because it allows the RNN architecture to be able to take into account events happened a long time ago. Traditionally, RNN architectures are heavily influenced by recent events, but LSTM overcomes that by updating the weights in the three newly introduced gates.<br />
<br />
In this paper, the authors examine the capabilities of several architectures (CNN, residual network, multi-layer LSTM, and phase LSTM) on AR-like artificial asynchronous and noisy time series, household electricity consumption dataset, and on real financial data from the credit default swap market with some inefficiencies.<br />
<br />
====AR Model====<br />
<br />
An autoregressive (AR) model describes the next value in a time-series as a combination of previous values, scaling factors, a bias, and noise [https://onlinecourses.science.psu.edu/stat501/node/358/ (source)]. For a p-th order (relating the current state to the p last states), the equation of the model is:<br />
<br />
<math> X_t = c + \sum_{i=1}^p \varphi_i X_{t-i}+ \varepsilon_t \,</math> [https://en.wikipedia.org/wiki/Autoregressive_model#Definition (equation source)]<br />
<br />
With parameters/coefficients <math>\varphi_i</math>, constant <math>c</math>, and noise <math>\varepsilon_t</math> This can be extended to vector form to create the VAR model mentioned in the paper.<br />
<br />
===Gating and weighting mechanisms===<br />
Gating mechanism for neural networks has ability to overcome the problem of vanishing gradients, and can be expressed as <math display="inline">f(x)=c(x) \otimes \sigma(x)</math>, where <math>f</math> is the output function, <math>c</math> is a "candidate output" (a nonlinear function of <math>x</math>), <math>\otimes</math> is an element-wise matrix product, and <math>\sigma : \mathbb{R} \rightarrow [0,1] </math> is a sigmoid non-linearity that controls the amount of output passed to the next layer. Different composition of functions of the same type as described above have proven to be an essential ingredient in popular recurrent architecture such as LSTM and GRU[11].<br />
<br />
The main purpose of the proposed gating system is to weight the outputs of the intermediate layers within neural networks, and is most closely related to softmax gating used in MuFuRu(Multi-Function Recurrent Unit)[12], i.e.<br />
<math display="inline"> f(x) = \sum_{l=1}^L p^l(x) \otimes f^l(x)\text{,}\ p(x)=\text{softmax}(\widehat{p}(x)), </math>, where <math>(f^l)_{l=1}^L </math>are candidate outputs (composition operators in MuFuRu), <math>(\widehat{p}^l)_{l=1}^L </math>are linear functions of inputs. <br />
<br />
This idea is also successfully used in attention networks[13] such as image captioning and machine translation. In this paper, the proposed method is similar as, the separate inputs (time series steps in this case) are weighted in accordance with learned functions of these inputs. The difference is that the functions are modelled using multi-layer CNNs. Another difference is that the proposed method is not using recurrent layers, which enables the network to remember parts of the sentence/image already translated/described.<br />
<br />
=Motivation=<br />
There are mainly five motivations that are stated in the paper by the authors:<br />
#The forecasting problem in this paper has been done almost independently by econometrics and machine learning communities. Unlike in machine learning, research in econometrics is more likely to explain variables rather than improving out-of-sample prediction power. These models tend to 'over-fit' on financial time series, their parameters are unstable and have poor performance on out-of-sample prediction.<br />
#It is difficult for the learning algorithms to deal with time series data where the observations have been made irregularly. Although Gaussian processes provide a useful theoretical framework that is able to handle asynchronous data, they are not suitable for financial datasets, which often follow heavy-tailed distribution .<br />
#Predictions of autoregressive time series may involve highly nonlinear functions if sampled irregularly. For AR time series with higher order and have more past observations, the expectation of it <math display="inline">\mathbb{E}[X(t)|{X(t-m), m=1,...,M}]</math> may involve more complicated functions that in general may not allow closed-form expression.<br />
#In practice, the dimensions of multivariate time series are often observed separately and asynchronously, such series at fixed frequency may lead to lose information or enlarge the dataset, which is shown in Figure 2(a). Therefore, the core of the proposed architecture SOCNN represents separate dimensions as a single one with dimension and duration indicators as additional features(Figure 2(b)).<br />
#Given a series of pairs of consecutive input values and corresponding durations, <math display="inline"> x_n = (X(t_n),t_n-t_{n-1}) </math>. One may expect that LSTM may memorize the input values in each step and weight them at the output according to the duration, but this approach may lead to an imbalance between the needs for memory and for linearity. The weights that are assigned to the memorized observations potentially require several layers of nonlinearity to be computed properly, while past observations might just need to be memorized as they are.<br />
<br />
[[File:Junyi2.png | 550px|thumb|center|Figure 2: (a) Fixed sampling frequency and its drawbacks; keep- ing all available information leads to much more datapoints. (b) Proposed data representation for the asynchronous series. Consecutive observations are stored together as a single value series, regardless of which series they belong to; this information, however, is stored in indicator features, alongside durations between observations.]]<br />
<br />
=Model Architecture=<br />
Suppose there exists a multivariate time series <math display="inline">(x_n)_{n=0}^{\infty} \subset \mathbb{R}^d </math>, we want to predict the conditional future values of a subset of elements of <math>x_n</math><br />
<div style="text-align: center;"><math>y_n = \mathbb{E} [x_n^I | \{x_{n-m}, m=1,2,...\}], </math></div><br />
where <math> I=\{i_1,i_2,...i_{d_I}\} \subset \{1,2,...,d\} </math> is a subset of features of <math>x_n</math>.<br />
<br />
Let <math> \textbf{x}_n^{-M} = (x_{n-m})_{m=1}^M </math>. <br />
<br />
The estimator of <math>y_n</math> can be expressed as:<br />
<div style="text-align: center;"><math>\tilde{y}_n = \sum_{m=1}^M [F(\textbf{x}_n^{-M}) \otimes \sigma(S(\textbf{x}_n^{-M}))].,_m ,</math></div><br />
The estimate is the summation of the columns of the matrix in bracket. Here<br />
#<math>F,S : \mathbb{R}^{d \times M} \rightarrow \mathbb{R}^{d_I \times M}</math> are neural networks. <br />
#* <math>S</math> is a fully convolutional network which is composed of convolutional layers only. <br />
#* <math display="inline">F(\textbf{x}_n^{-M}) = W \otimes [\text{off}(x_{n-m}) + x_{n-m}^I)]_{m=1}^M </math> <br />
#** <math> W \in \mathbb{R}^{d_I \times M}</math> <br />
#** <math> \text{off}: \mathbb{R}^d \rightarrow \mathbb{R}^{d_I} </math> is a multilayer perceptron.<br />
<br />
#<math>\sigma</math> is a normalized activation function independent at each row, i.e. <math display="inline"> \sigma ((a_1^T, ..., a_{d_I}^T)^T)=(\sigma(a_1)^T,..., \sigma(a_{d_I})^T)^T </math><br />
#* for any <math>a_{i} \in \mathbb{R}^{M}</math><br />
#* and <math>\sigma </math> is defined such that <math>\sigma(a)^{T} \mathbf{1}_{M}=1</math> for any <math>a \in \mathbb{R}^M</math>.<br />
# <math>\otimes</math> is element-wise matrix multiplication (also known as Hadamard matrix multiplication).<br />
#<math>A.,_m</math> denotes the m-th column of a matrix A.<br />
<br />
Since <math>\sum_{m=1}^M W.,_m=W\cdot(1,1,...,1)^T</math> and <math>\sum_{m=1}^M S.,_m=S\cdot(1,1,...,1)^T</math>, we can express <math>\hat{y}_n</math> as:<br />
<div style="text-align: center;"><math>\hat{y}_n = \sum_{m=1}^M W.,_m \otimes (off(x_{n-m}) + x_{n-m}^I) \otimes \sigma(S.,_m(\textbf{x}_n^{-M}))</math></div><br />
This is the proposed network, Significance-Offset Convolutional Neural Network, <math>\text{off}</math> and <math>S</math> in the equation are corresponding to Offset and Significance in the name respectively.<br />
Figure 3 shows the scheme of network.<br />
<br />
[[File:Junyi3.png | 600px|thumb|center|Figure 3: A scheme of the proposed SOCNN architecture. The network preserves the time-dimension up to the top layer, while the number of features per timestep (filters) in the hidden layers is custom. The last convolutional layer, however, has the number of filters equal to dimension of the output. The Weighting frame shows how outputs from offset and significance networks are combined in accordance with Eq. of <math>\hat{y}_n</math>.]]<br />
<br />
The form of <math>\tilde{y}_n</math> ensures the separation of the temporal dependence (obtained in weights <math>W_m</math>). <math>S</math>, which represents the local significance of observations, is determined by its filters which capture local dependencies and are independent of the relative position in time, and the predictors <math>\text{off}(x_{n-m})</math> are completely independent of position in time. An adjusted single regressor for the target variable is provided by each past observation through the offset network. Since in asynchronous sampling procedure, consecutive values of x come from different signals and might be heterogeneous, therefore adjustment of offset network is important. In addition, significance network provides data-dependent weight for each regressor and sums them up in an autoregressive manner.<br />
<br />
===Relation to asynchronous data===<br />
One common problem of time series is that durations are varying between consecutive observations, the paper states two ways to solve this problem<br />
#Data preprocessing: aligning the observations at some fixed frequency e.g. duplicating and interpolating observations as shown in Figure 2(a). However, as mentioned in the figure, this approach will tend to loss of information and enlarge the size of the dataset and model complexity.<br />
#Add additional features: Treating the duration or time of the observations as additional features, it is the core of SOCNN, which is shown in Figure 2(b).<br />
<br />
===Loss function===<br />
The L2 error is a natural loss function for the estimators of expected value: <math>L^2(y,y')=||y-y'||^2</math><br />
<br />
The output of the offset network is series of separate predictors of changes between corresponding observations <math>x_{n-m}^I</math> and the target value<math>y_n</math>, this is the reason why we use auxiliary loss function, which equals to mean squared error of such intermediate predictions:<br />
<div style="text-align: center;"><math>L^{aux}(\textbf{x}_n^{-M}, y_n)=\frac{1}{M} \sum_{m=1}^M ||off(x_{n-m}) + x_{n-m}^I -y_n||^2 </math></div><br />
The total loss for the sample <math> \textbf{x}_n^{-M},y_n) </math> is then given by:<br />
<div style="text-align: center;"><math>L^{tot}(\textbf{x}_n^{-M}, y_n)=L^2(\widehat{y}_n, y_n)+\alpha L^{aux}(\textbf{x}_n^{-M}, y_n)</math></div><br />
where <math>\widehat{y}_n</math> was mentioned before, <math>\alpha \geq 0</math> is a constant.<br />
<br />
=Experiments=<br />
The paper evaluated SOCNN architecture on three datasets: artificially generated datasets, [https://archive.ics.uci.edu/ml/datasets/Individual+household+electric+power+consumption household electric power consumption dataset], and the financial dataset of bid/ask quotes provided by several market participants active in the credit derivatives market. Comparing its performance with simple CNN, single and multiplayer LSTM and 25-layer ResNet. Apart from the evaluation of the SOCNN architecture, the paper also discussed the impact of network components such as auxiliary<br />
loss and the depth of the offset sub-network. The code and datasets are available [https://github.com/mbinkowski/nntimeseries here].<br />
<br />
==Datasets==<br />
Artificial data: They generated 4 artificial series, <math> X_{K \times N}</math>, where <math>K \in \{16,64\} </math>. Therefore there is a synchronous and an asynchronous series for each K value. Note that a series with K sources is K + 1-dimensional in synchronous case and K + 2-dimensional in asynchronous case. The base series in all processes was a stationary AR(10) series. Although that series has the true order of 10, in the experimental setting the input data included past 60 observations. The rationale behind that is twofold: not only is the data observed in irregular random times but also in real–life problems the order of the model is unknown.<br />
<br />
Electricity data: This UCI dataset contains 7 different features excluding date and time. The features include global active power, global reactive power, voltage, global intensity, sub-metering 1, sub-metering 2 and sub-metering 3, recorded every minute for 47 months. The data has been altered so that one observation contains only one value of 7 features, while durations between consecutive observations are ranged from 1 to 7 minutes. The goal is to predict all 7 features for the next time step.<br />
<br />
Non-anonymous quotes: The dataset contains 2.1 million quotes from 28 different sources from different market participants such as analysts, banks etc. Each quote is characterized by 31 features: the offered price, 28 indicators of the quoting source, the direction indicator (the quote refers to either a buy or a sell offer) and duration from the previous quote. For each source and direction, we want to predict the next quoted price from this given source and direction considering the last 60 quotes.<br />
<br />
[[File:async.png | 520px|center|]]<br />
<br />
==Training details==<br />
They applied grid search on some hyperparameters in order to get the significance of its components. The hyperparameters include the offset sub-network's depth and the auxiliary weight <math>\alpha</math>. For offset sub-network's depth, they use 1, 10,1 for artificial, electricity and quotes dataset respectively; and they compared the values of <math>\alpha</math> in {0,0.1,0.01}.<br />
<br />
They chose LeakyReLU as activation function for all networks:<br />
<div style="text-align: center;"><math>\sigma^{LeakyReLU}(x) = x</math> if <math>x\geq 0</math>, and <math>0.1x</math> otherwise </div><br />
They use the same number of layers, same stride and similar kernel size structure in CNN. In each trained CNN, they applied max pooling with the pool size of 2 every 2 convolutional layers.<br />
<br />
Table 1 presents the configuration of network hyperparameters used in comparison<br />
<br />
[[File:Junyi4.png | 520px|center|]]<br />
<br />
===Network Training===<br />
The training and validation data were sampled randomly from the first 80% of timesteps in each series, with ratio of 3 to 1. The remaining 20% of data was used as a test set.<br />
<br />
All models were trained using Adam optimizer because the authors found that its rate of convergence was much faster than standard Stochastic Gradient Descent in early tests.<br />
<br />
They used a batch size of 128 for artificial and electricity data, and 256 for quotes dataset, and applied batch normalization between each convolution and the following activation. <br />
<br />
At the beginning of each epoch, the training samples were randomly sampled. To prevent overfitting, they applied dropout and early stopping.<br />
<br />
Weights were initialized using the normalized uniform procedure proposed by Glorot & Bengio (2010).[14]<br />
<br />
The authors carried out the experiments on Tensorflow and Keras and used different GPU to optimize the model for different datasets. The artificial and electricity data was optimized using one NVIDIA K20, while the quotes data used only an Intel Core i7-6700 CPU.<br />
<br />
==Results==<br />
Table 2 shows all results performed from all datasets.<br />
[[File:Junyi5.png | 800px|center|]]<br />
We can see that SOCNN outperforms in all asynchronous artificial, electricity and quotes datasets. For synchronous data, LSTM might be slightly better, but SOCNN almost has the same results with LSTM. Phased LSTM and ResNet have performed really bad on artificial asynchronous dataset and quotes dataset respectively. Notice that having more than one layer of offset network would have negative impact on results. Also, the higher weights of auxiliary loss(<math>\alpha</math>considerably improved the test error on asynchronous dataset, see Table 3. However, for other datasets, its impact was negligible. This makes it hard to justify the introduction of the auxillary loss function <math>L^{aux}</math>.<br />
<br />
Also, using artificial dataset as experimental result is not a good practice in this paper. This is essentially an application paper, and such dataset makes results hard to reproduce, and cannot support the performance claim of the model.<br />
<br />
[[File:Junyi6.png | 480px|center|]]<br />
In general, SOCNN has significantly lower variance of the test and validation errors, especially in the early stage of the training process and for quotes dataset. This effect can be seen in the learning curves for Asynchronous 64 artificial dataset presented in Figure 5.<br />
[[File:Junyi7.png | 500px|thumb|center|Figure 5: Learning curves with different auxiliary weights for SOCNN model trained on Asynchronous 64 dataset. The solid lines indicate the test error while the dashed lines indicate the training error.]]<br />
<br />
Finally, we want to test the robustness of the proposed model SOCNN, adding noise terms to asynchronous 16 dataset and check how these networks perform. The result is shown in Figure 6.<br />
[[File:Junyi8.png | 600px|thumb|center|Figure 6: Experiment comparing robustness of the considered networks for Asynchronous 16 dataset. The plots show how the error would change if an additional noise term was added to the input series. The dotted curves show the total significance and average absolute offset (not to scale) outputs for the noisy observations. Interestingly, the significance of the noisy observations increases with the magnitude of noise; i.e. noisy observations are far from being discarded by SOCNN.]]<br />
From Figure 6, the purple lines and green lines seem to stay at the same position in training and testing process. SOCNN and single-layer LSTM are most robust and least prone to overfitting comparing to other networks.<br />
<br />
=Conclusion and Discussion=<br />
In this paper, the authors have proposed a new architecture called Significance-Offset Convolutional Neural Network, which combines AR-like weighting mechanism and convolutional neural network. This new architecture is designed for high-noise asynchronous time series and achieves outperformance in forecasting several asynchronous time series compared to popular convolutional and recurrent networks. <br />
<br />
The SOCNN can be extended further by adding intermediate weighting layers of the same type in the network structure. Another possible extension but needs further empirical studies is that we consider not just <math>1 \times 1</math> convolutional kernels on the offset sub-network. Also, this new architecture might be tested on other real-life datasets with relevant characteristics in the future, especially on econometric datasets and more generally for time series (stochastic processes) regression.<br />
<br />
=Critiques=<br />
#The paper is most likely an application paper, and the proposed new architecture shows improved performance over baselines in the asynchronous time series.<br />
#The quote data cannot be reached as they are proprietary. Also, only two datasets available.<br />
#The 'Significance' network was described as critical to the model in paper, but they did not show how the performance of SOCNN with respect to the significance network.<br />
#The transform of the original data to asynchronous data is not clear.<br />
#The experiments on the main application are not reproducible because the data is proprietary.<br />
#The way that train and test data were split is unclear. This could be important in the case of the financial data set.<br />
#Although the auxiliary loss function was mentioned as an important part, the advantages of it was not too clear in the paper. Maybe it is better that the paper describes a little more about its effectiveness.<br />
#It was not mentioned clearly in the paper whether the model training was done on a rolling basis for time series forecasting.<br />
#The noise term used in section 5's model robustness analysis uses evenly distributed noise (see Appendix B). While the analysis is a good start, analysis with different noise distributions would make the findings more generalizable.<br />
#The paper uses financial/economic data as one of its testing data set. Instead of comparing neural network models such as CNN which is known to work badly on time series data, it would be much better if the author compared to well-known econometric time series models such as GARCH and VAR.<br />
#The paper does not specify how training and testing set are separated in detail, which is quite important in time-series problems. Moreover, rolling or online-based learning scheme should be used in comparison, since they are standard in time-series prediction tasks.<br />
<br />
=References=<br />
[1] Hamilton, J. D. Time series analysis, volume 2. Princeton university press Princeton, 1994. <br />
<br />
[2] Fama, E. F. Efficient capital markets: A review of theory and empirical work. The journal of Finance, 25(2):383–417, 1970.<br />
<br />
[3] Petelin, D., Sˇindela ́ˇr, J., Pˇrikryl, J., and Kocijan, J. Financial modeling using gaussian process models. In Intelligent Data Acquisition and Advanced Computing Systems (IDAACS), 2011 IEEE 6th International Conference on, volume 2, pp. 672–677. IEEE, 2011.<br />
<br />
[4] Tobar, F., Bui, T. D., and Turner, R. E. Learning stationary time series using Gaussian processes with nonparametric kernels. In Advances in Neural Information Processing Systems, pp. 3501–3509, 2015.<br />
<br />
[5] Hwang, Y., Tong, A., and Choi, J. Automatic construction of nonparametric relational regression models for multiple time series. In Proceedings of the 33rd International Conference on Machine Learning, 2016.<br />
<br />
[6] Wilson, A. and Ghahramani, Z. Copula processes. In Advances in Neural Information Processing Systems, pp. 2460–2468, 2010.<br />
<br />
[7] Sirignano, J. Extended abstract: Neural networks for limit order books, February 2016.<br />
<br />
[8] Borovykh, A., Bohte, S., and Oosterlee, C. W. Conditional time series forecasting with convolutional neural networks, March 2017.<br />
<br />
[9] Heaton, J. B., Polson, N. G., and Witte, J. H. Deep learning in finance, February 2016.<br />
<br />
[10] Neil, D., Pfeiffer, M., and Liu, S.-C. Phased lstm: Accelerating recurrent network training for long or event-based sequences. In Advances In Neural Information Process- ing Systems, pp. 3882–3890, 2016.<br />
<br />
[11] Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. Empirical evaluation of gated recurrent neural networks on sequence modeling, December 2014.<br />
<br />
[12] Weissenborn, D. and Rockta ̈schel, T. MuFuRU: The Multi-Function recurrent unit, June 2016.<br />
<br />
[13] Cho, K., Courville, A., and Bengio, Y. Describing multi- media content using attention-based Encoder–Decoder networks. IEEE Transactions on Multimedia, 17(11): 1875–1886, July 2015. ISSN 1520-9210.<br />
<br />
[14] Glorot, X. and Bengio, Y. Understanding the difficulty of training deep feedforward neural net- works. In In Proceedings of the International Con- ference on Artificial Intelligence and Statistics (AIS- TATSaˆ10). Society for Artificial Intelligence and Statistics, 2010.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Reinforcement_Learning_of_Theorem_Proving&diff=42120Reinforcement Learning of Theorem Proving2018-11-30T21:40:38Z<p>R82zhang: [T]/* Experimental Results */</p>
<hr />
<div>== Introduction ==<br />
Automated reasoning over mathematical proof was a major motivation for the development of computer science. Automated theorem provers (ATP) can in principle be used to attack any formally stated mathematical problem and is a research area that has been present since the early 20th century [1]. As of today, state-of-art ATP systems rely on the fast implementation of complete proof calculi. such as resolution and tableau. However, they are still far weaker than trained mathematicians. Within current ATP systems, many heuristics are essential for their performance. As a result, <br />
in recent years machine learning has been used to replace such heuristics and improve the performance of ATPs.<br />
<br />
In this paper, the authors propose a reinforcement learning based ATP, rlCoP. The proposed ATP reasons within first-order logic. The underlying proof calculi are the connection calculi [2], and the reinforcement learning method is Monte Carlo tree search along with policy and value learning. It is shown that reinforcement learning results in a 42.1% performance increase compared to the base prover (without learning).<br />
<br />
== Related Work ==<br />
C. Kalizyk and J. Urban proposed a supervised learning based ATP, FEMaLeCoP, whose underlying proof calculi is the same as this paper in 2015 [3]. Their algorithm learns from existing proofs to choose the next tableau extension step. Since the MaLARea [8] system, number of iterations of a feedback loop between proving and learning have been explored, remarkably improving over human-designed heuristics when reasoning in large theories. However, such systems are known to only learn a high-level selection of relevant facts from a large knowledge base and delegate the internal proof search to standard ATP systems. S. Loos, et al. developed an supervised learning ATP system in 2017 [4], with superposition as their proof calculi. However, they chose deep neural network (CNNs and RNNs) as feature extractor. These systems are treated as black boxes in literature with not much understanding of their performances possible. <br />
<br />
In leanCoP [9], one of the simpler connection tableau systems, the next tableau extension step could be selected using supervised learning. In addition, the first experiments with Monte-Carlo guided proof search [5] have been done for connection tableau systems. The improvement over the baseline measured in that work is much less significant than here. This is closest to the authors' approach but the performance is poorer than this paper.<br />
<br />
On a different note, A. Alemi, et al. proposed a deep sequence model for premise selection in 2016 [6], and they claim to be the first team to involve deep neural networks in ATPs. Although premise selection is not directly linked to automated reasoning, it is still an important component in ATPs, and their paper provides some insights into how to process datasets of formally stated mathematical problems.<br />
<br />
== First Order Logic and Connection Calculi ==<br />
Here we assume basic first-order logic and theorem proving terminology, and we will offer a brief introduction of the bare prover and connection calculi. Let us try to prove the following first-order sentence.<br />
<br />
[[file:fof_sentence.png|frameless|450px|center]]<br />
<br />
This sentence can be transformed into a formula in Skolemized Disjunctive Normal Form (DNF), which is referred to as the "matrix".<br />
<br />
[[file:skolemized_dnf.png|frameless|450px|center]] <br />
[[file:matrix.png|frameless|center]] <br />
<br />
The original first-order sentence is valid if and only if the Skolemized DNF formula is a tautology. The connection calculi attempt to show that the Skolemized DNF formula is a tautology by constructing a tableau. We will start at the special node, root, which is an open leaf. At each step, we select a clause (for example, clause <math display="inline">P \wedge R</math> is selected in the first step), and add the literals as children for an existing open leaf. For every open leaf, examine the path from the root to this leaf. If two literals on this path are unifiable (for example, <math display="inline">Qx'</math> is unifiable with <math display="inline">\neg Qc</math>), this leaf is then closed. An example of a closed tableaux is shown in Figure 1. In standard terminology, it states that a connection is found on this branch.<br />
<br />
[[file:tableaux_example.png|thumb|center|Figure 1. An example of closed tableaux. Adapted from [2]]]<br />
<br />
The paper's goal is to close every leaf, i.e. on every branch, there exists a connection. If such state is reached, the paper has shown that the Skolemized DNF formula is a tautology, thus proving the original first-order sentence. As we can see from the constructed tableaux, the example sentence is indeed valid.<br />
<br />
In formal terms, the rules of connection calculi is shown in Figure 2, and the formal tableaux for the example sentence is shown in Figure 3. Each leaf is denoted as <math display="inline">subgoal, M, path</math> where <math display="inline">subgoal</math> is a list of literals that we need to find connection later, <math display="inline">M</math> stands for the matrix, and <math display="inline">path</math> stands for the path leading to this leaf.<br />
<br />
[[file:formal_calculi.png|thumb|600px|center|Figure 2. Formal connection calculi. Adapted from [2].]]<br />
[[file:formal_tableaux.png|thumb|600px|center|Figure 3. Formal tableaux constructed from the example sentence. Adapted from [2].]]<br />
<br />
To sum up, the bare prover follows a very simple algorithm. given a matrix, a non-negated clause is chosen as the first subgoal. The function ''prove(subgoal, M, path)'' is stated as follows:<br />
* If ''subgoal'' is empty<br />
** return ''TRUE''<br />
* If reduction is possible<br />
** Perform reduction, generating ''new_subgoal'', ''new_path''<br />
** return ''prove(new_subgoal, M, new_path)''<br />
* For all clauses in ''M''<br />
** If a clause can do extension with ''subgoal''<br />
** Perform extension, generating ''new_subgoal1'', ''new_path'', ''new_subgoal2''<br />
** return ''prove(new_subgoal1, M, new_path)'' and ''prove(new_subgoal2, M, path)''<br />
* return ''FALSE''<br />
<br />
It is important to note that the bare prover implemented in this paper is incomplete. Here is a pathological example. Suppose the following matrix (which is trivially a tautology) is feed into the bare prover. Let clause <math display="inline">P(0)</math> be the first subgoal. Clearly choosing <math display="inline">\neg P(0)</math> to extend will complete the proof.<br />
<br />
[[file:pathological.png|frameless|400px|center]] <br />
<br />
However, if we choose <math display="inline">\neg P(x) \lor P(s(x))</math> to do extension, the algorithm will generate an infinite branch <math display="inline">P(0), P(s(0)), P(s(s(0))) ...</math>. It is the task of reinforcement learning to guide the prover in such scenarios towards a successful proof.<br />
<br />
A technique called iterative deepening can be used to avoid such infinite loop, making the bare prover complete. Iterative deepening will force the prover to try all shorter proofs before moving into long ones, it is effective, but also waste valuable computing resource trying to enumerate all short proofs.<br />
<br />
In addition, the provability of first-order sentences is generally undecidable (this result is named the Church-Turing Thesis), which sheds light on the difficulty of automated theorem proving.<br />
<br />
== Mizar Math Library ==<br />
Mizar Math Library (MML) [7, 10] is a library of mathematical theories. The axioms behind the library is the Tarski-Grothendieck set theory, written in first-order logic. The library contains 57,000+ theorems and their proofs, along with many other lemmas, as well as unproven conjectures. Figure 4 shows a Mizar article of the theorem "If <math display="inline"> p </math> is prime, then <math display="inline"> \sqrt p </math> is irrational."<br />
<br />
[[file:mizar_article.png|thumb|center|Figure 4. An article from MML. Adapted from [6].]]<br />
<br />
The training and testing data for this paper is a subset of MML, the Mizar40, which is 32,524 theorems proved by automated theorem provers. Below is an example from the Mizar40 library, it states that with ''d3_xboole_0'' and ''t3_xboole_0'' as premises, we can prove ''t5_xboole_0''.<br />
<br />
[[file:mizar40_0.png|frameless|400px|center]]<br />
[[file:mizar40_1.png|frameless|600px|center]]<br />
[[file:mizar40_2.png|frameless|600px|center]]<br />
[[file:mizar40_3.png|frameless|600px|center]]<br />
<br />
== Monte Carlo Guidance ==<br />
<br />
Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes. The focus of Monte Carlo tree search is on the analysis of the most promising moves, expanding the search tree based on random sampling of the search space. Then the expansion will then be used to weight the node in the search tree.<br />
<br />
In the reinforcement learning setting, the action is defined as one inference (either reduction or extension). The proof state is defined as the whole tableaux. To implement Monte-Carlo tree search, each proof state <math display="inline"> i </math> needs to maintain three parameters, its prior probability <math display="inline"> p_i </math>, its total reward <math display="inline"> w_i </math>, and number of its visits <math display="inline"> n_i </math>. If no policy learning is used, the prior probabilities are all equal to one. <br />
<br />
A simple heuristic is used to estimate the future reward of leaf states: suppose leaf state <math display="inline"> i </math> has <math display="inline"> G_i </math> open subgoals, the reward is computed as <math display="inline"> 0.95 ^ {G_i} </math>. This will be replaced once value learning is implemented.<br />
<br />
The standard UCT formula is chosen to select the next actions in the playouts<br />
\begin{align}<br />
{\frac{w_i}{n_i}} + 2 \cdot p_i \cdot {\sqrt{\frac{\log N}{n_i}}}<br />
\end{align}<br />
where <math display="inline"> N </math> stands for the total number of visits of the parent node.<br />
<br />
The bare prover is asked to play <math display="inline"> b </math> playouts of length <math display="inline"> d </math> from the empty tableaux, each playout backpropagates the values of proof states it visits. After these <math display="inline"> b </math> playouts a special action (inference) is made, corresponding to an actual move, resulting in a new bigstep tableaux. The next <math display="inline"> b </math> playouts will start from this tableaux, followed by another bigstep, etc.<br />
<br />
== Policy Learning and Guidance ==<br />
<br />
From many runs of MCT, we will know the optimal prior probability of actions (inferences) in particular proof states, we can extract the frequency of each action <math display="inline"> a </math>, and normalize it by dividing with the average action frequency at that state, resulting in a relative proportion <math display="inline"> r_a \in (0, \infty) </math>. We characterize the proof states for policy learning by extracting human-engineered features. Also, we characterize actions by extracting features from the clause chosen and literal chosen as well. Thus we will have a feature vector <math display="inline"> (f_s, f_a) </math>. <br />
<br />
The feature vector <math display="inline"> (f_s, f_a) </math> is regressed against the associated <math display="inline"> r_a </math>.<br />
<br />
During the proof search, the prior probabilities <math display="inline"> p_i </math> of available actions <math display="inline"> a_i </math> in a state <math display="inline"> s </math> is computed as the softmax of their predictions.<br />
<br />
Training examples are only extracted from big step states, making the amount of training data manageable.<br />
<br />
== Value Learning and Guidance ==<br />
<br />
Bigstep states are also used for proof state evaluation. For a proof state <math display="inline"> s </math>, if it corresponds to a successful proof, the value is assigned as <math display="inline"> v_s = 1 </math>. If it corresponds to a failed proof, the value is assigned as <math display="inline"> v_s = 0 </math>. For other scenarios, denote the distance between state <math display="inline"> s </math> and a successful state as <math display="inline"> d_s </math>, then the value is assigned as <math display="inline"> v_s = 0.99^{d_s} </math> <br />
<br />
Proof state feature <math display="inline"> f_s </math> is regressed against the value <math display="inline"> v_s </math>. During the proof search, the reward of leaf states are computed from this prediction.<br />
<br />
== Features and Learners ==<br />
For proof states, features are collected from the whole tableaux (subgoals, matrix, and paths). Each unique symbol is represented by an integer, and the tableaux can be represented as a sequence of integers. Term walk is implemented to combine a sequence of integers into a single integer by multiplying components by a fixed large prime and adding them up. Then the resulting integer is reduced to a smaller feature space by taking modulo by a large prime.<br />
<br />
For actions the feature extraction process is similar, but the term walk is over the chosen literal and the chosen clause.<br />
<br />
In addition to the term walks, they also added several common features: number of goals, total symbol size of all goals, length of active paths, number of current variable instantiations, most common symbols.<br />
<br />
The whole project is implemented in OCaml, and XGBoost is ported into OCaml as the learner.<br />
<br />
== Experimental Results ==<br />
In the paper, the dataset they were using is Mizar40. They divided the mizar40 dataset into training and testing set, with a ratio of 9 to 1. According to the author, the split is a random split. During the experiment, the authors' method was able to prove 32524 statements out of 146700 statements. The authors' main approach is transforming the data from First-order logic form into DNF( disjunctive normal form), <br />
The authors use the M2k dataset to compare the performance of mlCoP, the bare prover and rlCoP using only UCT. <br />
*Performance without Learning<br />
Table 3 shows the baseline result. The Performance of the bare prover is significantly lower than mlCoP and rlCoP without policy/value.<br />
[[file:table3.png|550px|center]]<br />
*Reinforcement Learning of Policy Only<br />
In this experiment, the authors evaluated on the dataset rlCoP with UCT using policy learning only. They used the policy training data from previous iterations to train a new predictor after each iteration. Which means only the first iteration ran without policy while all the rest iterations used previous policy training data.<br />
From Table 4, rlCoP is better than mlCoP run with the much higher <math>4 ∗ 10^{6}</math> inference limit after fourth iteration. <br />
[[file:table4.png|550px|center]]<br />
*Reinforcement Learning of Value Only<br />
This experiment was similar to the last one, however, they used only values rather than learned policy. From Table 5, the performance of rlCoP is close to mlCoP but below it after 20 iterations, and it is far below rlCoP using only policy learning.<br />
[[file:table5.png|550px|center]]<br />
*Reinforcement Learning of Policy and Value<br />
From Table 6, the performance of rlCoP is 19.4% more than mlCoP with <math>4 ∗ 10^{6}</math> inferences, 13.6% more than the best iteration of rlCoP with policy only, and 44.3% more than the best iteration of rlCoP with value only after 20 iterations.<br />
[[file:table6.png|550px|center]]<br />
Besides, they also evaluated the effect of the joint reinforcement learning of both policy and value. Replacing final policy and value with the best one from policy-only or value-only both decreased performance.<br />
<br />
*Evaluation on the Whole Miz40 Dataset.<br />
The authors split Mizar40 dataset into 90% training examples and 10% testing examples. 200,000 inferences are allowed for each problem. 10 iterations of policy and value learning are performed (based on MCT). The training and testing results are shown as follows. In the table, ''mlCoP'' represents for the bare prover with iterative deepening (i.e. a complete automated theorem prover with connection calculi), and ''bare prover'' stands for the prover implemented in this paper, without MCT guidance.<br />
<br />
[[file:atp_result0.jpg|frane|550px|center|Figure 5a. Experimental result on Mizar40 dataset]]<br />
[[file:atp_result1.jpg|frame|550px|center|Figure 5b. More experimental result on Mizar40 dataset]]<br />
<br />
As shown by these results, reinforcement learning leads to a significant performance increase for automated theorem proving, the 42.1% performance improvement is unusually high, since the published improvement in this field is typically between 3% and 10%. [1]<br />
<br />
Besides these results, there were also found that some test problems could be solved with rlCoP easily but mlCoP could not.<br />
<br />
== Conclusions ==<br />
In this work, the authors developed an automated theorem prover that uses no domain engineering and instead replies on MCT guided by reinforcement learning. The resulting system is more than 40% stronger than the baseline system. The authors believe that this is a landmark in the field of automated reasoning, demonstrating that building general problem solvers by reinforcement learning is a viable approach. [1]<br />
<br />
The authors pose that some future research could include strong learning algorithms to characterize mathematical data. The development of suitable deep learning architectures will help the algorithm characterize semantic and syntactic features of mathematical objects which will be crucial to create strong assistants for mathematics and hard sciences.<br />
<br />
== Critiques ==<br />
Until now, automated reasoning is relatively new to the field of machine learning, and this paper shows a lot of promise in this research area.<br />
<br />
The feature extraction part of this paper is less than optimal. It is my opinion that with proper neural network architecture, deep learning extracted features will be superior to human-engineered features, which is also shown in [4, 6].<br />
<br />
Also, the policy-value learning iteration is quite inefficient. The learning loop is:<br />
* Loop <br />
** Run MCT with the previous model on an entire dataset<br />
** Collect MCT data<br />
** Train a new model<br />
If we adopt this to an online learning scheme by learning as soon as MCT generates new data, and update the model immediately, there might be some performance increase.<br />
<br />
The experimental design of this paper has some flaws. The authors compare the performance of ''mlCoP'' and ''rlCoP'' by limiting them to the same number of inference steps. However, every inference step of ''rlCoP'' requires additional machine learning prediction, which costs more time. A better way to compare their performance is to set a time limit.<br />
<br />
It would also be interesting to study automated theorem proving in another logic system, like high order logic, because many mathematical concepts can only be expressed in higher-order logic.<br />
<br />
== References ==<br />
[1] C. Kaliszyk, et al. Reinforcement Learning of Theorem Proving. NIPS 2018.<br />
<br />
[2] J. Otten and W. Bibel. leanCoP: Lean Connection-Based Theorem Proving. Journal of Symbolic Computation, vol. 36, pp. 139-161, 2003.<br />
<br />
[3] C. Kaliszyk and J. Urban. FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover. Lecture Notes in Computer Science. vol. 9450. pp. 88-96, 2015.<br />
<br />
[4] S. Loos, et al. Deep Network Guided Proof Search. LPAR-21, 2017.<br />
<br />
[5] M. F¨arber, C. Kaliszyk, and J. Urban. Monte Carlo tableau proof search. In L. de Moura, editor,<br />
26th International Conference on Automated Deduction (CADE), volume 10395 of LNCS,<br />
pages 563–579. Springer, 2017.<br />
<br />
[6] A. Alemi, et al. DeepMath-Deep Sequence Models for Premise Selection. NIPS 2016.<br />
<br />
[7] Mizar Math Library. http://mizar.org/library/<br />
<br />
[8] J. Urban, G. Sutcliffe, P. Pudla ́k, and J. Vyskocˇil. MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance. In A. Armando, P. Baumgartner, and G. Dowek, editors, IJCAR, volume 5195 of LNCS, pages 441–456. Springer, 2008.<br />
<br />
[9] J. Otten and W. Bibel. leanCoP: lean connection-based theorem proving. J. Symb. Comput., 36(1-2):139–161, 2003.<br />
<br />
[10] A. Grabowski, A. Korniłowicz, and A. Naumowicz. Mizar in a nutshell. J. Formalized Rea-<br />
soning, 3(2):153–245, 2010</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=a_neural_representation_of_sketch_drawings&diff=42115a neural representation of sketch drawings2018-11-30T21:28:42Z<p>R82zhang: [T]/* Critique */</p>
<hr />
<div><br />
== Introduction ==<br />
In this paper, the authors present a recurrent neural network, sketch-rnn, that can be used to construct stroke-based drawings. Besides new robust training methods, they also outline a framework for conditional and unconditional sketch generation.<br />
<br />
Neural networks have been heavily used as image generation tools. For example, Generative Adversarial Networks, Variational Inference, and Autoregressive models have been used. Most of those models are designed to generate pixels to construct images. However, people learn to draw using sequences of strokes, beginning when they are young. The authors propose a new generative model that creates vector images so that it might generalize abstract concepts in a manner more similar to how humans do. <br />
<br />
The model is trained with hand-drawn sketches as input sequences. The model is able to produce sketches in vector format. In the conditional generation model, they also explore the latent space representation for vector images and discuss a few future applications of this model. The model and dataset are now available as an open source project ([https://magenta.tensorflow.org/sketch_rnn link]).<br />
<br />
=== Terminology ===<br />
Pixel images, also referred to as raster or bitmap images are files that encode image data as a set of pixels. These are the most common image type, with extensions such as .png, .jpg, .bmp. <br />
<br />
Vector images are files that encode image data as paths between points. SVG and EPS file types are used to store vector images. <br />
<br />
For a visual comparison of raster and vector images, see this [https://www.youtube.com/watch?v=-Fs2t6P5AjY video]. As mentioned, vector images are generally simpler and more abstract, whereas raster images generally are used to store detailed images. <br />
<br />
For this paper, the important distinction between the two is that the encoding of images in the model will be inherently more abstract because of the vector representation. The intuition is that generating abstract representations is more effective using a vector representation. <br />
<br />
== Related Work ==<br />
There are some works in the history that used a similar approach to generate images such as Portrait Drawing by Paul the Robot [26, 28] and some reinforcement learning approaches[28], Reinforcement Learning to discover a set of paint brush strokes that can best represent a given input photograph. They work more like a mimic of digitized photographs. There are also some Neural networks based approaches, but those are mostly dealing with pixel images. Little work is done on vector images generation. There are models that use Hidden Markov Models [25] or Mixture Density Networks [2] to generate human sketches, continuous data points (modelling Chinese characters as a sequence of pen stroke actions) or vectorized Kanji characters [9,29].<br />
<br />
The model also allows us to explore the latent space representation of vector images. There are previous works that achieved similar functions as well, such as combining Sequence-to-Sequence models with Variational Autoencoder to model sentences into latent space and using probabilistic program induction to model Omniglot dataset.<br />
<br />
The dataset they use contains 50 million vector sketches. Before this paper, there is a Sketch data with 20k vector sketches, a Sketchy dataset with 70k vector sketches along with pixel images, and a ShadowDraw system that used 30k raster images along with extracted vectorized features. They are all comparatively small.<br />
<br />
== Major Contributions ==<br />
This paper makes the following major contributions: Authors outline a framework for both unconditional and<br />
conditional generation of vector images composed of a sequence of lines. The recurrent neural<br />
network-based generative model is capable of producing sketches of common objects in a vector<br />
format. The paper develops a training procedure unique to vector images to make the training more robust. The paper also made available<br />
a large dataset of hand drawn vector images to encourage further development of generative modelling<br />
for vector images, and also release an implementation of our model as an open source project<br />
<br />
== Methodology ==<br />
=== Dataset ===<br />
QuickDraw is a dataset with 50 million vector drawings collected by an online game [https://quickdraw.withgoogle.com/# Quick Draw!], where the players are required to draw objects belonging to a particular object class in less than 20 seconds. It contains hundreds of classes, each class has 70k training samples, 2.5k validation samples and 2.5k test samples.<br />
<br />
The data format of each sample is a representation of a pen stroke action event. The Origin is the initial coordinate of the drawing. The sketches are points in a list. Each point consists of 5 elements <math> (\Delta x, \Delta y, p_{1}, p_{2}, p_{3})</math> where x and y are the offset distance in x and y directions from the previous point. The parameters <math>p_{1}, p_{2}, p_{3}</math> represent three possible states in binary one-hot representation where <math>p_{1}</math> indicates the pen is touching the paper, <math>p_{2}</math> indicates the pen will be lifted from here, and <math>p_{3}</math> represents the drawing has ended.<br />
<br />
=== Sketch-RNN ===<br />
[[File:sketchfig2.png|700px|center]]<br />
<br />
The model is a Sequence-to-Sequence Variational Autoencoder(VAE). <br />
<br />
==== Encoder ====<br />
The encoder is a bidirectional RNN. The input is a sketch sequence denoted by <math>S =\{S_0, S_1, ... S_{N_{s}}\}</math> and a reversed sketch sequence denoted by <math>S_{reverse} = \{S_{N_{s}},S_{N_{s}-1}, ... S_0\}</math>. The final hidden layer representations of the two encoded sequences <math>(h_{ \rightarrow}, h_{ \leftarrow})</math> are concatenated to form a latent vector, <math>h</math>, of size <math>N_{z}</math>,<br />
<br />
\begin{split}<br />
&h_{ \rightarrow} = encode_{ \rightarrow }(S), \\<br />
&h_{ \leftarrow} = encode_{ \leftarrow }(S_{reverse}), \\<br />
&h = [h_{\rightarrow}; h_{\leftarrow}].<br />
\end{split}<br />
<br />
Then the authors project <math>h</math> into two vectors <math>\mu</math> and <math>\hat{\sigma}</math> of size <math>N_{z}</math>. The projection is performed using a fully connected layer. These two vectors are the parameters of the latent space Gaussian distribution that will estimate the distribution of the input data. Because standard deviations cannot be negative, an exponential function is used to convert it to all positive values. Next, a random variable with mean <math>\mu</math> and standard deviation <math>\sigma</math> is constructed by scaling a normalized IID Gaussian, <math>\mathcal{N}(0,I)</math>, <br />
<br />
\begin{split}<br />
& \mu = W_\mu h + b_\mu, \\<br />
& \hat \sigma = W_\sigma h + b_\sigma, \\<br />
& \sigma = exp( \frac{\hat \sigma}{2}), \\<br />
& z = \mu + \sigma \odot \mathcal{N}(0,I). <br />
\end{split}<br />
<br />
<br />
Note that <math>z</math> is not deterministic but a random vector that can be conditioned on an input sketch sequence.<br />
<br />
==== Decoder ====<br />
The decoder is an autoregressive RNN. The initial hidden and cell states are generated using <math>[h_0;c_0] = \tanh(W_z z + b_z)</math>. Here, <math>c_0</math> is utilized if applicable (eg. if an LSTM decoder is used). <math>S_0</math> is defined as <math>(0,0,1,0,0)</math> (the pen is touching the paper at location 0, 0). <br />
<br />
For each step <math>i</math> in the decoder, the input <math>x_i</math> is the concatenation of the previous point <math>S_{i-1}</math> and the latent vector <math>z</math>. The outputs of the RNN decoder <math>y_i</math> are parameters for a probability distribution that will generate the next point <math>S_i</math>. <br />
<br />
The authors model <math>(\Delta x,\Delta y)</math> as a Gaussian mixture model (GMM) with <math>M</math> normal distributions and model the ground truth data <math>(p_1, p_2, p_3)</math> as a categorical distribution <math>(q_1, q_2, q_3)</math> where <math>q_1, q_2\ \text{and}\ q_3</math> sum up to 1,<br />
<br />
\begin{align*}<br />
p(\Delta x, \Delta y) = \sum_{j=1}^{M} \Pi_j \mathcal{N}(\Delta x,\Delta y | \mu_{x,j}, \mu_{y,j}, \sigma_{x,j},\sigma_{y,j}, \rho _{xy,j}), where \sum_{j=1}^{M}\Pi_j = 1<br />
\end{align*}<br />
<br />
Where <math>\mathcal{N}(\Delta x,\Delta y | \mu_{x,j}, \mu_{y,j}, \sigma_{x,j},\sigma_{y,j}, \rho _{xy,j})</math> is a bi-variate Normal Distribution, with parameters means <math>\mu_x, \mu_y</math>, standard deviations <math>\sigma_x, \sigma_y</math> and correlation parameter <math>\rho_{xy}</math>. There are <math>M</math> such distributions. <math>\Pi</math> is a categorical distribution vector of length <math>M</math>. Collectively these form the mixture weights of the Gaussian Mixture model.<br />
<br />
The output vector <math>y_i</math> is generated using a fully-connected forward propagation in the hidden state of the RNN.<br />
<br />
\begin{split}<br />
&x_i = [S_{i-1}; z], \\<br />
&[h_i; c_i] = forward(x_i,[h_{i-1}; c_{i-1}]), \\<br />
&y_i = W_y h_i + b_y, \\<br />
&y_i \in \mathbb{R}^{6M+3}. \\<br />
\end{split}<br />
<br />
The output consists the probability distribution of the next data point.<br />
<br />
\begin{align*}<br />
[(\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_1\ (\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_2\ ...\ (\hat\Pi_1\ \mu_x\ \mu_y\ \hat\sigma_x\ \hat\sigma_y\ \hat\rho_{xy})_M\ (\hat{q_1}\ \hat{q_2}\ \hat{q_3})] = y_i<br />
\end{align*}<br />
<br />
<math>\exp</math> and <math>\tanh</math> operations are applied to ensure that the standard deviations are non-negative and the correlation value is between -1 and 1.<br />
<br />
\begin{align*}<br />
\sigma_x = \exp (\hat \sigma_x),\ <br />
\sigma_y = \exp (\hat \sigma_y),\ <br />
\rho_{xy} = \tanh(\hat \rho_{xy}). <br />
\end{align*}<br />
<br />
Categorical distribution probabilities for <math>(p_1, p_2, p_3)</math> using <math>(q_1, q_2, q_3)</math> can be obtained as :<br />
<br />
\begin{align*}<br />
q_k = \frac{\exp{(\hat q_k)}}{ \sum\nolimits_{j = 1}^{3} \exp {(\hat q_j)}},<br />
k \in \left\{1,2,3\right\}, <br />
\Pi _k = \frac{\exp{(\hat \Pi_k)}}{ \sum\nolimits_{j = 1}^{M} \exp {(\hat \Pi_j)}},<br />
k \in \left\{1,...,M\right\}.<br />
\end{align*}<br />
<br />
It is hard for the model to decide when to stop drawing because the probabilities of the three events <math>(p_1, p_2, p_3)</math> are very unbalanced. Researchers in the past have used different weights for each pen event probability, but the authors found this approach lacking elegance and inadequate. They define a hyperparameter representing the max length of the longest sketch in the training set denoted by <math>N_{max}</math>, and set the <math>S_i</math> to be <math>(0, 0, 0, 0, 1)</math> for <math>i > N_s</math>.<br />
<br />
The outcome sample <math>S_i^{'}</math> can be generated in each time step during sample process and fed as input for the next time step. The process will stop when <math>p_3 = 1</math> or <math>i = N_{max}</math>. The output is not deterministic but conditioned random sequences. The level of randomness can be controlled using a temperature parameter <math>\tau</math>.<br />
<br />
\begin{align*}<br />
\hat q_k \rightarrow \frac{\hat q_k}{\tau}, <br />
\hat \Pi_k \rightarrow \frac{\hat \Pi_k}{\tau}, <br />
\sigma_x^2 \rightarrow \sigma_x^2\tau, <br />
\sigma_y^2 \rightarrow \sigma_y^2\tau. <br />
\end{align*}<br />
<br />
The <math>\tau</math> ranges from 0 to 1. When <math>\tau = 0</math> the output will be deterministic as the sample will consist of the points on the peak of the probability density function.<br />
<br />
=== Unconditional Generation ===<br />
There is a special case that only the decoder RNN module is trained. The decoder RNN could work as a standalone autoregressive model without latent variables. In this case, initial states are 0, the input <math>x_i</math> is only <math>S_{i-1}</math> or <math>S_{i-1}^{'}</math>. In the Figure 3, generating sketches unconditionally from the temperature parameter <math>\tau = 0.2</math> at the top in blue, to <math>\tau = 0.9</math> at the bottom in red.<br />
<br />
[[File:sketchfig3.png|700px|center]]<br />
<br />
=== Training ===<br />
The training process is the same as a Variational Autoencoder. The loss function is the sum of Reconstruction Loss <math>L_R</math> and the Kullback-Leibler Divergence Loss <math>L_{KL}</math>. The reconstruction loss <math>L_R</math> can be obtained with generated parameters of pdf and training data <math>S</math>. It is the sum of the <math>L_s</math> and <math>L_p</math>, which are the log loss of the offset <math>(\Delta x, \Delta y)</math> and the pen state <math>(p_1, p_2, p_3)</math>.<br />
<br />
\begin{align*}<br />
L_s = - \frac{1 }{N_{max}} \sum_{i = 1}^{N_s} \log(\sum_{i = 1}^{M} \Pi_{j,i} \mathcal{N}(\Delta x,\Delta y | \mu_{x,j,i}, \mu_{y,j,i}, \sigma_{x,j,i},\sigma_{y,j,i}, \rho _{xy,j,i})), <br />
\end{align*}<br />
\begin{align*}<br />
L_p = - \frac{1 }{N_{max}} \sum_{i = 1}^{N_{max}} \sum_{k = 1}^{3} p_{k,i} \log (q_{k,i}), <br />
L_R = L_s + L_p.<br />
\end{align*}<br />
<br />
<br />
Both terms are normalized by <math>N_{max}</math>.<br />
<br />
<math>L_{KL}</math> measures the difference between the distribution of the latent vector <math>z</math> and an i.i.d. Gaussian vector with zero mean and unit variance.<br />
<br />
\begin{align*}<br />
L_{KL} = - \frac{1}{2 N_z} (1+\hat \sigma - \mu^2 - \exp(\hat \sigma))<br />
\end{align*}<br />
<br />
The overall loss is weighted as:<br />
<br />
\begin{align*}<br />
Loss = L_R + w_{KL} L_{KL}<br />
\end{align*}<br />
<br />
When <math>w_{KL} = 0</math>, the model becomes a standalone unconditional generator. Specially, there will be no <math>L_{KL} </math> term as we only optimize for <math>L_{R} </math>. By removing the <math>L_{KL} </math> term the model approaches a pure autoencoder, meaning it sacrifices the ability to enforce a prior over the latent space and gains better reconstruction loss metrics.<br />
<br />
While the aforementioned loss function could be used, it was found that annealing the KL term (as shown below) in the loss function produces better results.<br />
<br />
<center><math><br />
\eta_{step} = 1 - (1 - \eta_{min})R^{step}<br />
</math></center><br />
<br />
<center><math><br />
Loss_{train} = L_R + w_{KL} \eta_{step} max(L_{KL}, KL_{min})<br />
</math></center><br />
<br />
As shown in Figure 4, the <math>L_{R} </math> metric for the standalone decoder model is actually an upper bound for different models using a latent vector. The reason is the unconditional model does not access to the entire sketch it needs to generate.<br />
<br />
[[File:s.png|600px|thumb|center|Figure 4. Tradeoff between <math>L_{R} </math> and <math>L_{KL} </math>, for two models trained on single class datasets (left).<br />
Validation Loss Graph for models trained on the Yoga dataset using various <math>w_{KL} </math>. (right)]]<br />
<br />
== Experiments ==<br />
The authors experiment with the sketch-rnn model using different settings and recorded both losses. They used a Long Short-Term Memory(LSTM) model as an encoder and a HyperLSTM as a decoder. HyperLSTM is a type of RNN cell that excels at sequence generation tasks. The ability for HyperLSTM to spontaneously augment its own weights enables it to adapt to many different regimes<br />
in a large diverse dataset. They also conduct multi-class datasets. The result is as follows.<br />
<br />
[[File:sketchtable1.png|700px|center]]<br />
<br />
We could see the trade-off between <math>L_R</math> and <math>L_{KL}</math> in this table clearly. Furthermore, <math>L_R</math> decreases as <math>w_{KL} </math> is halfed. <br />
<br />
=== Conditional Reconstruction ===<br />
The authors assess the reconstructed sketch with a given sketch with different <math>\tau</math> values. We could see that with high <math>\tau</math> value on the right, the reconstructed sketches are more random.<br />
<br />
[[File:sketchfig5.png|700px|center]]<br />
<br />
They also experiment on inputting a sketch from a different class. The output will still keep some features from the class that the model is trained on.<br />
<br />
=== Latent Space Interpolation ===<br />
The authors visualize the reconstruction sketches while interpolating between latent vectors using different <math>w_{KL}</math> values. With high <math>w_{KL}</math> values, the generated images are more coherently interpolated.<br />
<br />
[[File:sketchfig6.png|700px|center]]<br />
<br />
=== Sketch Drawing Analogies ===<br />
Since the latent vector <math>z</math> encode conceptual features of a sketch, those features can also be used to augment other sketches that do not have these features. This is possible when models are trained with low <math>L_{KL}</math> values. The authors are able to perform vector arithmetic on latent vectors from different sketches and explore how the model generates sketches base on these latent spaces.<br />
<br />
=== Predicting Different Endings of Incomplete Sketches === <br />
This model is able to predict an incomplete sketch by encoding the sketch into hidden state <math>h</math> using the decoder and then using <math>h</math> as an initial hidden state to generate the remaining sketch. The authors train on individual classes by using decoder-only models and set <math>τ = 0.8</math> to complete samples. Figure 7 shows the results.<br />
<br />
[[File:sketchfig7.png|700px|center]]<br />
<br />
== Limitations ==<br />
<br />
Although sketch-rnn can model a large variety of sketch drawings, there are several limitations in the current approach. For most single-class datasets, sketch-rnn is capable of modelling around 300 data points. The model becomes increasingly difficult to train beyond this length. For the author's dataset, the Ramer-Douglas-Peucker algorithm is used to simplify the strokes of sketch data to less than 200 data points.<br />
<br />
For more complicated classes of images, such as mermaids or lobsters, the reconstruction loss metrics are not as good compared to simpler classes such as ants, faces or firetrucks. The models trained on these more challenging image classes tend to draw smoother, more circular line segments that do not resemble individual sketches, but rather resemble an averaging of many sketches in the training set. This smoothness may be analogous to the blurriness effect produced by a Variational Autoencoder that is trained on pixel images. Depending on the use case of the model, smooth circular lines can be viewed as aesthetically pleasing and a desirable property.<br />
<br />
While both conditional and unconditional models are capable of training on datasets of several classes, sketch-rnn is ineffective at modelling a large number of classes simultaneously. The samples generated will be incoherent, with different classes are shown in the same sketch.<br />
<br />
== Applications and Future Work ==<br />
The authors believe this model can assist artists by suggesting how to finish a sketch, helping them to find interesting intersections between different drawings or objects, or generating a lot of similar but different designs. In the simplest use, pattern designers can apply sketch-rnn to generate a large number of similar, but unique designs for textile or wallpaper prints. The creative designers can also come up with abstract designs which enables them to resonate more with their target audience<br />
<br />
This model may also find its place on teaching students how to draw. Even with the simple sketches in QuickDraw, the authors of this work have become much more proficient at drawing animals, insects, and various sea creatures after conducting these experiments. <br />
When the model is trained with a high <math>w_{KL}</math> and sampled with a low <math>\tau</math>, it may help to turn a poor sketch into a more aesthetical one. Latent vector augmentation could also help to create a better drawing by inputting user-rating data during training processes.<br />
<br />
The authors conclude by providing the following future directions to this work:<br />
# Investigate using user-rating data to augmenting the latent vector in the direction that maximizes the aesthetics of the drawing.<br />
# Look into combining variations of sequence-generation models with unsupervised, cross-domain pixel image generation models.<br />
<br />
It's exciting that they manage to combine this model with other unsupervised, cross-domain pixel image generation models to create photorealistic images from sketches.<br />
<br />
The authors have also mentioned the opposite direction of converting a photograph of an object into an unrealistic, but similar looking<br />
sketch of the object composed of a minimal number of lines to be a more interesting problem.<br />
<br />
Moreover, it would be interesting to see how varying loss will be represented as a drawing. Some exotic form of loss function may change the way that the network behaves, which can lead to various applications.<br />
<br />
== Conclusion ==<br />
The paper presents a methodology to model sketch drawings using recurrent neural networks. The sketch-rnn model that can encode and decode sketches, generate and complete unfinished sketches is introduced in this paper. In addition, Authors demonstrated how to both interpolate between latent spaces from a different class, and use it to augment sketches or generate similar looking sketches. Furthermore, the importance of enforcing a prior distribution on latent vector while interpolating coherent sketch generations is shown. Finally, a large sketch drawings dataset for future research work is created.<br />
<br />
== Critique ==<br />
This paper presents both a novel large dataset of sketches and a new RNN architecture to generate new sketches. It is very exciting to read but there are still some aspect to improve.<br />
<br />
* The performance of the decoder model can hardly be evaluated. The authors present the performance of the decoder by showing the generated sketches, it is clear and straightforward, however, not very efficient. It would be great if the authors could present a way, or a metric to evaluate how well the sketches are generated rather than printing them out and evaluate with human judgment. The authors didn't present an evaluation of the algorithms either. They provided <math>L_R</math> and <math>L_{KL}</math> for reference, however, a lower loss doesn't represent a better performance. Training loss alone likely does not capture the quality of a sketch.<br />
<br />
* Algorithm lacks comparison to the prior state of the art on standard metrics, which made the novelty unclear. Using strokes as inputs is a novel and innovative move, however, the paper does not provide a baseline or any comparison with other methods or algorithms. Some other researches were mentioned in the paper, using similar and smaller datasets. It would be great if the authors could use some basic or existing methods a baseline and compare with the new algorithm.<br />
<br />
* Besides the comparison with other algorithms, it would also be great if the authors could remove or replace some component of the algorithm in the model to show if one part is necessary, or what made them decide to include a specific component in the algorithm.<br />
<br />
* The authors did not present better complexity and deeper mathematical analysis on the algorithms in the paper. It also does not include comparison using some more standard metrics compare to previous results. Therefore, it lacks some algorithmic contribution. It would be better to include some more formal analysis on the algorithmic side. <br />
<br />
* The authors proposed a few future applications for the model, however, the current output seems somehow not very close to their descriptions. But I do believe that this is a very good beginning, with the release of the sketch dataset, it must attract more scholars to research and improve with it!<br />
<br />
== References == <br />
# Jimmy L. Ba, Jamie R. Kiros, and Geoffrey E. Hinton. Layer normalization. NIPS, 2016.<br />
# Christopher M. Bishop. Mixture density networks. Technical Report, 1994. URL http://publications.aston.ac.uk/373/.<br />
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# H. Dong, P. Neekhara, C. Wu, and Y. Guo. Unsupervised Image-to-Image Translation with Generative Adversarial Networks. ArXiv e-prints, January 2017.<br />
# David H. Douglas and Thomas K. Peucker. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112–122, October 1973. doi: 10.3138/fm57-6770-u75u-7727. URL http://dx.doi.org/10.3138/fm57-6770-u75u-7727.<br />
# Mathias Eitz, James Hays, and Marc Alexa. How Do Humans Sketch Objects? ACM Trans. Graph.(Proc. SIGGRAPH), 31(4):44:1–44:10, 2012.<br />
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# Alex Graves. Generating sequences with recurrent neural networks. arXiv:1308.0850, 2013.<br />
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# P. Isola, J.-Y. Zhu, T. Zhou, and A. A. Efros. Image-to-Image Translation with Conditional Adversarial Networks. ArXiv e-prints, November 2016.<br />
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# C. Kaae Sønderby, T. Raiko, L. Maaløe, S. Kaae Sønderby, and O. Winther. Ladder Variational Autoencoders. ArXiv e-prints, February 2016.<br />
# T. Kim, M. Cha, H. Kim, J. Lee, and J. Kim. Learning to Discover cross-domain Relations with Generative Adversarial Networks. ArXiv e-prints, March 2017.<br />
# D. P Kingma and M. Welling. Auto-Encoding Variational Bayes. ArXiv e-prints, December 2013.<br />
# Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
# Diederik P. Kingma, Tim Salimans, and Max Welling. Improving variational inference with inverse autoregressive flow. CoRR, abs/1606.04934, 2016. URL http://arxiv.org/abs/1606.04934.<br />
# Brenden M. Lake, Ruslan Salakhutdinov, and Joshua B. Tenenbaum. Human level concept learning through probabilistic program induction. Science, 350(6266):1332–1338, December 2015. ISSN 1095-9203. doi: 10.1126/science.aab3050. URL http://dx.doi.org/10.1126/science.aab3050.<br />
# Yong Jae Lee, C. Lawrence Zitnick, and Michael F. Cohen. Shadowdraw: Real-time user guidance for freehand drawing. In ACM SIGGRAPH 2011 Papers, SIGGRAPH ’11, pp. 27:1–27:10, New York, NY, USA, 2011. ACM. ISBN 978-1-4503-0943-1. doi: 10.1145/1964921.1964922. URL http://doi.acm.org/10.1145/1964921.1964922.<br />
# M.-Y. Liu, T. Breuel, and J. Kautz. Unsupervised Image-to-Image Translation Networks. ArXiv e-prints, March 2017.<br />
# S. Reed, A. van den Oord, N. Kalchbrenner, S. Gómez Colmenarejo, Z. Wang, D. Belov, and N. de Freitas. Parallel Multiscale Autoregressive Density Estimation. ArXiv e-prints, March 2017.<br />
# Patsorn Sangkloy, Nathan Burnell, Cusuh Ham, and James Hays. The Sketchy Database: Learning to Retrieve Badly Drawn Bunnies. ACM Trans. Graph., 35(4):119:1–119:12, July 2016. ISSN 0730-0301. doi: 10.1145/2897824.2925954. URL http://doi.acm.org/10.1145/2897824.2925954.<br />
# Mike Schuster, Kuldip K. Paliwal, and A. General. Bidirectional recurrent neural networks. IEEE Transactions on Signal Processing, 1997.<br />
# Saul Simhon and Gregory Dudek. Sketch interpretation and refinement using statistical models. In Proceedings of the Fifteenth Eurographics Conference on Rendering Techniques, EGSR’04, pp. 23–32, Aire-la-Ville, Switzerland, Switzerland, 2004. Eurographics Association. ISBN 3-905673-12-6. doi: 10.2312/EGWR/EGSR04/023-032. URL http://dx.doi.org/10.2312/EGWR/EGSR04/023-032.<br />
# Patrick Tresset and Frederic Fol Leymarie. Portrait drawing by paul the robot. Comput. Graph.,37(5):348–363, August 2013. ISSN 0097-8493. doi: 10.1016/j.cag.2013.01.012. URL http://dx.doi.org/10.1016/j.cag.2013.01.012.<br />
# T. White. Sampling Generative Networks. [https://arxiv.org/abs/1609.04468 ArXiv e-prints], September 2016.<br />
#Ning Xie, Hirotaka Hachiya, and Masashi Sugiyama. Artist agent: A reinforcement learning approach to automatic stroke generation in oriental ink painting. In ICML. icml.cc / Omnipress, 2012. URL http://dblp.uni-trier.de/db/conf/icml/icml2012.html#XieHS12.<br />
# Xu-Yao Zhang, Fei Yin, Yan-Ming Zhang, Cheng-Lin Liu, and Yoshua Bengio. Drawing and Recognizing Chinese Characters with Recurrent Neural Network. CoRR, abs/1606.06539, 2016. URL http://arxiv.org/abs/1606.06539.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Unsupervised_Neural_Machine_Translation&diff=42108Unsupervised Neural Machine Translation2018-11-30T19:58:06Z<p>R82zhang: [T] /* 2.2 STATISTICAL DECIPHERMENT FOR MACHINE TRANSLATION */</p>
<hr />
<div>This paper was published in ICLR 2018, authored by Mikel Artetxe, Gorka Labaka, Eneko Agirre, and Kyunghyun Cho. Open source implementation of this paper is available [https://github.com/artetxem/undreamt here]<br />
<br />
= Introduction =<br />
The paper presents an unsupervised Neural Machine Translation (NMT) method that uses monolingual corpora (single language texts) only. This contrasts with the usual supervised NMT approach which relies on parallel corpora (aligned text) from the source and target languages being available for training. This problem is important because parallel pairing for a majority of languages, e.g. for German-Russian, do not exist. Often, languages can also suffer from having poor resources for translation (e.g. Basque), which could lead to the problem of the dataset being too small (Koehn & Knowles, 2017).<br />
<br />
Other authors have recently tried to address this problem using semi-supervised approaches (small set of parallel corpora). Their approaches have included pivoting or triangulation techniques [Chen et al., 2017], and semi supervised approaches [He, 2016]. However, these methods still require a strong cross-lingual signal. The proposed method eliminates the need for cross-lingual information all together and relies solely on monolingual data. The proposed method builds upon the work done recently on unsupervised cross-lingual embeddings by Artetxe et al., 2017 and Zhang et al., 2017.<br />
<br />
The general approach of the methodology is to:<br />
<br />
# Use monolingual corpora in the source and target languages to learn single language word embeddings for both languages separately.<br />
# Align the 2 sets of word embeddings into a single cross lingual (language independent) embedding.<br />
Then iteratively perform:<br />
# Train an encoder-decoder model to reconstruct noisy versions of sentences in both source and target languages separately. The model uses a single encoder and different decoders for each language. The encoder uses cross lingual word embedding.<br />
# Tune the decoder in each language by back-translating between the source and target language.<br />
<br />
= Background =<br />
<br />
===Word Embedding Alignment===<br />
<br />
The paper uses word2vec [Mikolov, 2013] to convert each monolingual corpora to vector embeddings. They improve the continuous Skip-gram model for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. These embeddings have been shown to contain the contextual and syntactic features independent of language, and so, in theory, there could exist a linear map that maps the embeddings from language L1 to language L2. <br />
<br />
Figure 1 shows an example of aligning the word embeddings in English and French.<br />
<br />
[[File:Figure1_lwali.png|frame|400px|center|Figure 1: the word embeddings in English and French (a & b), and (c) shows the aligned word embeddings after some linear transformation.[Gouws,2016]]]<br />
<br />
Most cross-lingual word embedding methods use bilingual signals in the form of parallel corpora. Usually, the embedding mapping methods train the embeddings in different languages using monolingual corpora, then use a linear transformation to map them into a shared space based on a bilingual dictionary.<br />
<br />
The paper uses the methodology proposed by [Artetxe, 2017] to do cross-lingual embedding aligning in an unsupervised manner and without parallel data. Without going into the details, the general approach of this paper is starting from a seed dictionary of numeral pairings (e.g. 1-1, 2-2, etc.), to iteratively learn the mapping between 2 language embeddings, while concurrently improving the dictionary with the learned mapping at each iteration. This is in contrast to earlier work which used dictionaries of a few thousand words.<br />
<br />
===Other related work and inspirations===<br />
====Statistical Decipherment for Machine Translation====<br />
There has been significant work in statistical deciphering techniques (decipherment is the discovery of the meaning of texts written in ancient or obscure languages or scripts) to develop a machine translation model from monolingual data (Ravi & Knight, 2011; Dou & Knight, 2012). These techniques treat the source language as ciphertext (encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher for decoding) and model the generation process of the ciphertext as a two-stage process, which includes the generation of the original English sequence and the probabilistic replacement of the words in it. This approach takes advantage of the incorporation of syntactic knowledge of the languages. The use of word embeddings has also shown improvements in statistical decipherment.<br />
<br />
====Low-Resource Neural Machine Translation====<br />
There are also proposals that use techniques other than direct parallel corpora to do NMT. Some use a third intermediate language that is well connected to the source and target languages independently. For example, if we want to translate German into Russian, we can use English as an intermediate language (German-English and then English-Russian) since there are plenty of resources to connect English and other languages. Johnson et al. (2017) show that a multilingual extension of a standard NMT architecture performs reasonably well for language pairs when no parallel data for the source and target data was used during training. Firat et al. (2016) and Chen et al. (2017) showed that the use of advanced models like teacher-student framework can be used to improve over the baseline of translating using a third intermediate language.<br />
<br />
Other works use monolingual data in combination with scarce parallel corpora. A simple but effective technique is back-translation [Sennrich et al, 2016]. First, a synthetic parallel corpus in the target language is created. Translated sentence and back-translated to the source language and compared with the original sentence.<br />
<br />
The most important contribution to the problem of training an NMT model with monolingual data was from [He, 2016], which trains two agents to translate in opposite directions (e.g. French → English and English → French) and teach each other through reinforcement learning. However, this approach still required a large parallel corpus for a warm start (about 1.2 million sentences), while this paper does not use parallel data.<br />
<br />
= Related Works =<br />
<br />
=== 2.1 UNSUPERVISED CROSS-LINGUAL EMBEDDINGS ===<br />
<br />
A majority of methods for learning cross-lingual word embeddings depend on some bilingual signal at the document level. Embedding mapping methods independently train the embeddings in different languages using monolingual corpora and subsequently learn a linear transformation that maps them to a shared space based on a bilingual dictionary. While the dictionary used in these earlier work typically contains a few thousands entries, Artetxe et al. (2017) propose a simple self-learning extension that gives comparable results with an automatically generated list of numerals, which is used as a shortcut for practical unsupervised learning.<br />
<br />
=== 2.2 STATISTICAL DECIPHERMENT FOR MACHINE TRANSLATION ===<br />
<br />
A considerable body of work in statistical decipherment techniques treat the source language as ciphertext and model the process by which this ciphertext is generated as a two-stage process involving the generation of the original English sequence and the probabilistic replacement of the words in it. The English generative process is modeled using a standard n-gram language model, and the channel model parameters are estimated using either expectation maximization or Bayesian inference. This approach was shown to benefit from the incorporation of syntactic knowledge of the languages involved (Dou & Knight, 2013; Dou et al., 2015). More in line with our proposal, the use of word embeddings has also been shown to bring significant improvements in statistical decipherment for machine translation (Dou et al., 2015). Another newly developed method is using a relatively new deep architecture called Sum-Product network to do machine translation. Hoifung Poon, Pedro Domingos[2011] It is a hybrid model that combines the probabilistic modeling and deep architectures. The main advantage of this model is that it has clear semantics and provide great interoperability, and like many other deep architectures, it can be trained using gradient descent. Sum-product network can be applied in the machine translation field, where one can model the language translation in the following one P(English | French) = p(French / English) * p(English) / p(French), where P(English / French) is the probability that an English text corresponds to a given French text, and P(French/ English) is vice versa. We can use Sum-product network to model each of the above probability and thus doing machine translation.<br />
<br />
=== 2.3 LOW-RESOURCE NEURAL MACHINE TRANSLATION ===<br />
<br />
A simple yet effective approach is to create a synthetic parallel corpus by back-translating a monolingual corpus in the target language (Sennrich et al., 2016a). At the same time, Currey et al. (2017) showed that training an NMT system to directly copy target language text is also helpful and complementary with back-translation. Finally, Ramachandran et al. (2017) pre-train the encoder and the decoder in language modeling. Another method trains two agents to translate in opposite directions (e.g. French → English and English → French), and make them teach each other through a reinforcement learning process. This approach still requires a parallel corpus of a considerable size for a good start.<br />
<br />
= Methodology =<br />
<br />
The corpora data is first preprocessed in a standard way to tokenize and case the words. The authors also experimented with an alternate way of tokenizing words by using Byte-Pair Encoding (BPE) [Sennrich, 2016] (Byte pair encoding or digram coding is a simple form of data compression in which the most common pair of consecutive bytes of data is replaced with a byte that does not occur within that data). BPE has been shown to improve embeddings of rare-words. The vocabulary was limited to the most frequent 50,000 tokens (BPE tokens or words).<br />
<br />
The tokens were then converted to word embeddings using word2vec with 300 dimensions and then aligned between languages using the method proposed by [Artetxe, 2017]. The alignment method proposed by [Artetxe, 2017] is also used as a baseline to evaluate this model as discussed later in Results.<br />
<br />
The translation model uses a standard encoder-decoder model with attention. The encoder is a 2-layer bidirectional RNN, and the decoder is a 2 layer RNN. All RNNs use GRU cells with 600 hidden units. The encoder is shared by the source and target language, while the decoder is different for each language.<br />
<br />
Although the architecture uses standard models, the proposed system differs from the standard NMT through 3 aspects:<br />
<br />
#Dual structure: NMT usually are built for one direction translations English<math>\rightarrow</math>French or French<math>\rightarrow</math>English, whereas the proposed model trains both directions at the same time translating English<math>\leftrightarrow</math>French.<br />
#Shared encoder: one encoder is shared for both source and target languages in order to produce a representation in the latent space independent of language, and each decoder learns to transform the representation back to its corresponding language. <br />
#Fixed embeddings in the encoder: Most NMT systems initialize the embeddings and update them during training, whereas the proposed system trains the embeddings in the beginning and keeps these fixed throughout training, so the encoder receives language-independent representations of the words. This approach ensures that the encoder only learns how to compose the language independent representations to build representations of the larger phrases. This requires existing unsupervised methods to create embeddings using monolingual corpora as discussed in the background. In the proposed method, even though the embeddings used are cross-lingual, the vocabulary used for each language is different. This way if the same word occurs in two different languages and has a different meaning in the respective languages then each word would get a different vector in the respective languages despite being in the same vector space. <br />
<br />
[[File:Figure2_lwali.png|600px|center]]<br />
<br />
The translation model iteratively improves the encoder and decoder by performing 2 tasks: Denoising, and Back-translation.<br />
<br />
'''Note on the need for alignment:''' To train the decoders (in an admittedly “supervised” manner) we make the assumption that they decode from the same latent space. Thus, given a sentence in either language, it needs to represent it in the same latent space to allow training. However, during the back-translation training, the shared encoder stays fixed. This implies that the encoder needs to be set beforehand. For this reason, the process of embedding and alignment is needed. <br />
<br />
===Denoising===<br />
Random noise is added to the input sentences in order to allow the model to learn some structure of languages. Without noise, the model would simply learn to copy the input word by word. Noise also allows the shared encoder to compose the embeddings of both languages in a language-independent fashion, and then be decoded by the language dependent decoder.<br />
<br />
Denoising works by reconstructing a noisy version of a sentence back into the original sentence in the same language. In mathematical form, if <math>x</math> is a sentence in language L1:<br />
<br />
# Construct <math>C(x)</math>, noisy version of <math>x</math>. In the proposed model, <math>C(x)</math> is constructed by randomly swapping contiguous words. If the length of the input sequence <math>x</math> is <math>N</math>, then a total of <math>\frac{N}{2}</math> such swaps are made.<br />
# Input <math>C(x)</math> into the current iteration of the shared encoder and use decoder for L1 to get reconstructed <math>\hat{x}</math>.<br />
<br />
The training objective is to minimize the cross entropy loss between <math>{x}</math> and <math>\hat{x}</math>.<br />
<br />
In other words, the whole system is optimized to take an input sentence in a given language, encode it using the shared encoder, and reconstruct the original sentence using the decoder of that language.<br />
<br />
The proposed noise function is to perform <math>N/2</math> random swaps of words that are contiguous, where <math>N</math> is the number of words in the sentence. This noise model also helps reduce the reliance of the model on the order of words in a sentence which may be different in the source and target languages. The system will also need to correctly learn the internal structure of a language to decode the sentence into the correct order.<br />
<br />
===Back-Translation===<br />
<br />
With only denoising, the system doesn't have a goal to improve the actual translation. Back-translation works by using the decoder of the target language to create a translation, then encoding this translation and decoding again using the source decoder to reconstruct the original sentence. In mathematical form, if <math>C(x)</math> is a noisy version of sentence <math>x</math> in language L1:<br />
<br />
# Input <math>C(x)</math> into the current iteration of shared encoder and the decoder in L2 to construct translation <math>y</math> in L2,<br />
# Construct <math>C(y)</math>, noisy version of translation <math>y</math>,<br />
# Input <math>C(y)</math> into the current iteration of shared encoder and the decoder in L1 to reconstruct <math>\hat{x}</math> in L1.<br />
<br />
The training objective is to minimize the cross entropy loss between <math>{x}</math> and <math>\hat{x}</math>.<br />
<br />
This approach alleviates issues that would have resulted from the training procedure only dealing with a single language at a time. The corpus of a language is converted to a synthetic translation, and trained to predict the original sentence from this translation. <br />
<br />
Contrary to standard back-translation that uses an independent model to back-translate the entire corpus at once, the system uses mini-batches and the dual architecture to generate pseudo-translations and then train the model with the translation, improving the model iteratively as the training progresses.<br />
<br />
===Training===<br />
<br />
Training is done by alternating these 2 objectives from mini-batch to mini-batch. Each iteration would perform one mini-batch of denoising for L1, another one for L2, one mini-batch of back-translation from L1 to L2, and another one from L2 to L1. The procedure is repeated until convergence. <br />
During decoding, greedy decoding was used at training time for back-translation, but actual inference at test time was done using beam-search with a beam size of 12.<br />
<br />
Optimizer choice and other hyperparameters can be found in the paper.<br />
<br />
=Experiments and Results=<br />
<br />
The model was evaluated using the Bilingual Evaluation Understudy (BLEU) Score, which is typically used to evaluate the quality of the translation, using a reference (ground-truth) translation.<br />
<br />
The paper trained translation model under 3 different settings to compare the performance (Table 1). All training and testing data used was from a standard NMT dataset, WMT'14.<br />
<br />
[[File:Table1_lwali.png|600px|center]]<br />
<br />
The results exhibit that for the proposed system to work properly, back-translation is necessary. The denoising technique alone is below the baseline while big improvements appear when introducing back-translation.<br />
<br />
===Unsupervised===<br />
<br />
The model only has access to monolingual corpora, using the News Crawl corpus with articles from 2007 to 2013. The baseline for unsupervised is the method proposed by [Artetxe, 2017], which was the unsupervised word vector alignment method discussed in the Background section.<br />
<br />
The paper adds each component piece-wise when doing an evaluation to test the impact each piece has on the final score. As shown in Table 1, Unsupervised results compared to the baseline of word-by-word results are strong, with improvement between 40% to 140%. Results also show that back-translation is essential. Denoising doesn't show a big improvement however it is required for back-translation, because otherwise, back-translation would translate nonsensical sentences. The addition of back-translation, however, does show large improvement on all tested cases.<br />
<br />
For the BPE experiment, results show it helps in some language pairs but detract in some other language pairs. This is because while BPE helped to translate some rare words, it increased the error rates in other words. It also did not perform well when translating named entities which occur infrequently.<br />
<br />
===Semi-supervised===<br />
<br />
Since there is often some small parallel data but not enough to train a Neural Machine Translation system, the authors test a semi-supervised setting with the same monolingual data from the unsupervised settings together with either 10,000 or 100,000 random sentence pairs from the News Commentary parallel corpus. The supervision is included to improve the model during the back-translation stage to directly predict sentences that are in the parallel corpus.<br />
<br />
Table 1 shows that the model can greatly benefit from the addition of a small parallel corpus to the monolingual corpora. It is surprising that semi-supervised in row 6 outperforms supervised in row 7, one possible explanation is that both the semi-supervised training set and the test set belong to the news domain, whereas the supervised training set is all domains of corpora.<br />
<br />
===Supervised===<br />
<br />
This setting provides an upper bound to the unsupervised proposed system. The data used was the combination of all parallel corpora provided at WMT 2014, which includes Europarl, Common Crawl and News Commentary for both language pairs plus the UN and the Gigaword corpus for French- English. Moreover, the authors use the same subsets of News Commentary alone to run the separate experiments in order to compare with the semi-supervised scenario.<br />
<br />
The Comparable NMT was trained using the same proposed model except it does not use monolingual corpora, and consequently, it was trained without denoising and back-translation. The proposed model under a supervised setting does much worse than the state of the NMT in row 10, which suggests that adding the additional constraints to enable unsupervised learning also limits the potential performance. To improve these results, the authors also suggest using larger models, longer training times, and incorporating several well-known NMT techniques.<br />
<br />
===Qualitative Analysis===<br />
<br />
[[File:Table2_lwali.png|600px|center]]<br />
<br />
Table 2 shows 4 examples of French to English translations, which shows that the high-quality translations are produced by the proposed system, and this system adequately models non-trivial translation relations. Example 1 and 2 show that the model is able to not only go beyond a literal word-by-word substitution but also model structural differences in the languages (ex.e, it correctly translates "l’aeroport international de Los Angeles" as "Los Angeles International Airport", and it is capable of producing high-quality translations of long and more complex sentences. However, in Example 3 and 4, the system failed to translate the months and numbers correctly and having difficulty with comprehending odd sentence structures, which means that the proposed system has limitations. Especially, the authors point that the proposed model has difficulties to preserve some concrete details from source sentences. Results also show, the proposed model's translation quality often lags behind that of a standard supervised NMT system and also there are also some cases where there are both fluency and adequacy problems that severely hinders understanding the original message from the proposed translation, suggesting that there is still room for improvement and possible future work.<br />
<br />
=Conclusions and Future Work=<br />
<br />
The paper presented an unsupervised model to perform translations with monolingual corpora by using an attention-based encoder-decoder system and training using denoise and back-translation.<br />
<br />
Although experimental results show that the proposed model is effective as an unsupervised approach, there is significant room for improvement when using the model in a supervised way, suggesting the model is limited by the architectural modifications. Some ideas for future improvement include:<br />
*Instead of using fixed cross-lingual word embeddings at the beginning which forces the encoder to learn a common representation for both languages, progressively update the weight of the embeddings as training progresses.<br />
*Decouple the shared encoder into 2 independent encoders at some point during training<br />
*Progressively reduce the noise level<br />
*Incorporate character level information into the model, which might help address some of the adequacy issues observed in our manual analysis<br />
*Use other noise/denoising techniques, and analyze their effect in relation to the typological divergences of different language pairs.<br />
<br />
= Critique =<br />
<br />
While the idea is interesting and the results are impressive for an unsupervised approach, much of the model had actually already been proposed by other papers that are referenced. The paper doesn't add a lot of new ideas but only builds on existing techniques and combines them in a different way to achieve good experimental results. The paper is not a significant algorithmic contribution. <br />
<br />
As pointed out, in order to critically analyze the effect of the algorithm, we need to formulate the algorithm in terms of mathematics.<br />
<br />
The results showed that the proposed system performed far worse than the state of the art when used in a supervised setting, which is concerning and shows that the techniques used creates a limitation and a ceiling for performance.<br />
<br />
Additionally, there was no rigorous hyperparameter exploration/optimization for the model. As a result, it is difficult to conclude whether the performance limit observed in the constrained supervised model is the absolute limit, or whether this could be overcome in both supervised/unsupervised models with the right constraints to achieve more competitive results. <br />
<br />
The best results shown are between two very closely related languages(English and French), and does much worse for English - German, even though English and German are also closely related (but less so than English and French) which suggests that the model may not be successful at translating between distant language pairs. More testing would be interesting to see.<br />
<br />
The results comparison could have shown how the semi-supervised version of the model scores compared to other semi-supervised approaches as touched on in the other works section.<br />
<br />
Their qualitative analysis just checks whether their proposed unsupervised NMT generates a sensible translation. It is limited and it needs further detailed analysis regarding the characteristics and properties of translation which is generated by unsupervised NMT.<br />
<br />
* (As pointed out by an anonymous reviewer [https://openreview.net/forum?id=Sy2ogebAW])Future work is vague: “we would like to detect and mitigate the specific causes…” “We also think that a better handling of rare words…” That’s great, but how will you do these things? Do you have specific reasons to think this, or ideas on how to approach them? Otherwise, this is just hand-waving.<br />
<br />
= References =<br />
#'''[Mikolov, 2013]''' Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. "Distributed representations of words and phrases and their compositionality."<br />
#'''[Artetxe, 2017]''' Mikel Artetxe, Gorka Labaka, Eneko Agirre, "Learning bilingual word embeddings with (almost) no bilingual data".<br />
#'''[Gouws,2016]''' Stephan Gouws, Yoshua Bengio, Greg Corrado, "BilBOWA: Fast Bilingual Distributed Representations without Word Alignments."<br />
#'''[He, 2016]''' Di He, Yingce Xia, Tao Qin, Liwei Wang, Nenghai Yu, Tieyan Liu, and Wei-Ying Ma. "Dual learning for machine translation."<br />
#'''[Sennrich,2016]''' Rico Sennrich and Barry Haddow and Alexandra Birch, "Neural Machine Translation of Rare Words with Subword Units."<br />
#'''[Ravi & Knight, 2011]''' Sujith Ravi and Kevin Knight, "Deciphering foreign language."<br />
#'''[Dou & Knight, 2012]''' Qing Dou and Kevin Knight, "Large scale decipherment for out-of-domain machine translation."<br />
#'''[Johnson et al. 2017]''' Melvin Johnson,et al, "Google’s multilingual neural machine translation system: Enabling zero-shot translation."<br />
#'''[Zhang et al. 2017]''' Meng Zhang, Yang Liu, Huanbo Luan, and Maosong Sun. "Adversarial training for unsupervised bilingual lexicon induction"<br />
#'''[ Koehn & Knowles, 2017]''' Philipp Koehn and Rebecca Knowles. Six challenges for neural machine translation.<br />
#'''[Chen et al., 2017]''' Yun Chen, Yang Liu, Yong Cheng, and Victor O.K. Li. A teacher-student framework for zero-resource neural machine translation.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=42105Countering Adversarial Images Using Input Transformations2018-11-30T19:41:03Z<p>R82zhang: [E] Gramma fixes</p>
<hr />
<div>The code for this paper is available here[https://github.com/facebookresearch/adversarial_image_defenses]<br />
<br />
==Motivation ==<br />
As the use of machine intelligence has increased, robustness has become a critical feature to guarantee the reliability of deployed machine-learning systems. However, recent research has shown that existing models are not robust to small, adversarially designed perturbations to the input. Adversarial examples are inputs to Machine Learning models so that an attacker has intentionally designed to cause the model to make a mistake. Adversarially perturbed examples have been deployed to attack image classification services (Liu et al., 2016)[11], speech recognition systems (Cisse et al., 2017a)[12], and robot vision (Melis et al., 2017)[13]. The existence of these adversarial examples has motivated proposals for approaches that increase the robustness of learning systems to such examples. In the example below (Goodfellow et. al) [17], a small perturbation is applied to the original image of a panda, changing the prediction to a gibbon.<br />
<br />
[[File:Panda.png|center]]<br />
<br />
==Introduction==<br />
The paper studies strategies that defend against adversarial example attacks on image classification systems by transforming the images before feeding them to a Convolutional Network Classifier. <br />
Generally, defenses against adversarial examples fall into two main categories:<br />
<br />
# Model-Specific – They enforce model properties such as smoothness and invariance via the learning algorithm. <br />
# Model-Agnostic – They try to remove adversarial perturbations from the input. <br />
<br />
Model-specific defense strategies make strong assumptions about expected adversarial attacks. As a result, they violate the Kerckhoffs principle, which states that adversaries can circumvent model-specific defenses by simply changing how an attack is executed. This paper focuses on increasing the effectiveness of model-agnostic defense strategies. Specifically, they investigated the following image transformations as a means for protecting against adversarial images:<br />
<br />
# Image Cropping and Re-scaling (Graese et al, 2016). <br />
# Bit Depth Reduction (Xu et. al, 2017) <br />
# JPEG Compression (Dziugaite et al, 2016) <br />
# Total Variance Minimization (Rudin et al, 1992) <br />
# Image Quilting (Efros & Freeman, 2001). <br />
<br />
These image transformations have been studied against Adversarial attacks such as the fast gradient sign method (Goodfelow et. al., 2015), its iterative extension (Kurakin et al., 2016a), Deepfool (Moosavi-Dezfooli et al., 2016), and the Carlini & Wagner (2017) <math>L_2</math>attack. <br />
<br />
The authors in this paper try to focus on increasing the effectiveness of model-agnostic defense strategies through approaches that:<br />
# remove the adversarial perturbations from input images,<br />
# maintain sufficient information in input images to correctly classify them,<br />
# and are still effective in situations where the adversary has information about the defense strategy being used.<br />
<br />
From their experiments, the strongest defenses are based on Total Variance Minimization and Image Quilting. These defenses are non-differentiable and inherently random which makes it difficult for an adversary to get around them.<br />
<br />
==Previous Work==<br />
Recently, a lot of research has focused on countering adversarial threats. Wang et al [4], proposed a new adversary resistant technique that obstructs attackers from constructing impactful adversarial images. This is done by randomly nullifying features within images. Tramer et al [2], showed the state-of-the-art Ensemble Adversarial Training Method, which augments the training process but not only included adversarial images constructed from their model but also including adversarial images generated from an ensemble of other models. Their method implemented on an Inception V2 classifier finished 1st among 70 submissions of NIPS 2017 competition on Defenses against Adversarial Attacks. Graese, et al. [3], showed how input transformation such as shifting, blurring and noise can render the majority of the adversarial examples as non-adversarial. Xu et al.[5] demonstrated, how feature squeezing methods, such as reducing the color bit depth of each pixel and spatial smoothing, defends against attacks. Dziugaite et al [6], studied the effect of JPG compression on adversarial images. Chen et al. [7] introduce an advanced denoising algorithm with GAN based noise modeling in order to improve the blind denoising performance in low-level vision processing. The GAN is trained to estimate the noise distribution over the input noisy images and to generate noise samples. Although meant for image processing, this method can be generalized to target adversarial examples where the unknown noise generating algorithm can be leveraged.<br />
<br />
==Terminology==<br />
<br />
'''Gray Box Attack''' : Model Architecture and parameters are Public<br />
<br />
'''Black Box Attack''': Adversary does not have access to the model.<br />
<br />
An interesting and important observation of adversarial examples is that they generally are not model or architecture specific. Adversarial examples generated for one neural network architecture will transfer very well to another architecture. In other words, if you wanted to trick a model you could create your own model and adversarial examples based off of it. Then these same adversarial examples will most probably trick the other model as well. This has huge implications as it means that it is possible to create adversarial examples for a completely black box model where we have no prior knowledge of the internal mechanics. [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]<br />
<br />
'''Non Targeted Adversarial Attack''': The goal of the attack is to modify a source image in a way such that the image will be classified incorrectly by the network.<br />
<br />
This is an example on non-targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:non-targeted O.JPG| 600px|center]]<br />
<br />
'''Targeted Adversarial Attack''': The goal of the attack is to modify a source image in way such that image will be classified as a ''target'' class by the network.<br />
<br />
This is an example on targeted adversarial attacks to be more clear [https://ml.berkeley.edu/blog/2018/01/10/adversarial-examples/ reference]:<br />
[[File:Targeted O.JPG| 600px|center]]<br />
<br />
'''Defense''': A defense is a strategy that aims make the prediction on an adversarial example h(x') equal to the prediction on the corresponding clean example h(x).<br />
<br />
== Problem Definition ==<br />
The paper discusses non-targeted adversarial attacks for image recognition systems. Given image space <math>\mathcal{X} = [0,1]^{H \times W \times C}</math>, a source image <math>x \in \mathcal{X}</math>, and a classifier <math>h(.)</math>, a non-targeted adversarial example of <math>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity function <math>d(·, ·)</math> and <math>\rho \geq 0</math>. In the best case scenario, <math>d(·, ·)</math> measures the perceptual difference between the original image <math>x</math> and the perturbed image <math>x'</math>, but usually, Euclidean distance (<math>||x - x'||_2</math>) or the Chebyshov distance (<math>||x - x'||_{\infty}</math>) are used.<br />
<br />
From a set of N clean images <math>[{x_{1}, …, x_{N}}]</math>, an adversarial attack aims to generate <math>[{x'_{1}, …, x'_{N}}]</math> images, such that (<math>x'_{n}</math>) is an adversary of (<math>x_{n}</math>).<br />
<br />
The success rate of an attack is given as: <br />
<br />
<center><math><br />
\frac{1}{N}\sum_{n=1}^{N}I[h(x_n) &ne; h({x_n}^\prime)],<br />
</math></center><br />
<br />
which is the proportions of predictions that were altered by an attack.<br />
<br />
The success rate is generally measured as a function of the magnitude of perturbations performed by the attack. In this paper, L2 perturbations are used and are quantified using the normalized L2-dissimilarity metric:<br />
<math> \frac{1}{N} \sum_{n=1}^N{\frac{\vert \vert x_n - x'_n \vert \vert_2}{\vert \vert x_n \vert \vert_2}} </math><br />
<br />
A strong adversarial attack has a high rate, while its normalized L2-dissimilarity given by the above equation is less.<br />
<br />
==Adversarial Attacks==<br />
<br />
Although the exact effect that adversarial examples have on the network is unknown, Ian Goodfellow et. al's Deep Learning book states that adversarial examples exploit the linearity of neural networks to perturb the cost function to force incorrect classifications. Images are often high resolution, and thus have thousands of pixels (millions for HD images). An epsilon ball perturbation when dimensionality is in the magnitude of thousands/millions greatly effects the cost function (especially if it increases loss at every pixel). Hence, although the following methods such as FGSM and Iterative FGSM are very straightforward, they greatly influence the network under a white box attack. <br />
<br />
For the experimental purposes, below 4 attacks have been studied in the paper:<br />
<br />
1. '''Fast Gradient Sign Method (FGSM; Goodfellow et al. (2015)) [17]''': Given a source input <math>x</math>, and true label <math>y</math>, and let <math>l(.,.)</math> be the differentiable loss function used to train the classifier <math>h(.)</math>. Then the corresponding adversarial example is given by:<br />
<br />
<math>x' = x + \epsilon \cdot sign(\nabla_x l(x, y))</math><br />
<br />
for some <math>\epsilon \gt 0</math> which controls the perturbation magnitude.<br />
<br />
2. '''Iterative FGSM ((I-FGSM; Kurakin et al. (2016b)) [14]''': iteratively applies the FGSM update, where M is the number of iterations. It is given as:<br />
<br />
<math>x^{(m)} = x^{(m-1)} + \epsilon \cdot sign(\nabla_{x^{m-1}} l(x^{m-1}, y))</math><br />
<br />
where <math>m = 1,...,M; x^{(0)} = x;</math> and <math>x' = x^{(M)}</math>. M is set such that <math>h(x) \neq h(x')</math>.<br />
<br />
Both FGSM and I-FGSM work by minimizing the Chebyshev distance between the inputs and the generated adversarial examples.<br />
<br />
3. '''DeepFool ((Moosavi-Dezfooliet al., 2016) [15]''': projects x onto a linearization of the decision boundary defined by binary classifier h(.) for M iterations. This can be particularly effictive when a network uses ReLU activation functions. It is given as:<br />
<br />
[[File:DeepFool.PNG|400px |]]<br />
<br />
4. '''Carlini-Wagner's L2 attack (CW-L2; Carlini & Wagner (2017)) [16]''': propose an optimization-based attack that combines a differentiable surrogate for the model’s classification accuracy with an L2-penalty term which encourages the adversary image to be close to the original image. Let <math>Z(x)</math> be the operation that computes the logit vector (i.e., the output before the softmax layer) for an input <math>x</math>, and <math>Z(x)_k</math> be the logit value corresponding to class <math>k</math>. The untargeted variant<br />
of CW-L2 finds a solution to the unconstrained optimization problem. It is given as:<br />
<br />
[[File:Carlini.PNG|500px |]]<br />
<br />
As mentioned earlier, the first two attacks minimize the Chebyshev distance whereas the last two attacks minimize the Euclidean distance between the inputs and the adversarial examples.<br />
<br />
All the methods described above maintain <math>x' \in \mathcal{X}</math> by performing value clipping. <br />
<br />
Below figure shows adversarial images and corresponding perturbations at five levels of normalized L2-dissimilarity for all four attacks, mentioned above.<br />
<br />
[[File:Strength.PNG|thumb|center| 600px |Figure 1: Adversarial images and corresponding perturbations at five levels of normalized L2- dissimilarity for all four attacks.]]<br />
<br />
==Defenses==<br />
Defense is a strategy that aims to make the prediction on an adversarial example equal to the prediction on the corresponding clean example, and the particular structure of adversarial perturbations <math> x-x' </math> have been shown in Figure 1.<br />
Five image transformations that alter the structure of these perturbations have been studied:<br />
# Image Cropping and Re-scaling, <br />
# Bit Depth Reduction, <br />
# JPEG Compression, <br />
# Total Variance Minimization, <br />
# Image Quilting.<br />
<br />
'''Image cropping and Rescaling''' has the effect of altering the spatial positioning of the adversarial perturbation. In this study, images are cropped and re-scaled during training time as part of data-augmentation. At test time, the predictions of randomly cropped are averaged.<br />
<br />
'''Bit Depth Reduction (Xu et. al) [5]''' performs a simple type of quantization that can remove small (adversarial) variations in pixel values from an image. Images are reduced to 3 bits in the experiment.<br />
<br />
'''JPEG Compression and Decompression (Dziugaite etal., 2016)''' removes small perturbations by performing simple quantization. The authors use a quality level of 75/100 in their experiments<br />
<br />
'''Total Variance Minimization (Rudin et. al) [9]''' :<br />
This combines pixel dropout with total variance minimization. This approach randomly selects a small set of pixels, and reconstructs the “simplest” image that is consistent with the selected pixels. The reconstructed image does not contain the adversarial perturbations because these perturbations tend to be small and localized.Specifically, we first select a random set of pixels by sampling a Bernoulli random variable <math>X(i; j; k)</math> for each pixel location <math>(i; j; k)</math>;we maintain a pixel when <math>(i; j; k)</math>= 1. Next, we use total variation, minimization to constructs an image z that is similar to the (perturbed) input image x for the selected<br />
set of pixels, whilst also being “simple” in terms of total variation by solving:<br />
<br />
[[File:TV!.png|300px|]] , <br />
<br />
where <math>TV_{p}(z)</math> represents <math>L_{p}</math> total variation of '''z''' :<br />
<br />
[[File:TV2.png|500px|]]<br />
<br />
The total variation (TV) measures the amount of fine-scale variation in the image z, as a result of which TV minimization encourages removal of small (adversarial) perturbations in the image. The objective function is convex in <math>z</math>, which makes solving for z straightforward. In the paper, p = 2 and a special-purpose solver based on the split Bregman method (Goldstein & Osher, 2009) to perform total variance minimization efficiently is employed.<br />
The effectiveness of TV minimization is illustrated by the images in the middle column of the figure below: in particular, note that the adversarial perturbations that were present in the background for the non- transformed image (see bottom-left image) have nearly completely disappeared in the TV-minimized adversarial image (bottom-center image). As expected, TV minimization also changes image structure in non-homogeneous regions of the image, but as these perturbations were not adversarially designed we expect the negative effect of these changes to be limited.<br />
<br />
[[File:tvx.png]]<br />
<br />
The figure above represents an illustration of total variance minimization and image quilting applied to an original and an adversarial image (produced using I-FGSM with ε = 0.03, corresponding to a normalized L2 - dissimilarity of 0.075). From left to right, the columns correspond to (1) no transformation, (2) total variance minimization, and (3) image quilting. From top to bottom, rows correspond to: (1) the original image, (2) the corresponding adversarial image produced by I-FGSM, and (3) the absolute difference between the two images above. Difference images were multiplied by a constant scaling factor to increase visibility.<br />
<br />
<br />
'''Image Quilting (Efros & Freeman, 2001) [8]'''<br />
Image Quilting is a non-parametric technique that synthesizes images by piecing together small patches that are taken from a database of image patches. The algorithm places appropriate patches in the database for a predefined set of grid points and computes minimum graph cuts in all overlapping boundary regions to remove edge artifacts. Image Quilting can be used to remove adversarial perturbations by constructing a patch database that only contains patches from "clean" images ( without adversarial perturbations); the patches used to create the synthesized image are selected by finding the K nearest neighbors ( in pixel space) of the corresponding patch from the adversarial image in the patch database, and picking one of these neighbors uniformly at random. The motivation for this defense is that resulting image only contains pixels that were not modified by the adversary - the database of real patches is unlikely to contain the structures that appear in adversarial images.<br />
<br />
=Experiments=<br />
<br />
Five experiments were performed to test the efficacy of defenses. The first four experiments consider gray and black box attacks. The gray-box attack applies defenses on input adversarial images for the convolutional networks. The adversary is able to read model architecture and parameters but not the defense strategy. The black-box attack replaces convolutional network by a trained network with image-transformations. The final experiment compares the authors' defenses with prior work. <br />
<br />
'''Set up:'''<br />
Experiments are performed on the ImageNet image classification dataset. The dataset comprises 1.2 million training images and 50,000 test images that correspond to one of 1000 classes. The adversarial images are produced by attacking a ResNet-50 model, with different kinds of attacks mentioned in Section5. The strength of an adversary is measured in terms of its normalized L2-dissimilarity. To produce the adversarial images, L2 dissimilarity for each of the attack was set as below:<br />
<br />
- FGSM. Increasing the step size <math>\epsilon</math>, increases the normalized L2-dissimilarity.<br />
<br />
- I-FGSM. We fix M=10, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- DeepFool. We fix M=5, and increase <math>\epsilon</math> to increase the normalized L2-dissimilarity.<br />
<br />
- CW-L2. We fix <math>k</math>=0 and <math>\lambda_{f}</math> =10, and multiply the resulting perturbation <br />
<br />
The hyperparameters of the defenses have been fixed in all the experiments. Specifically the pixel dropout probability was set to <math>p</math>=0.5 and regularization parameter of total variation minimizer <math>\lambda_{TV}</math>=0.03.<br />
<br />
Below figure shows the difference between the set up in different experiments below. The network is either trained on a) regular images or b) transformed images. The different settings are marked by 8.1, 8.2 and 8.3 <br />
[[File:models3.png |center]] <br />
<br />
==GrayBox - Image Transformation at Test Time== <br />
This experiment applies a transformation on adversarial images at test time before feeding them to a ResNet -50 which was trained to classify clean images. Below figure shows the results for five different transformations applied and their corresponding Top-1 accuracy. Few of the interesting observations from the plot are: All of the image transformations partly eliminate the effects of the attack, Crop ensemble gives the best accuracy around 40-60 percent, with an ensemble size of 30. The accuracy of Image Quilting Defense hardly deteriorates as the strength of the adversary increases. However, it does impact accuracy on non-adversarial examples.<br />
<br />
[[File:sFig4.png|center|600px |]]<br />
<br />
==BlackBox - Image Transformation at Training and Test Time==<br />
ResNet-50 model was trained on transformed ImageNet Training images. Before feeding the images to the network for training, standard data augmentation (from He et al) along with bit depth reduction, JPEG Compression, TV Minimization, or Image Quilting were applied on the images. The classification accuracy on the same adversarial images as in the previous case is shown Figure below. (Adversary cannot get this trained model to generate new images - Hence this is assumed as a Black Box setting!). Below figure concludes that training Convolutional Neural Networks on images that are transformed in the same way at test time, dramatically improves the effectiveness of all transformation defenses. Nearly 80 -90 % of the attacks are defended successfully, even when the L2- dissimilarity is high.<br />
<br />
<br />
[[File:sFig5.png|center|600px |]]<br />
<br />
<br />
==Blackbox - Ensembling==<br />
Four networks ResNet-50, ResNet-10, DenseNet-169, and Inception-v4 along with an ensemble of defenses were studied, as shown in Table 1. The adversarial images are produced by attacking a ResNet-50 model. The results in the table conclude that Inception-v4 performs best. This could be due to that network having a higher accuracy even in non-adversarial settings. The best ensemble of defenses achieves an accuracy of about 71% against all the other attacks. The attacks deteriorate the accuracy of the best defenses (a combination of cropping, TVM, image quilting, and model transfer) by at most 6%. Gains of 1-2% in classification accuracy could be found from ensembling different defenses, while gains of 2-3% were found from transferring attacks to different network architectures.<br />
<br />
<br />
[[File:sTab1.png|600px|thumb|center|Table 1. Top-1 classification accuracy of ensemble and model transfer defenses (columns) against four black-box attacks (rows). The four networks we use to classify images are ResNet-50 (RN50), ResNet-101 (RN101), DenseNet-169 (DN169), and Inception-v4 (Iv4). Adversarial images are generated by running attacks against the ResNet-50 model, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. Higher is better. The best defense against each attack is typeset in boldface.]]<br />
<br />
==GrayBox - Image Transformation at Training and Test Time ==<br />
In this experiment, the adversary has access to the network and the related parameters (but does not have access to the input transformations applied at test time). From the network trained in-(BlackBox: Image Transformation at Training and Test Time), novel adversarial images were generated by the four attack methods. The results show that Bit-Depth Reduction and JPEG Compression are weak defenses in such a gray box setting. In contrast, image cropping, rescaling, variation minimization, and image quilting are more robust against adversarial images in this setting.<br />
The results for this experiment are shown in below figure. Networks using these defenses classify up to 50 % of images correctly.<br />
<br />
[[File:sFig6.png|center| 600px |]]<br />
<br />
==Comparison With Ensemble Adversarial Training==<br />
The results of the experiment are compared with the state of the art ensemble adversarial training approach proposed by Tramer et al. [2]. Ensemble Training fits the parameters of a Convolutional Neural Network on adversarial examples that were generated to attack an ensemble of pre-trained models. The model release by Tramer et al [2]: an Inception-Resnet-v2, trained on adversarial examples generated by FGSM against Inception-Resnet-v2 and Inception-v3 models. The authors compared their ResNet-50 models with image cropping, total variance minimization and image quilting defenses. Two assumption differences need to be noticed. Their defenses assume the input transformation is unknown to the adversary and no prior knowledge of the attacks is being used. The results of ensemble training and the pre-processing techniques mentioned in this paper are shown in Table 2. The results show that ensemble adversarial training works better on FGSM attacks (which it uses at training time), but is outperformed by each of the transformation-based defenses all other attacks.<br />
<br />
<br />
<br />
[[File:sTab2.png|600px|thumb|center|Table 2. Top-1 classification accuracy on images perturbed using attacks against ResNet-50 models trained on input-transformed images and an Inception-v4 model trained using ensemble adversarial. Adversarial images are generated by running attacks against the models, aiming for an average normalized <math>L_2</math>-dissimilarity of 0.06. The best defense against each attack is typeset in boldface.]]<br />
<br />
=Discussion/Conclusions=<br />
The paper proposed reasonable approaches to countering adversarial images. The authors evaluated Total Variance Minimization and Image Quilting and compared it with already proposed ideas like Image Cropping - Rescaling, Bit Depth Reduction, JPEG Compression, and Decompression on the challenging ImageNet dataset.<br />
Previous work by Wang et al. [10] shows that a strong input defense should be nondifferentiable and randomized. Two of the defenses - namely Total Variation Minimization and Image Quilting, both possess this property.<br />
<br />
Image quilting involves a discrete variable that conducts the selection of a patch from the database, which is a non-differentiable operation.<br />
Additionally, total variation minimization randomly conducts pixels selection from the pixels it uses to measure reconstruction<br />
error during creation of the de-noised image. Image quilting conducts a random selection of a particular K<br />
nearest neighbor uniformly but in a random manner. This inherent randomness makes it difficult to attack the model. <br />
<br />
Future work suggests applying the same techniques to other domains such as speech recognition and image segmentation. For example, in speech recognition, total variance minimization can be used to remove perturbations from waveforms and "spectrogram quilting" techniques that reconstruct a spectrogram could be developed. The proposed input-transformation defenses can also be combined with ensemble adversarial training by Tramèr et al.[2] to study new attack methods.<br />
<br />
=Critiques=<br />
1. The terminology of Black Box, White Box, and Grey Box attack is not exactly given and clear.<br />
<br />
2. White Box attacks could have been considered where the adversary has a full access to the model as well as the pre-processing techniques.<br />
<br />
3. Though the authors did a considerable work in showing the effect of four attacks on ImageNet database, much stronger attacks (Madry et al) [7], could have been evaluated.<br />
<br />
4. Authors claim that the success rate is generally measured as a function of the magnitude of perturbations, performed by the attack using the L2- dissimilarity, but the claim is not supported by any references. None of the previous work has used these metrics.<br />
<br />
5. ([https://openreview.net/forum?id=SyJ7ClWCb])In the new draft of the paper, the authors add the sentence "our defenses assume that part of the defense strategy (viz., the input transformation) is unknown to the adversary".<br />
<br />
This is a completely unreasonable assumption. Any algorithm which hopes to be secure must allow the adversary to, at the very least, understand what the defense is that's being used. Consider a world where the defense here is implemented in practice: any attacker in the world could just go look up the paper, read the description of the algorithm, and know how it works.<br />
<br />
=References=<br />
<br />
1. Chuan Guo , Mayank Rana & Moustapha Ciss´e & Laurens van der Maaten , Countering Adversarial Images Using Input Transformations<br />
<br />
2. Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, Patrick McDaniel, Ensemble Adversarial Training: Attacks and defenses.<br />
<br />
3. Abigail Graese, Andras Rozsa, and Terrance E. Boult. Assessing threat of adversarial examples of deep neural networks. CoRR, abs/1610.04256, 2016. <br />
<br />
4. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Adversary resistant deep neural networks with an application to malware detection. CoRR, abs/1610.01239, 2016a.<br />
<br />
5. Weilin Xu, David Evans, and Yanjun Qi. Feature squeezing: Detecting adversarial examples in deep neural networks. CoRR, abs/1704.01155, 2017. <br />
<br />
6. Gintare Karolina Dziugaite, Zoubin Ghahramani, and Daniel Roy. A study of the effect of JPG compression on adversarial images. CoRR, abs/1608.00853, 2016.<br />
<br />
7. Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, Adrian Vladu .Towards Deep Learning Models Resistant to Adversarial Attacks, arXiv:1706.06083v3<br />
<br />
8. Alexei Efros and William Freeman. Image quilting for texture synthesis and transfer. In Proc. SIGGRAPH, pp. 341–346, 2001.<br />
<br />
9. Leonid Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.<br />
<br />
10. Qinglong Wang, Wenbo Guo, Kaixuan Zhang, Alexander G. Ororbia II, Xinyu Xing, C. Lee Giles, and Xue Liu. Learning adversary-resistant deep neural networks. CoRR, abs/1612.01401, 2016b.<br />
<br />
11. Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. CoRR, abs/1611.02770, 2016.<br />
<br />
12. Moustapha Cisse, Yossi Adi, Natalia Neverova, and Joseph Keshet. Houdini: Fooling deep structured prediction models. CoRR, abs/1707.05373, 2017 <br />
<br />
13. Marco Melis, Ambra Demontis, Battista Biggio, Gavin Brown, Giorgio Fumera, and Fabio Roli. Is deep learning safe for robot vision? adversarial examples against the icub humanoid. CoRR,abs/1708.06939, 2017.<br />
<br />
14. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. Adversarial examples in the physical world. CoRR, abs/1607.02533, 2016b.<br />
<br />
15. Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: A simple and accurate method to fool deep neural networks. In Proc. CVPR, pp. 2574–2582, 2016.<br />
<br />
16. Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In IEEE Symposium on Security and Privacy, pp. 39–57, 2017.<br />
<br />
17. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In Proc. ICLR, 2015.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DeepVO_Towards_end_to_end_visual_odometry_with_deep_RNN&diff=42104DeepVO Towards end to end visual odometry with deep RNN2018-11-30T19:37:19Z<p>R82zhang: [T]/* Architecture Overview + LSTM*/</p>
<hr />
<div>== Introduction ==<br />
Visual Odometry (VO) is a computer vision technique for estimating an object’s position and orientation from camera images. It is an important technique commonly used for “pose estimation and robot localization” with notable applications in Mars Exploration Rovers and Autonomous Vehicles [x1] [x2]. While the research field of VO is broad, this paper focuses on the topic of monocular visual odometry. Particularly, the authors examine prominent VO methods and argue that mainstream geometry based monocular VO methods should be amended with deep learning approaches. Deep Learning (DL) has recently achieved promising results in computer vision tasks but does not include the VO field, thus the paper proposes a novel deep-learning based end-to-end VO algorithm and then empirically demonstrates its viability.<br />
<br />
== Related Work ==<br />
<br />
Visual odometry algorithms can be grouped into two main categories. The first is known as the conventional methods, and they are based on established principles of geometry. Specifically, an object’s position and orientation (pose) are obtained by identifying reference points and calculating how those points change over the image sequence. Algorithms in this category can be further divided into two: sparse feature based methods and direct methods, which differ in the method employed to select reference points. Sparse feature based methods establish reference points using image salient features such as corners and edges [8]. Direct methods, on the other hand, make use of the whole image and consider every pixel as a reference point [11]. Recently, semi-direct methods that combine the benefits of both approaches are gaining popularity [16].<br />
<br />
Today, most of the state-of-the-art VO algorithms belong to the geometry family. However, they suffer significant limitations. For example, direct methods assume “photometric consistency” [11]. Sparse feature based methods are also prone to “drifting” because of outliers and noises. As a result, the paper argues that geometry-based methods are difficult to engineer and calibrate, limiting its practicality. Figure 1 illustrates the general architecture of geometry-based algorithms and it outlines necessary drift correction techniques such as Camera Calibration, Feature Detection, Feature Matching (tracking), Outlier Rejection, Motion Estimation, Scale Estimation, and Local optimization (bundle adjustment).<br />
<br />
[[File:DeepVO_Figure_1.png | center]]<br />
<br />
<div align="center">Figure 1. Architectures of the conventional geometry-based monocular VO method.</div><br />
<br />
The second category of VO algorithms is based on learning. Namely, they try to learn an object’s motion model from labeled optical flows. Initially, these models are trained using classic Machine Learning techniques such as k-nearest neighbors (KNNs) [15], Gaussian Processes [16], and Support Vector Machines [17]. However, these models were inefficient to handle highly non-linear and high-dimensional inputs, leading to poor performance in comparison with geometry-based methods. For this reason, Deep Learning-based approaches are dominating research in this field and are producing many promising results. For example, CNN based models can now recognize places based on appearance [18] and detect direction and velocity from stereo inputs [20]. Moreover, a deep learning model even achieved robust VO with blurred and under-exposed images [21]. While these successes are encouraging, the authors observe that a CNN based architecture is “incapable of modeling sequential information.” Instead, they proposed to use RNN to tackle this problem.<br />
<br />
== End-to-End Visual odometry through RCNN ==<br />
<br />
=== Architecture Overview ===<br />
An end-to-end monocular VO model is proposed by utilizing deep Recurrence Convolutional Neural Network (RCNN). Figure 2 depicts the end-to-end model, which is comprised of three main stages. First, the model takes a monocular video as input and pre-processes the image sequences by “subtracting the mean RGB values of all frames” from each frame. Then, consecutive image sequences are stacked to form tensors, which become the inputs for the CNN stage. The purpose of the CNN stages is to extract salient features from the image tensors. The structure of the CNN is inspired by FlowNet [24], which is a model designed to extract optical flows. Details of the CNN structure is shown in Table 1. Using CNN optical flow features as input, the RNN stage tries to estimate the temporal and sequential relations among the features. The RNN stage does this by utilizing two Long Short-Term Memory networks (LSTM), which estimate object poses for each time step using both long-term and short-term dependencies. Figure 3 illustrates the RNN architecture.<br />
<br />
Without the LSTM framework, RNNs often experience vanishing gradients or gradient exploding. If the gradient is small and the network is deep, when it is propagated to the shallower layers during the backward pass, it often just becomes too small to have an effect on the weights. This forces standard RNN architectures to be relatively shallow for temporal prediction over time. In other words, the weight update for recent events will have a much larger effect on the network weights than events happened long-time ago. Visual odometry is a very complex problem, and thus we attempt to learn highly complex functions within the network. Hence, to circumvent the vanishing gradient issue, we use LSTM nodes. Conversely, LSTM can handle long-term dependencies and has deep temporal structure, but needs depth on network layers to learn complex high-level representation. LSTM define three additional gates: forget gate, input gate and update gate to help better capture the long-term dependencies. Deep RNNs have been shown to perform well on complex dynamic representations (e.g. speech recognition), and thus we leverage this architecture and layer multiple LSTM layers to mitigate vanishing gradient without losing the network's ability to represent complex dynamics.<br />
<br />
[[File:DeepVO_Figure_2.png | center]]<br />
<div align="center">Figure 2. Architectures of the proposed RCNN based monocular VO system.</div><br />
<br />
[[File:DeepVO_Table_1.png | center]]<br />
<div align="center">Table 1. CNN structure</div><br />
<br />
[[File:DeepVO_Figure_3.png | center]]<br />
<div align="center">Figure 3. Folded and unfolded LSTMs and its internal structure.</div><br />
<br />
=== Training and Optimization ===<br />
The proposed RCNN model can be represented as a conditional probability of poses given an image sequence: <br />
<br />
<math><br />
p(Y_{t}|X_{t}) = p(y_{1},...,y_{t}|x_{1},...,x_{t})<br />
</math><br />
<br />
Given this probability function is expressed by a deep RCNN.<br />
To find the optimal hyperparameters, the DNN maximizes:<br />
<br />
<math><br />
\theta^{*}=argmax(Y{t}|X{t};\theta)<br />
</math><br />
<br />
To learn the hyperparameters <math>\theta</math> of the DNNs, the loss function that is composed of Mean Square Error (MSE) of all positions p and orientations <math>\varphi</math> minimizes:<br />
<br />
<math><br />
\theta^{*}=argmin\frac{1}{N}\sum_{N}^{i=1}\sum_{t}^{k=1}||\hat{p}_{k}-p_{k}||_{2}^{2}+\kappa||\hat{\varphi}_{k}-\varphi_{k}||_{2}^{2}<br />
</math><br />
<br />
where || *|| is <math>L_{2}-norm</math>, <math>\kappa</math> (100 in the experiments) is a scale factor to balance the weights of positions and orientations, N is the number of samples, and the orientation φ is represented by Euler angles.<br />
<br />
== Experiments and Results ==<br />
The paper evaluates the proposed RCNN VO model by comparing it empirically with the open-source VO library of LIBVISO2 [7], which is a well-known geometry based model. The comparison is done using the KITTI VO/SLAM benchmark [3], which contains 22 image sequences, 11 of which are labeled with ground truths. Two separate experiments are performed. <br />
<br />
1. Quantitatively Analysis is performed using only labeled image sequence. Namely, 4 of 11 image sequences were used for training and the others reserved for testing. Table 2 and Figure 6 outlines the result, showing that the proposed RCNN model performs consistently better than the monocular VISO2_M model. However, it performs worse than the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Table_2.png |500px| center]]<br />
<br />
<br />
[[File:DeepVO_Figure_6.png |500px| center]]<br />
<br />
<br />
2. The generalizability of the proposed RCNN model is evaluated using the unlabeled image sequences. Figure 8 outlines the test result, showing that the proposed model is able to generalize better than the monocular VISO2_M model and performs roughly the same as the stereo VISO2_S model.<br />
<br />
<br />
[[File:DeepVO_Figure_8.png |600px| center]]<br />
<br />
== Conclusions ==<br />
The paper presents a new RCNN VO model that combines the CNNs with the RNNs under the power of Deep RCNNs. It can achieve representation learning while sequential modelling of the the monocular VO. Although it is considered a viable approach, it is not expected to be a replacement to the classic geometry-based approach. However, from the experiment result, it can be a viable complement by combining geometry and DNN learning representations, knowledge and models to further improve VO's accuracy and robustness. The main contribution of the paper is threefold: <br />
<br />
# The authors demonstrate that the monocular VO problem can be addressed in an end-to-end fashion based on DL, i.e., directly estimating poses from raw RGB images. Neither prior knowledge nor parameter is needed to recover the absolute scale. <br />
#The authors propose a RCNN architecture enabling the DL based VO algorithm to be generalised to totally new environments by using the geometric feature representation learnt by the CNN. <br />
# Sequential dependence and complex motion dynamics of an image sequence, which are of importance to the VO but cannot be explicitly or easily modelled by human, are implicitly encapsulated and automatically learnt by the RCNN.<br />
<br />
== Critiques ==<br />
<br />
This paper cannot be considered as a critical advance to the state of the art as the authors just suggest a method combining CNN and RNNs for the visual odometry problem. The authors also state that deep learning in terms of simple feed-forward Neural networks and CNNs has already been used in this problem. Only an RNN approach seems to have been not tried on this problem. The authors propose a combined RCNN and geometric-based approach towards the end of the paper. But it is not intuitive how these two potentially very diverse methods could be combined. The authors also do not explain any proposed methods for the combination. The authors don't build a compelling case against the state of the art methods or convincingly prove the superiority of the RCNN or a combined method. For example, the RCNN and other state of the art geometry-based methods have a deficiency of getting lower accuracies when shown a large open area in the images as mentioned by the authors. The authors put forth some techniques to solve this problem for the geometry approaches but they state that they do not have a similar method for the deep learning based approaches. Thus, in such scenarios, the methods proposed by the authors don't seem to work at all. <br />
<br />
The paper advances the field of deep-learning based VO by creating a pioneering end-to-end model that is capable of extracting features and learning sequential dynamics from monocular videos. While the new model clearly outperforms the LIBVISO2_M algorithm, it fails to demonstrate any advantage over the LIBVISO2_S algorithm. Hence, it makes one question whether the complexity of deep-learning based monocular VO methods is justified and whether robots or autonomous vehicles designers should opt for stereo visions as much as possible. Nonetheless, this end-to-end model is beneficial for situations where monocular VO is the only viable option. Furthermore, the paper could have benefited by including a qualitative comparison of the algorithm’s computation requirements, such as hardware specification, engineering time, and training time. Though the justification for input sequence pre-processing is not explained completely, but it can be attributed to the fact that they are using standard pre-processing techniques like mean Subtraction and normalization, which helps in easier optimization of cost functions. Perhaps, future-works could involve adapting the model for real-time visual odometry.<br />
<br />
== References ==<br />
[1] S. Wang, R. Clark, H. Wen and N. Trigoni, "DeepVO: Towards end-to-end visual odometry with deep Recurrent Convolutional Neural Networks," 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 2017, pp. 2043-2050.<br />
<br />
[2] M. Maimone, Y. Cheng, and L. Matthies, "Two years of Visual Odometry on the Mars Exploration Rovers," Journal of Field Robotics. 24 (3): 169–186, 2007.<br />
<br />
[3] A. Geiger, P. Lenz, and R. Urtasun, “Are we ready for autonomous driving? the KITTI vision benchmark suite,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2012.<br />
<br />
[7] A. Geiger, J. Ziegler, and C. Stiller, “Stereoscan: Dense 3D reconstruction in real-time,” in Intelligent Vehicles Symposium (IV), 2011.<br />
<br />
[8] A. J. Davison, I. D. Reid, N. D. Molton, and O. Stasse, “MonoSLAM: Real-time single camera SLAM,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 1052–1067, 2007.<br />
<br />
[11] R. A. Newcombe, S. J. Lovegrove, and A. J. Davison, “DTAM: Dense tracking and mapping in real-time,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2011, pp. 2320–2327.<br />
<br />
[15] R. Roberts, H. Nguyen, N. Krishnamurthi, and T. Balch, “Memory-based learning for visual odometry,” in Proceedings of IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2008, pp. 47–52.<br />
<br />
[16] V. Guizilini and F. Ramos, “Semi-parametric learning for visual odometry,” The International Journal of Robotics Research, vol. 32, no. 5, pp. 526–546, 2013.<br />
<br />
[17] T. A. Ciarfuglia, G. Costante, P. Valigi, and E. Ricci, “Evaluation of non-geometric methods for visual odometry,” Robotics and Autonomous Systems, vol. 62, no. 12, pp. 1717–1730, 2014.<br />
<br />
[18] N. Su ̈nderhauf, S. Shirazi, A. Jacobson, F. Dayoub, E. Pepperell, B. Upcroft, and M. Milford, “Place recognition with convnet landmarks: Viewpoint-robust, condition-robust, training-free,” in Proceedings of Robotics: Science and Systems (RSS), 2015.<br />
<br />
[20] A. Kendall, M. Grimes, and R. Cipolla, “Convolutional networks for real-time 6-DoF camera relocalization,” in Proceedings of International Conference on Computer Vision (ICCV), 2015.<br />
<br />
[21] G. Costante, M. Mancini, P. Valigi, and T. A. Ciarfuglia, “Exploring representation learning with CNNs for frame-to-frame ego-motion estimation,” IEEE Robotics and Automation Letters, vol. 1, no. 1, pp.18–25, 2016.<br />
<br />
[24] A. Dosovitskiy, P. Fischery, E. Ilg, C. Hazirbas, V. Golkov, P. van der Smagt, D. Cremers, T. Brox et al., “Flownet: Learning optical flow with convolutional networks,” in Proceedings of IEEE International Conference on Computer Vision (ICCV). IEEE, 2015, pp. 2758–2766.<br />
<br />
[25]http://cs231n.github.io/neural-networks-2/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DETECTING_STATISTICAL_INTERACTIONS_FROM_NEURAL_NETWORK_WEIGHTS&diff=42102DETECTING STATISTICAL INTERACTIONS FROM NEURAL NETWORK WEIGHTS2018-11-30T19:20:38Z<p>R82zhang: [T] /* Add Sum Product Network as one of the research area where it combines interpretability and performance */</p>
<hr />
<div>=Introduction=<br />
<br />
It has been commonly believed that one major advantage of neural networks is their capability of modelling complex statistical interactions between features for automatic feature learning. Statistical interactions capture important information on where features often have joint effects with other features on predicting an outcome. The discovery of interactions is especially useful for scientific discoveries and hypothesis validation. For example, physicists may be interested in understanding what joint factors provide evidence for new elementary particles; doctors may want to know what interactions are accounted for in risk prediction models, to compare against known interactions from existing medical literature.<br />
<br />
With the growth in the computational power available Neural Networks have been able to solve many of the complex tasks in a wide variety of fields. This is mainly due to their ability to model complex and non-linear interactions. Neural networks have traditionally been treated as “black box” models, preventing their adoption in many application domains, such as those where explainability is desirable. It has been noted that complex machine learning models can learn unintended patterns from data, raising significant risks to stakeholders [14]. Therefore, in applications where machine learning models are intended for making critical decisions, such as healthcare or finance, it is paramount to understand how they make predictions [9]. Within several areas, like eg: computation social science, interpretability is of utmost importance. Since we do not understand how a neural network comes to its decision, practitioners in these areas tend to prefer simpler models like linear regression, decision trees, etc. which are much more interpretable. In this paper, we are going to present one way of implementing interpretability in a neural network.<br />
<br />
Existing approaches to interpreting neural networks can be summarized into two types. One type is direct interpretation, which focuses on 1) explaining individual feature importance, for example by computing input gradients [13] and decomposing predictions [8], 2) developing attention-based models, which illustrate where neural networks focus during inference [11], and 3) providing model-specific visualizations, such as feature map and gate activation visualizations [15]. The other type is indirect interpretation, for example post-hoc interpretations of feature importance [12] and knowledge distillation to simpler interpretable models [10].<br />
<br />
In this paper, the authors propose Neural Interaction Detection (NID), which can detect any order or form of statistical interaction captured by the feedforward neural network by examining its weight matrix. This approach is efficient because it avoids searching over an exponential solution space of interaction candidates by making an approximation of hidden unit importance at the first hidden layer via all weights above and doing a 2D traversal of the input weight matrix.<br />
<br />
Note that in this paper, we only consider one specific types of neural network, feedforward neural network. Based on the methodology discussed here, the authors suggest that we can build an interpretation method for other types of networks also.<br />
<br />
=Related Work=<br />
<br />
1. Interaction Detection approaches: <br />
* Conduct individual tests for all features' combination such as ANOVA and Additive Groves.<br />
* Define all interaction forms of interest, then later finds the important ones.<br />
- The paper's goal is to detect interactions without compromising the functional forms. Our method accomplishes higher-order interaction detection, which has the benefit of avoiding a high false positive or false discovery rate.<br />
<br />
2. Interpretability: A lot of work has also been done in this particular area and it can be divided it the following broad categories:<br />
* Feature Importance through Decomposition: Methods like Input Gradient(Sundararajan et al., 2017) learns the importance of features through a gradient-based approach similar to backpropagation. Works like Li et al(2017), Murdoch(2017) and Murdoch(2018) study interpretability of LSTMs by looking at phrase and word level importance scores. Bach et al. 2015 and Shrikumar et al. 2016 (DeepLift) study pixel importance in CNNs.<br />
* Studying Visualizations in Models - Karpathy et al. (2015) worked with character generating LSTMs and tried to study activation and firing in certain hidden units for meaningful attributes. (Yosinski et al., 2015 studies feature map visualizations. <br />
* Attention-Based Models: Bahdanau et al. (2014) - These are a different class of models which use attention modules(different architectures) to help focus the neural network to decide the parts of the input that it should look more closely or give more importance to. Looking at the results of these type of model an indirect sense of interpretability can be gauged.<br />
* Sum product networks, Hoifun Poon, Pedro Domingos (2011) It is a new deep architecture that provides clear semantics. In its core, it is a probabilistic model, with two types of nodes: Sum node and <br />
Product nodes. The sum nodes are trying to model the mixture of distributions and product node is trying to model joint distributions. It can be trained using gradient descent and other methods as well. The main advantage of the Sum-Product Network is that it has clear semantics, where people can interpret exactly how the network models make decisions. Therefore, it has better interpretability than most of the current deep architectures. <br />
<br />
The approach in this paper is to extract non-additive interactions between variables from the neural network weights.<br />
<br />
=Notations=<br />
Before we dive in to methodology, we are going to define a few notations here. Most of them will be trivial.<br />
<br />
1. Vector: Vectors are defined with bold-lowercases, '''v, w'''<br />
<br />
2. Matrix: Matrice are defined with blod-uppercases, '''V, W'''<br />
<br />
3. Interger Set: For some interger p <math>\in</math> Z, we define [p] := {1,2,3,...,p}<br />
<br />
=Interaction=<br />
First of all, in order to explain the model, we need to be able to explain the interactions and their effects to output. Therefore, we define 'interacion' between variables as below. <br />
<br />
[[File:def_interaction.PNG|900px|center]]<br />
<br />
From the definition above, for a function like, <math>x_1x_2 + sin(x_3 + x_4 + x_5)</math>, we have <math>{[x_1, x_2]}</math> and <math>{[x_3, x_4, x_5]}</math> interactions. And we say that the latter interaction to be 3-way interaction.<br />
<br />
Note that from the definition above, we can naturally deduce that d-way interaction can exist if and only if all of its (d-1) interactions exist. For example, 3-way interaction above shows that we have 2-way interactions <math>{[3,4], [4,5]}</math> and <math>{[3,5]}</math>.<br />
<br />
One thing that we need to keep in mind is that for models like neural network, most of interactions are happening within hidden layers. This means that we needa proper way of measuring interaction strength.<br />
<br />
The key observation is that for any kinds of interaction, at a some hidden unit of some hidden layer, two interacting features the ancestors. In graph-theoretical language, interaction map can be viewed as an associated directed graph and for any interaction <math>\Gamma \in [p]</math>, there exists at least one vertix that has all of features of <math>\Gamma</math> as ancestors. The statement can be rigorized as the following:<br />
<br />
<br />
[[File:prop2.PNG|900px|center]]<br />
<br />
Now, the above mathematical statement gurantees us to measure interaction strengths at ANY hidden layers. For example, if we want to study about interactions at some specific hidden layer, now we now that there exists corresponding vertices between the hidden layer and output layer. Therefore all we need to do is now to find approprite measure which can summarize the information between those two layers.<br />
<br />
Before doing so, let's think about a single-layered neural network. For any one hidden unit, we can have possibly, <math>2^{||W_i,:||}</math>, number of interactions. This means that our search space might be too huge for multi-layered networks. Therefore, we need a some descent way of approximate out search space. Moreover, the authors realized a fast interaction detection by limiting the search complexity of the task by only quantifying interactions created at the first hidden layer. The figure below illustrates an interaction within a fully connected feedforward neural network, where the box contains later layers in the network.<br />
<br />
[[File:network1.PNG|500px|center]]<br />
<br />
==Measuring influence in hidden layers==<br />
As we discussed above, in order to consider interaction between units in any layers, we need to think about their out-going paths. However, we soon encountered the fact that for some fully-connected multi-layer neural network, the search space might be too huge to compare. Therefore, we use information about out-going paths gredient upper bond. To represent the influence of out-going paths at <math>l</math>-hidden layer, we define cumulative impact of weights between output layer and <math>l+1</math>. We define aggregated weights as, <br />
<br />
[[File:def3.PNG|900px|center]]<br />
<br />
<br />
Note that <math>z^{(l)} \in R^{(p_l)}</math> where <math>p_l</math> is the number of hidden units in <math>l</math>-layer.<br />
Moreover, this is the lipschitz constant of gredients. Gredient has been an import variable of measuring influence of features, especially when we consider that input layer's derivative computes the direction normal to decision boundaries.<br />
<br />
==Quantifying influence==<br />
For some <math>i</math> hidden unit at the first hidden layer, which is the closet layer to the input layer, we define the influence strength of some interaction as, <br />
<br />
[[File:measure1.PNG|900px|center]]<br />
<br />
The function <math>\mu</math> will be defined later. Essentially, the formula shows that the strength of influence is defined as the product of the aggregated weight on the first hidden layer and some measure of influence between the first hidden layer and the input layer. <br />
<br />
For the function, <math>\mu</math>, any positive-real valued functions such as max, min and average can be candidates. The effects of those candidates will be tested later.<br />
<br />
Now based on the specifications above, the author suggested the algorithm for searching influential interactions between input layer units as follows:<br />
<br />
It was pointed out that restricting to the first hidden layer might miss some important feature interactions, however, the author state that it is not straightforward how to incorporate the idea of hidden units at intermediate layers to get better interaction detection performance.<br />
[[File:algorithm1.PNG|850px|center]]<br />
<br />
=Cut-off Model=<br />
Now using the greedy algorithm defined above, we can rank the interactions by their strength. However, in order to access true interactions, we are building the cut-off model which is a generalized additive model (GAM) as below,<br />
<br />
<center><math><br />
c_K('''x''') = \sum_{i=1}^{p}g_i(x_i) + \sum_{i=1}^{K}{g_i}^\prime(x_\chi)<br />
</math></center><br />
<br />
From the above model, each <math>g</math> and <math>g^*</math> are Feed-Forward neural network. We are keep adding interactions until the performance reaches plateaus.<br />
<br />
=Experiment=<br />
For the experiment, the authors have compared three neural network model with traditional statistical interaction detecting algorithms. For the nueral network models, first model will be MLP, second model will be MLP-M, which is MLP with additional univariate network at the output. The last one is the cut-off model defined above, which is denoted by MLP-cutoff. In the experiments that the authors performed, all the networks which modelled feature interactions consisted of four hidden layers containing 140, 100, 60, and 20 units respectively. Whereas, all the individual univariate networks contained three hidden layers with each layer containing 10 units. All of these networks used ReLu activation and backpropagation for training. The MLP-M model is graphically represented below.<br />
<br />
[[File:output11.PNG|300px|center]]<br />
<br />
For the experiment, the authors study our interaction detection framework on both simulated and real-world experiments. For simulated experiments, the authors are going to test on 10 synthetic functions as shown in table I.<br />
<br />
[[File:synthetic.PNG|900px|center]]<br />
<br />
The authors use four real-world datasets, of which two are regression datasets, and the other two are binary classification datasets. The datasets are a mixture of common prediction tasks in the cal housing<br />
and bike sharing datasets, a scientific discovery task in the higgs boson dataset, and an example of very-high order interaction detection in the letter dataset.<br />
<br />
And the authors also reported the results of comparisons between the models. As you can see, neural network based models are performing better on average. Compare to the traditional methods like ANOVA, MLP and MLP-M method shows 20% increases in performance.<br />
<br />
[[File:performance_mlpm.PNG|900px|center]]<br />
<br />
<br />
[[File:performance2_mlpm.PNG|900px|center]]<br />
<br />
The above result shows that MLP-M almost perfectly capture the most influential pair-wise interactions.<br />
<br />
=Highe-order interatcion detection=<br />
The authors use their greedy interaction ranking algorithm to perform higher-order interactiondetection without an exponential search of interaction candidates.<br />
[[File:higher-order_interaction_detection.png|700px|center]]<br />
<br />
=Limitations=<br />
Even though for the above synthetic experiment MLP methods showed superior performances, the method still have some limitations. For example, fir the function like, <math>x_1x_2 + x_2x_3 + x_1x_3</math>, neural network fails to distinguish between interlinked interactions to single higher order interaction. Moreoever, correlation between features deteriorates the ability of the network to distinguish interactions. However, correlation issues are presented most of interaction detection algorithms. <br />
<br />
Because this method relies on the neural network fitting the data well, there are some additional concerns. Notably, if the NN is unable to make an appropriate fit (under/overfitting), the resulting interactions will be flawed. This can occur if the datasets that are too small or too noisy, which often occurs in practical settings. <br />
<br />
=Conclusion=<br />
Here we presented the method of detecting interactions using MLP. Compared to other state-of-the-art methods like Additive Groves (AG), the performances are competitive yet computational powers required is far less. Therefore, it is safe to claim that the method will be extremly useful for practitioners with (comparably) less computational powers. Moreover, the NIP algorithm successfully reduced the computation sizes. After all, the most important aspect of this algorithm is that now users of nueral networks can impose interpretability in the model usage, which will change the level of usability to another level for most of practitioners outside of those working in machine learning and deep learning areas.<br />
<br />
For future work, the authors want to detect feature interactions by using the common units in the intermediate hidden layers of feedforward networks, and also want to use such interaction detection to interpret weights in other deep neural networks. Also, it was pointed out that the neural network weights heavily depend on L-1 regularized neural network training, but a group lasso penalty may work better.<br />
<br />
=Critique=<br />
1. Authors need to do large-scale experiments, instead of just conducting experiments on some synthetic dataset with small feature dimensionality, to make their claim stronger.<br />
<br />
2. Although the method proposed in this paper is interesting, the paper would benefit from providing some more explanations to support its idea and fill the possible gaps in its experimental evaluation. In some parts there are repetitive explanations that could be replaced by other essential clarifications.<br />
<br />
3. Greedy algorithm is implemented but nothing is mentioned about the speed of this algorithm which is definitely not fast. So, this has the potential to be a weak point of the study.<br />
<br />
=Reference=<br />
<br />
[1] Jacob Bien, Jonathan Taylor, and Robert Tibshirani. A lasso for hierarchical interactions. Annals of statistics, 41(3):1111, 2013. <br />
<br />
[2] G David Garson. Interpreting neural-network connection weights. AI Expert, 6(4):46–51, 1991.<br />
<br />
[3] Yotam Hechtlinger. Interpretation of prediction models using the input gradient. arXiv preprint arXiv:1611.07634, 2016.<br />
<br />
[4] Shiyu Liang and R Srikant. Why deep neural networks for function approximation? 2016. <br />
<br />
[5] David Rolnick and Max Tegmark. The power of deeper networks for expressing natural functions. International Conference on Learning Representations, 2018. <br />
<br />
[6] Daria Sorokina, Rich Caruana, and Mirek Riedewald. Additive groves of regression trees. Machine Learning: ECML 2007, pp. 323–334, 2007.<br />
<br />
[7] Simon Wood. Generalized additive models: an introduction with R. CRC press, 2006<br />
<br />
[8] Sebastian Bach, Alexander Binder, Gre ́goire Montavon, Frederick Klauschen, Klaus-Robert Mu ̈ller, and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 10(7):e0130140, 2015.<br />
<br />
[9] Rich Caruana, Yin Lou, Johannes Gehrke, Paul Koch, Marc Sturm, and Noemie Elhadad. Intel- ligible models for healthcare: Predicting pneumonia risk and hospital 30-day readmission. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1721–1730. ACM, 2015.<br />
<br />
[10] Zhengping Che, Sanjay Purushotham, Robinder Khemani, and Yan Liu. Interpretable deep models for icu outcome prediction. In AMIA Annual Symposium Proceedings, volume 2016, pp. 371. American Medical Informatics Association, 2016.<br />
<br />
[11] Laurent Itti, Christof Koch, and Ernst Niebur. A model of saliency-based visual attention for rapid scene analysis. IEEE Transactions on pattern analysis and machine intelligence, 20(11):1254– 1259, 1998.<br />
<br />
[12] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Why should i trust you?: Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135–1144. ACM, 2016.<br />
<br />
[13]Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Vi- sualising image classification models and saliency maps. arXiv preprint arXiv:1312.6034, 2013.<br />
<br />
[14] Kush R Varshney and Homa Alemzadeh. On the safety of machine learning: Cyber-physical sys- tems, decision sciences, and data products. arXiv preprint arXiv:1610.01256, 2016.<br />
<br />
[15] Jason Yosinski, Jeff Clune, Anh Nguyen, Thomas Fuchs, and Hod Lipson. Understanding neural networks through deep visualization. arXiv preprint arXiv:1506.06579, 2015.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=learn_what_not_to_learn&diff=42100learn what not to learn2018-11-30T18:30:56Z<p>R82zhang: [T] /* Introduction+ MCTS + learn what not to learn*/</p>
<hr />
<div>=Introduction=<br />
<br />
In reinforcement learning, it is often difficult for an agent to learn when the action space is large, especially the difficulties from function approximation and exploration. Some previous work has been trying to use Monte Carlo Tree Search to help address this problem. Monte Carlo Tree Search is a heuristic search algorithm that helps provides some indication of how good is an action, it works relatively well in a problem where the action space is large(like the one in this paper). One of the famous examples would be Google's Alphago that defeated the world champion in 2016, which uses MCTS in their reinforcement learning algorithm for the board game Go. When the action space is large, one com In some cases many actions are irrelevant and it is sometimes easier for the algorithm to learn which action not to take. The paper proposes a new reinforcement learning approach for dealing with large action spaces based on action elimination by restricting the available actions in each state to a subset of the most likely ones. There is a core assumption being made in the proposed method that it is easier to predict which actions in each state are invalid or inferior and use that information for control. More specifically, it proposes a system that learns the approximation of a Q-function and concurrently learns to eliminate actions. The method utilizes an external elimination signal which incorporates domain-specific prior knowledge. For example, in parser-based text games, the parser gives feedback regarding irrelevant actions after the action is played (e.g., Player: "Climb the tree." Parser: "There are no trees to climb"). Then a machine learning model can be trained to generalize to unseen states. <br />
<br />
The paper focuses on tasks where both states and the actions are natural language. It introduces a novel deep reinforcement learning approach which has a Deep Q-Network (DQN) and an Action Elimination Network (AEN), both using the Convolutional Neural Networks (CNN) for Natural Language Processing (NLP) tasks. The AEN is trained to predict invalid actions, supervised by the elimination signal from the environment. The proposed method uses the final layer activations of AEN to build a linear contextual bandit model which allows the elimination of sub-optimal actions with high probability. '''Note that the core assumption is that it is easy to predict which actions are invalid or inferior in each state and leverage that information for control.'''<br />
<br />
The text-based game called "Zork", which lets players to interact with a virtual world through a text-based interface is tested by using the elimination framework. <br />
In this game, the player explores an environment using imagination of the text he/she reads. For more info, you can watch this video: [https://www.youtube.com/watch?v=xzUagi41Wo0 Zork].<br />
<br />
The AEN algorithm has achieved a faster learning rate than the baseline agents by eliminating irrelevant actions.<br />
<br />
Below shows an example for the Zork interface:<br />
<br />
[[File:lnottol_fig1.png|500px|center]]<br />
<br />
All states and actions are given in natural language. Input for the game contains more than a thousand possible actions in each state since the player can type anything.<br />
<br />
=Related Work=<br />
<br />
Text-Based Games(TBG): The state of the environment in TBG is described by simple language. The player interacts with the environment with text command which respects a pre-defined grammar. A popular example is Zork which has been tested in the paper. TBG is a good research intersection of RL and NLP, it requires language understanding, long-term memory, planning, exploration, affordability extraction, and common sense. It also often introduce stochastic dynamics to increase randomness.<br />
<br />
Representations for TBG: Good word representation is necessary in order to learn control policies from high-dimensional complex data such as text. Previous work on TBG used pre-trained embeddings directly for control, other works combined pre-trained embedding with neural networks. For example, He<br />
et al. (2015) proposed to consider an input as Bag Of Words features for a neural network, learned separately<br />
embeddings for states and actions, and then computed the Q function from autocorrelations between<br />
these embeddings.<br />
<br />
DRL with linear function approximation: DRL methods such as the DQN have achieved state-of-the-art results in a variety of challenging, high-dimensional domains. This is mainly because neural networks can learn rich domain representations for value function and policy. On the other hand, linear representation batch reinforcement learning methods are more stable and accurate, while feature engineering is necessary.<br />
<br />
RL in Large Action Spaces: Prior work concentrated on factorizing the action space into binary subspace(Pazis and Parr, 2011; Dulac-Arnold et al., 2012; Lagoudakis and Parr, 2003), other works proposed to embed the discrete actions into a continuous space, then choose the nearest discrete action according to the optimal actions in the continuous space(Dulac-Arnold et al., 2015; Van Hasselt and Wiering, 2009). He et. al. (2015)extended DQN to unbounded(natural language) action spaces.<br />
Learning to eliminate actions was first mentioned by (Even-Dar, Mannor, and Mansour, 2003). They proposed to learn confidence intervals around the value function in each state. Lipton et al.(2016a) proposed to learn a classifier that detects hazardous state and then use it to shape the reward. Fulda et al.(2017) presented a method for affordability extraction via inner products of pre-trained word embedding.<br />
<br />
=Action Elimination=<br />
<br />
The approach in the paper builds on the standard Reinforcement Learning formulation. At each time step <math>t</math>, the agent observes state <math display="inline">s_t </math> and chooses a discrete action <math display="inline">a_t\in\{1,...,|A|\} </math>. Then, after action execution, the agent obtains a reward <math display="inline">r_t(s_t,a_t) </math> and observes next state <math display="inline">s_{t+1} </math> according to a transition kernel <math>P(s_{t+1}|s_t,a_t)</math>. The goal of the algorithm is to learn a policy <math display="inline">\pi(a|s) </math> which maximizes the expected future discounted cumulative return <math display="inline">V^\pi(s)=E^\pi[\sum_{t=0}^{\infty}\gamma^tr(s_t,a_t)|s_0=s]</math>, where <math> 0< \gamma <1 </math>. The Q-function is <math display="inline">Q^\pi(s,a)=E^\pi[\sum_{t=0}^{\infty}\gamma^tr(s_t,a_t)|s_0=s,a_0=a]</math>, and it can be optimized by Q-learning algorithm.<br />
<br />
After executing an action, the agent observes a binary elimination signal <math>e(s, a)</math> to determine which actions not to take. It equals 1 if action <math>a</math> may be eliminated in state <math>s</math> (and 0 otherwise). The signal helps mitigating the problem of large discrete action spaces. We start with the following definitions:<br />
<br />
'''Definition 1:''' <br />
<br />
Valid state-action pairs with respect to an elimination signal are state action pairs which the elimination process should not eliminate. <br />
<br />
The set of valid state-action pairs contains all of the state-action pairs that are a part of some optimal policy, i.e., only strictly suboptimal state-actions can be invalid.<br />
<br />
'''Definition 2:'''<br />
<br />
Admissible state-action pairs with respect to an elimination algorithm are state action pairs which the elimination algorithm does not eliminate.<br />
<br />
'''Definition 3:'''<br />
<br />
Action Elimination Q-learning is a Q-learning algorithm which updates only admissible state-action pairs and chooses the best action in the next state from its admissible actions. We allow the base Q-learning algorithm to be any algorithm that converges to <math display="inline">Q^*</math> with probability 1 after observing each state-action infinitely often.<br />
<br />
==Advantages of Action Elimination==<br />
<br />
The main advantage of action elimination is that it allows the agent to overcome some of the main difficulties in large action spaces which are Function Approximation and Sample Complexity. <br />
<br />
Function approximation: Errors in the Q-function estimates may cause the learning algorithm to converge to a suboptimal policy, this phenomenon becomes more noticeable when the action space is large. Action elimination mitigates this effect by taking the max operator only on valid actions, thus, reducing potential overestimation errors. Besides, by ignoring the invalid actions, the function approximation can also learn a simpler mapping (i.e., only the Q-values of the valid state-action pairs) leading to faster convergence and better solution.<br />
<br />
Sample complexity: The sample complexity measures the number of steps during learning, in which the policy is not <math display="inline">\epsilon</math>-optimal. Assume that there are <math>A'</math> actions that should be eliminated and are <math>\epsilon</math>-optimal, i.e. their value is at least <math>V^*(s)-\epsilon</math>. The invalid action often returns no reward and doesn't change the state, (Lattimore and Hutter, 2012)resulting in an action gap of <math display="inline">\epsilon=(1-\gamma)V^*(s)</math>, and this translates to <math display="inline">V^*(s)^{-2}(1-\gamma)^{-5}log(1/\delta)</math> wasted samples for learning each invalid state-action pair. Practically, elimination algorithm can eliminate these invalid actions and therefore speed up the learning process approximately by <math display="inline">A/A'</math>.<br />
<br />
Because it is difficult to embed the elimination signal into the MDP, the authors use contextual multi-armed bandits to decouple the elimination signal from the MDP, which can correctly eliminate actions when applying standard Q learning into learning process.<br />
<br />
==Action elimination with contextual bandits==<br />
<br />
Contextual bandit problem is a famous probability problem and is a natural extension from the multi-arm bandit problem.<br />
<br />
Let <math display="inline">x(s_t)\in R^d </math> be the feature representation of <math display="inline">s_t </math>. We assume that under this representation there exists a set of parameters <math display="inline">\theta_a^*\in \mathbb{R}^d </math> such that the elimination signal in state <math display="inline">s_t </math> is <math display="inline">e_t(s_t,a) = \theta_a^{*T}x(s_t)+\eta_t </math>, where <math display="inline"> \Vert\theta_a^*\Vert_2\leq S</math>. <math display="inline">\eta_t</math> is an R-subgaussian random variable with zero mean that models additive noise to the elimination signal. When there is no noise in the elimination signal, R=0. Otherwise, <math display="inline">R\leq 1</math> since the elimination signal is bounded in [0,1]. Assume the elimination signal satisfies: <math display="inline">0\leq E[e_t(s_t,a)]\leq l </math> for any valid action and <math display="inline"> u\leq E[e_t(s_t, a)]\leq 1</math> for any invalid action. And <math display="inline"> l\leq u</math>. Denote by <math display="inline">X_{t,a}</math> as the matrix whose rows are the observed state representation vectors in which action a was chosen, up to time t. <math display="inline">E_{t,a}</math> as the vector whose elements are the observed state representation elimination signals in which action a was chosen, up to time t. Denote the solution to the regularized linear regression <math display="inline">\Vert X_{t,a}\theta_{t,a}-E_{t,a}\Vert_2^2+\lambda\Vert \theta_{t,a}\Vert_2^2 </math> (for some <math display="inline">\lambda>0</math>) by <math display="inline">\hat{\theta}_{t,a}=\bar{V}_{t,a}^{-1}X_{t,a}^TE_{t,a} </math>, where <math display="inline">\bar{V}_{t,a}=\lambda I + X_{t,a}^TX_{t,a}</math>.<br />
<br />
<br />
According to Theorem 2 in (Abbasi-Yadkori, Pal, and Szepesvari, 2011), <math display="inline">|\hat{\theta}_{t,a}^{T}x(s_t)-\theta_a^{*T}x(s_t)|\leq\sqrt{\beta_t(\delta)x(s_t)^T\bar{V}_{t,a}^{-1}x(s_t)}\ \forall t>0</math>, where <math display="inline">\sqrt{\beta_t(\delta)}=R\sqrt{2\ \text{log}(\text{det}(\bar{V}_{t,a})^{1/2}\text{det}(\lambda I)^{-1/2}/\delta)}+\lambda^{1/2}S</math>, with probability of at least <math display="inline">1-\delta</math>. If <math display="inline">\forall s\ ,\Vert x(s)\Vert_2 \leq L</math>, then <math display="inline">\beta_t</math> can be bounded by <math display="inline">\sqrt{\beta_t(\delta)} \leq R \sqrt{d\ \text{log}(1+tL^2/\lambda/\delta)}+\lambda^{1/2}S</math>. Next, define <math display="inline">\tilde{\delta}=\delta/k</math> and bound this probability for all the actions. i.e., <math display="inline">\forall a,t>0</math><br />
<br />
<math display="inline">Pr(|\hat{\theta}_{t-1,a}^{T}x(s_t)-\theta_{t-1, a}^{*T}x(s_t)|\leq\sqrt{\beta_t(\tilde\delta)x(s_t)^T\bar{V}_{t - 1,a}^{-1}x(s_t)}) \leq 1-\delta</math><br />
<br />
Recall that <math display="inline">E[e_t(s,a)]=\theta_a^{*T}x(s_t)\leq l</math> if a is a valid action. Then we can eliminate action a at state <math display="inline">s_t</math> if it satisfies:<br />
<br />
<math display="inline">\hat{\theta}_{t-1,a}^{T}x(s_t)-\sqrt{\beta_{t-1}(\tilde\delta)x(s_t)^T\bar{V}_{t-1,a}^{-1}x(s_t)})>l</math><br />
<br />
with probability <math display="inline">1-\delta</math> that we never eliminate any valid action. Note that <math display="inline">l, u</math> are not known. In practice, choosing <math display="inline">l</math> to be 0.5 should suffice.<br />
<br />
==Concurrent Learning==<br />
In fact, Q-learning and contextual bandit algorithms can learn simultaneously, resulting in the convergence of both algorithms, i.e., finding an optimal policy and a minimal valid action space. <br />
<br />
If the elimination is done based on the concentration bounds of the linear contextual bandits, it can be ensured that Action Elimination Q-learning converges, as shown in Proposition 1.<br />
<br />
'''Proposition 1:'''<br />
<br />
Assume that all state action pairs (s,a) are visited infinitely often, unless eliminated according to <math display="inline">\hat{\theta}_{t-1,a}^Tx(s)-\sqrt{\beta_{t-1}(\tilde{\delta})x(s)^T\bar{V}_{t-1,a}^{-1}x(s))}>l</math>. Then, with a probability of at least <math display="inline">1-\delta</math>, action elimination Q-learning converges to the optimal Q-function for any valid state-action pairs. In addition, actions which should be eliminated are visited at most <math display="inline">T_{s,a}(t)\leq 4\beta_t/(u-l)^2<br />
+1</math> times.<br />
<br />
Notice that when there is no noise in the elimination signal(R=0), we correctly eliminate actions with probability 1. so invalid actions will be sampled a finite number of times.<br />
<br />
=Method=<br />
<br />
The assumption that <math display="inline">e_t(s_t,a)=\theta_a^{*T}x(s_t)+\eta_t </math> generally does not hold when using raw features like word2vec. So the paper proposes to use the neural network's last layer as feature representation of states. A practical challenge here is that the features must be fixed over time when used by the contextual bandit. So batch-updates framework(Levine et al., 2017;Riquelme, Tucker, and Snoek, 2018) is used, where a new contextual bandit model is learned for every few steps that uses the last layer activation of the AEN as features.<br />
<br />
==Architecture of action elimination framework==<br />
<br />
[[File:lnottol_fig1b.png|300px|center]]<br />
<br />
After taking action <math display="inline">a_t</math>, the agent observes <math display="inline">(r_t,s_{t+1},e_t)</math>. The agent uses it to learn two function approximation deep neural networks: A DQN and an AEN. AEN provides an admissible actions set <math display="inline">A'</math> to the DQN, which uses this set to decide how to act and learn. The architecture for both the AEN and DQN is an NLP CNN(100 convolutional filters for AEN and 500 for DQN, with three different 1D kernels of length (1,2,3)), based on(Kim, 2014). The state is represented as a sequence of words, composed of the game descriptor and the player's inventory. These are truncated or zero padded to a length of 50 descriptor + 15 inventory words and each word is embedded into continuous vectors using word2vec in <math display="inline">R^{300}</math>. The features of the last four states are then concatenated together such that the final state representations s are in <math display="inline">R^{78000}</math>. The AEN is trained to minimize the MSE loss, using the elimination signal as a label. The code, the Zork domain, and the implementation of the elimination signal can be found [https://github.com/TomZahavy/CB_AE_DQN here.]<br />
<br />
==Psuedocode of the Algorithm==<br />
<br />
[[File:lnottol_fig2.png|750px|center]]<br />
<br />
AE-DQN trains two networks: a DQN denoted by Q and an AEN denoted by E. The algorithm creates a linear contextual bandit model from it every L iterations with procedure AENUpdate(). This procedure uses the activations of the last hidden layer of E as features, which are then used to create a contextual linear bandit model.AENUpdate() then solved this model and plugin it into the target AEN. The contextual linear bandit model <math display="inline">(E^-,V)</math> is then used to eliminate actions via the ACT() and Target() functions. ACT() follows an <math display="inline">\epsilon</math>-greedy mechanism on the admissible actions set. For exploitation, it selects the action with highest Q-value by taking an argmax on Q-values among <math display="inline">A'</math>. For exploration, it selects an action uniformly from <math display="inline">A'</math>. The targets() procedure is estimating the value function by taking max over Q-values only among admissible actions, hence, reducing function approximation errors.<br />
<br />
=Experiments=<br />
==Grid Domain==<br />
The authors start by evaluating our algorithm on a small grid world domain with 9 rooms, where they ca analyze the effect of the action elimination (visualization can be found in the appendix). In this domain, the agent starts at the center of the grid and needs to navigate to its upper-left corner. On every step, the agent suffers a penalty of (−1), with a terminal reward of 0. Prior to the game, the states are randomly divided into K categories. The environment has 4K navigation actions, 4 for each category, each with a probability to move in a random direction. If the chosen action belongs to the same category as the state, the action is performed correctly in probability pTc = 0.75. Otherwise, it will be performed correctly in probability pFc = 0.5. If the action does not fit the state category, the elimination signal equals 1, and if the action and state belong to the same category, then e = 0. The optimal policy will only use the navigation actions from the same type as the state, and all of the other actions are strictly suboptimal. A basic comparison between vanilla Q-learning without action elimination (green) and a tabular version of the action elimination Q-learning (blue) can be found in the figure below. In all of the figures, the results are compared to the case with one category (red), i.e., only 4 basic navigation actions, which forms an upper bound on performance with multiple categories. In Figure (a),(c), the episode length is T = 150, and in Figure (b) it is T = 300, to allow sufficient exploration for the vanilla Q-Learning. It is clear from the simulations that the action elimination dramatically improves the results in large action spaces. Also, note that the gain from action elimination increases with the grid size since the elimination allows the agent to reach the goal earlier.<br />
<br />
<br />
[[File:griddomain.png|1200px|thumb|center|Performance of agents in grid world]]<br />
==Zork domain==<br />
<br />
The world of Zork presents a rich environment with a large state and action space. <br />
Zork players describe their actions using natural language instructions. For example, "open the mailbox". Then their actions were processed by a sophisticated natural language parser. Based on the results, the game presents the outcome of the action. The goal of Zork is to collect the Twenty Treasures of Zork and install them in the trophy case. Points that are generated from the game's scoring system are given to the agent as the reward. For example, the player gets the points when solving the puzzles. Placing all treasures in the trophy will get 350 points. The elimination signal is given in two forms, "wrong parse" flag, and text feedback "you cannot take that". These two signals are grouped together into a single binary signal which then provided to the algorithm. <br />
<br />
[[File:zork_domain.png|1200px|thumb|center|Left:the world of Zork.Right:subdomains of Zork.]]<br />
<br />
Experiments begin with the two subdomains of Zork domains: Egg Quest and the Troll Quest. For these subdomains, an additional reward signal is provided to guide the agent towards solving specific tasks and make the results more visible. A reward of -1 is applied at every time step to encourage the agent to favor short paths. Each trajectory terminates is upon completing the quest or after T steps are taken. The discounted factor for training is <math display="inline">\gamma=0.8</math> and <math display="inline">\gamma=1</math> during evaluation. Also <math display="inline">\beta=0.5, l=0.6</math> in all experiments. <br />
<br />
===Egg Quest===<br />
<br />
The goal for this quest is to find and open the jewel-encrusted egg hidden on a tree in the forest. An egg-splorer goes on an adventure to find a mystical ancient relic with his furry companion. You can have a look at the game at [https://scratch.mit.edu/projects/212838126/ EggQuest]<br />
<br />
The agent will get 100 points upon completing this task. For action space, there are 9 fixed actions for navigation, and a second subset which consisting <math display="inline">N_{Take}</math> actions for taking possible objects in the game. <math display="inline">N_{Take}=200 (set A_1), N_{Take}=300 (set A_2)</math> has been tested separately.<br />
AE-DQN (blue) and a vanilla DQN agent (green) has been tested in this quest.<br />
<br />
[[File:AEF_zork_comparison.png|1200px|thumb|center|Performance of agents in the egg quest.]]<br />
<br />
Figure a) corresponds to the set <math display="inline">A_1</math>, with T=100, b) corresponds to the set <math display="inline">A_2</math>, with T=100, and c) corresponds to the set <math display="inline">A_2</math>, with T=200. Both agents have performed well on sets a and c. However, the AE-DQN agent has learned much faster than the DQN on set b, which implies that action elimination is more robust to hyperparameter optimization when the action space is large. One important observation to note is that the three figures have different scales for the cumulative reward. While the AE-DQN outperformed the standard DQN in figure b, both models performed significantly better with the hyperparameter configuration in figure c.<br />
<br />
===Troll Quest===<br />
<br />
The goal of this quest is to find the troll. To do it the agent needs to find the way to the house, use a lantern to expose the hidden entrance to the underworld. It will get 100 points upon achieving the goal. This quest is a larger problem than Egg Quest. The action set <math display="inline">A_1</math> is 200 take actions and 15 necessary actions, 215 in total.<br />
<br />
[[File:AEF_troll_comparison.png|400px|thumb|center|Results in the Troll Quest.]]<br />
<br />
The red line above is an "optimal elimination" baseline which consists of only 35 actions(15 essential and 20 relevant take actions). We can see that AE-DQN still outperforms DQN and its improvement over DQN is more significant in the Troll Quest than the Egg quest. Also, it achieves compatible performance to the "optimal elimination" baseline.<br />
<br />
===Open Zork===<br />
<br />
Lastly, the "Open Zork" domain has been tested which only the environment reward has been used. 1M steps have been trained. Each trajectory terminates after T=200 steps. Two action sets have been used:<math display="inline">A_3</math>, the "Minimal Zork" action set, which is the minimal set of actions (131) that is required to solve the game. <math display="inline">A_4</math>, the "Open Zork" action set (1227) which composed of {Verb, Object} tuples for all the verbs and objects in the game.<br />
<br />
[[]]<br />
<br />
[[File:AEF_open_zork_comparison.png|600px|thumb|center|Results in "Open Zork".]]<br />
<br />
<br />
The above Figure shows the learning curve for both AE-DQN and DQN. We can see that AE-DQN (blue) still outperform the DQN (blue) in terms of speed and cumulative reward.<br />
<br />
=Conclusion=<br />
In this paper, the authors proposed a Deep Reinforcement Learning model for sub-optimal actions while performing Q-learning. Moreover, they showed that by eliminating actions, using linear contextual bandits with theoretical guarantees of convergence, the size of the action space is reduced, exploration is more effective, and learning is improved when tested on Zork, a text-based game.<br />
<br />
For future work the authors aim to investigate more sophisticated architectures and tackle learning shared representations for elimination and control which may boost performance on both tasks.<br />
<br />
They also hope to to investigate other mechanisms for action elimination, such as eliminating actions that result from low Q-values as in Even-Dar, Mannor, and Mansour, 2003.<br />
<br />
The authors also hope to generate elimination signals in real-world domains and achieve the purpose of eliminating the signal implicitly.<br />
<br />
=Critique=<br />
The paper is not a significant algorithmic contribution and it merely adds an extra layer of complexity to the very famous DQN algorithm. All the experimental domains considered in the paper are discrete action problems that have so many actions that it could have been easily extended to a continuous action problem. In continuous action space there are several policy gradient based RL algorithms that have provided stronger performances. The authors should have ideally compared their methods to such algorithms like PPO or DRPO.<br />
<br />
Even with the critique above, the paper presents mathematical/theoretical justifications of the methodology. Moreover, since the methodology is built on the standard RL framework, this means that other variant RL algorithms can apply the idea to decrease the complexity and increase the performance. Moreover, the there are some rooms for applying technical variations for the algorithm.<br />
<br />
Also, since we are utilizing the system's response to irrelevant actions, an intuitive approach to eliminate such irrelevant actions is to add a huge negative reward for such actions, which will be much easier than the approach suggested by this paper. However, the in experiments, the author only compares AE-DQN to traditional DQN, not traditional DQN with negative rewards assigned to irrelevant actions.<br />
<br />
After all, the name that the authors have chosen is a good and attractive choice and matches our brain's structure which in so many real-world scenarios detects what not to learn.<br />
<br />
=Reference=<br />
1. Chu, W.; Li, L.; Reyzin, L.; and Schapire, R. 2011. Contextual bandits with linear payoff functions. In Proceedings of the Fourteenth International Conference on Artiﬁcial Intelligence and Statistics.<br />
<br />
2. Côté,M.-A.;Kádár,Á.;Yuan,X.;Kybartas,B.;Barnes,T.;Fine,E.;Moore,J.;Hausknecht,M.;Asri, L. E.; Adada, M.; et al. 2018. Textworld: A learning environment for text-based games. arXiv.<br />
<br />
3. Dulac-Arnold, G.; Evans, R.; van Hasselt, H.; Sunehag, P.; Lillicrap, T.; Hunt, J.; Mann, T.; Weber, T.; Degris, T.; and Coppin, B. 2015. Deep reinforcement learning in large discrete action spaces. arXiv.<br />
<br />
4. He, J.; Chen, J.; He, X.; Gao, J.; Li, L.; Deng, L.; and Ostendorf, M. 2015. Deep reinforcement learning with an unbounded action space. CoRR abs/1511.04636.<br />
<br />
5. Kim, Y. 2014. Convolutional neural networks for sentence classiﬁcation. [https://arxiv.org/abs/1408.5882 arXiv preprint].<br />
<br />
6. VanHasselt,H.,andWiering,M.A. 2009. Usingcontinuousactionspacestosolvediscreteproblems. In Neural Networks, 2009. IJCNN 2009. International Joint Conference on, 1149–1156. IEEE.<br />
<br />
7. Watkins, C. J., and Dayan, P. 1992. Q-learning. Machine learning 8(3-4):279–292.<br />
<br />
8. Su, P.-H.; Gasic, M.; Mrksic, N.; Rojas-Barahona, L.; Ultes, S.; Vandyke, D.; Wen, T.-H.; and Young, S. 2016. Continuously learning neural dialogue management. arXiv preprint.<br />
<br />
9. Wu, Y.; Schuster, M.; Chen, Z.; Le, Q. V.; Norouzi, M.; Macherey, W.; Krikun, M.; Cao, Y.; Gao, Q.; Macherey, K.; et al. 2016. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint.<br />
<br />
10. Yuan, X.; Côté, M.-A.; Sordoni, A.; Laroche, R.; Combes, R. T. d.; Hausknecht, M.; and Trischler, A. 2018. Counting to explore and generalize in text-based games. arXiv preprint arXiv:1806.1152<br />
<br />
11. Zahavy, T.; Haroush, M.; Merlis, N.; Mankowitz, D. J.; 2018. Learn What Not to Learn: Action Elimination with Deep Reinforcement Learning. arXiv:1809.02121v1</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=conditional_neural_process&diff=42099conditional neural process2018-11-30T18:00:17Z<p>R82zhang: [T]/* More info about Meta Learning */</p>
<hr />
<div>== Motivation ==<br />
<br />
Deep neural networks are good at function approximations, yet they are typically trained from scratch for each new function. While Bayesian methods, such as Gaussian Processes (GPs), exploit prior knowledge to quickly infer the shape of a new function at test time. Yet GPs<br />
are computationally expensive, and it can be hard to design appropriate priors. Hence the authors propose a propose a family of neural models called, Conditional Neural Processes (CNPs), that combine the benefits of both. <br />
<br />
== Introduction ==<br />
<br />
To train a model effectively, deep neural networks typically require large datasets. To mitigate this data efficiency problem, learning in two phases is one approach: the first phase learns the statistics of a generic domain without committing to a specific learning task; the second phase learns a function for a specific task but does so using only a small number of data points by exploiting the domain-wide statistics already learned. Taking a probabilistic stance and specifying a distribution over functions (stochastic processes) is another approach -- Gaussian Processes being a commonly used example of this. Such Bayesian methods can be computationally expensive. <br />
<br />
The authors of the paper propose a family of models that represent solutions to the supervised problem, and an end-to-end training approach to learning them that combines neural networks with features reminiscent of Gaussian Processes. They call this family of models Conditional Neural Processes (CNPs). CNPs can be trained on very few data points to make accurate predictions, while they also have the capacity to scale to complex functions and large datasets.<br />
<br />
== Model ==<br />
Consider a data set <math display="inline"> \{x_i, y_i\} </math> with evaluations <math display="inline">y_i = f(x_i) </math> for some unknown function <math display="inline">f</math>. Assume <math display="inline">g</math> is an approximating function of f. The aim is to minimize the loss between <math display="inline">f</math> and <math display="inline">g</math> on the entire space <math display="inline">X</math>. In practice, the routine is evaluated on a finite set of observations.<br />
<br />
<br />
Let training set be <math display="inline"> O = \{x_i, y_i\}_{i = 0} ^{n-1}</math>, and test set be <math display="inline"> T = \{x_i, y_i\}_{i = n} ^ {n + m - 1} \subset X</math> of unlabelled points.<br />
<br />
P be a probability distribution over functions <math display="inline"> F : X \to Y</math>, formally known as a stochastic process. Thus, P defines a joint distribution over the random variables <math display="inline"> {f(x_i)}_{i = 0} ^{n + m - 1}</math>. Therefore, for <math display="inline"> P(f(x)|O, T)</math>, our task is to predict the output values <math display="inline">f(x_i)</math> for <math display="inline"> x_i \in T</math>, given <math display="inline"> O</math>. <br />
<br />
A common assumption made on P is that all function evaluations of <math display="inline"> f </math> is Gaussian distributed. The random functions class is called Gaussian Processes (GPs). This framework of the stochastic process allows a model to be data efficient, however, it's hard to get appropriate priors and stochastic processes are expensive in computation, scaling poorly with <math>n</math> and <math>m</math>. One of the examples is GPs, which has running time <math>O(n+3)^3</math>.<br />
<br />
[[File:001.jpg|300px|center]]<br />
<br />
== Conditional Neural Process ==<br />
<br />
Conditional Neural Process models directly parametrize conditional stochastic processes without imposing consistency with respect to some prior process. CNP parametrize distributions over <math display="inline">f(T)</math> given a distributed representation of <math display="inline">O</math> of fixed dimensionality. Thus, the mathematical guarantees associated with stochastic processes is traded off for functional flexibility and scalability.<br />
<br />
CNP is a conditional stochastic process <math display="inline">Q_\theta</math> defines distributions over <math display="inline">f(x_i)</math> for <math display="inline">x_i \in T</math>, given a set of observations <math display="inline">O</math>. For stochastic processs, the authors assume that <math display="inline">Q_{\theta}</math> is invariant to permutations, and <math display="inline">Q_\theta(f(T) | O, T)= Q_\theta(f(T') | O, T')=Q_\theta(f(T) | O', T) </math> when <math> O', T'</math> are permutations of <math display="inline">O</math> and <math display="inline">T </math>. In this work, we generally enforce permutation invariance with respect to <math display="inline">T</math> be assuming a factored structure, which is the easiest way to ensure a valid stochastic process. That is, <math display="inline">Q_\theta(f(T) | O, T) = \prod _{x \in T} Q_\theta(f(x) | O, x)</math>. Moreover, this framework can be extended to non-factored distributions.<br />
<br />
In detail, the following architecture is used<br />
<br />
<math display="inline">r_i = h_\theta(x_i, y_i)</math> &forall; <math display="inline">(x_i, y_i) \in O</math>, where <math display="inline">h_\theta : X \times Y \to \mathbb{R} ^ d</math><br />
<br />
<math display="inline">r = r_i * r_2 * ... * r_n</math>, where <math display="inline">*</math> is a commutative operation that takes elements in <math display="inline">\mathbb{R}^d</math> and maps them into a single element of <math display="inline">\mathbb{R} ^ d</math><br />
<br />
<math display="inline">\Phi_i = g_\theta</math> &forall; <math display="inline">x_i \in T</math>, where <math display="inline">g_\theta : X \times \mathbb{R} ^ d \to \mathbb{R} ^ e</math> and <math display="inline">\Phi_i</math> are parameters for <math display="inline">Q_\theta</math><br />
<br />
Note that this architecture ensures permutation invariance and <math display="inline">O(n + m)</math> scaling for conditional prediction. Also, <math display="inline">r = r_i * r_2 * ... * r_n</math> can be computed in <math display="inline">O(n)</math>, this architecture supports streaming observation with minimal overhead.<br />
<br />
We train <math display="inline">Q_\theta</math> by asking it to predict <math display="inline">O</math> conditioned on a randomly<br />
chosen subset of <math display="inline">O</math>. This gives the model a signal of the uncertainty over the space X inherent in the distribution<br />
P given a set of observations. The authors let <math display="inline"> f \sim P</math>, <math display="inline"> O = \{(x_i, y_i)\}_{i = 0} ^{n-1}</math>, and N ~ uniform[0, 1, ..... ,n-1]. Subset <math display="inline"> O = \{(x_i, y_i)\}_{i = 0} ^{N}</math> that is first N elements of <math display="inline">O</math> is regarded as condition. The negative conditional log probability is given by<br />
\[\mathcal{L}(\theta)=-\mathbb{E}_{f \sim p}[\mathbb{E}_{N}[\log Q_\theta(\{y_i\}_{i = 0} ^{n-1}|O_{N}, \{x_i\}_{i = 0} ^{n-1})]]\]<br />
Thus, the targets it scores <math display="inline">Q_\theta</math> on include both the observed <br />
and unobserved values. In practice, Monte Carlo estimates of the gradient of this loss is taken by sampling <math display="inline">f</math> and <math display="inline">N</math>. <br />
<br />
This approach shifts the burden of imposing prior knowledge from an analytic prior to empirical data. This has the advantage of liberating a practitioner from having to specify an analytic form for the prior, which is ultimately<br />
intended to summarize their empirical experience. Still, we emphasize that the <math display="inline">Q_\theta</math> are not necessarily a consistent set of conditionals for all observation sets, and the training routine does not guarantee that.<br />
<br />
In summary,<br />
<br />
1. A CNP is a conditional distribution over functions<br />
trained to model the empirical conditional distributions<br />
of functions <math display="inline">f \sim P</math>.<br />
<br />
2. A CNP is permutation invariant in <math display="inline">O</math> and <math display="inline">T</math>.<br />
<br />
3. A CNP is scalable, achieving a running time complexity<br />
of <math display="inline">O(n + m)</math> for making <math display="inline">m</math> predictions with <math display="inline">n</math><br />
observations.<br />
<br />
== Related Work ==<br />
<br />
===Gaussian Process Framework===<br />
<br />
A Gaussian Process (GP) is a non-parametric method for regression, used extensively for regression and classification problems in the machine learning community. A GP is defined as a collection of random variables, any finite number of which have a joint Gaussian distribution.<br />
A standard approach is to model data as <math>y = m(X, φ) + \epsilon</math><br />
where m is the mean function with parameter vector <math>φ</math>, and <math>\epsilon</math> represents independent and identically distributed (i.i.d.) Gaussian noise: <math>N\sim (0,\sigma^2)</math><br />
<br />
For more info on Gaussian Process Framework:<br />
[https://arxiv.org/abs/1506.07304 A Gaussian process framework for modeling instrumental systematics: application to transmission spectroscopy]<br />
<br />
Several papers attempt to address various issues with GPs. These include:<br />
* Using sparse GPs to aid in scaling (Snelson & Ghahramani, 2006)<br />
* Using Deep GPs to achieve more expressiveness (Damianou & Lawrence, 2013; Salimbeni & Deisenroth, 2017)<br />
* Using neural networks to learn more expressive kernels (Wilson et al., 2016)<br />
<br />
A Python resource for Gaussian Process Framework implementation: [https://github.com/SheffieldML/GPyimplementation Gaussian Process Framework in Python]<br />
<br />
<br />
The goal of this paper is to incorporate ideas from standard neural networks with Gaussian processes in order to overcome drawbacks of both. Bayesian techniques work better with less data, but complex Bayesian networks become intractable on even moderate sized data sizes. NNs on the other hand, cannot make use of prior knowledge and often have to be retrained from scratch. Without sufficient data, they also perform poorly. Combining both frameworks, we get Conditional Neural Processes serves to learn the kernels of the Gaussian Process through neural networks and uses these learned kernels on a framework similar to GPs for prediction.<br />
<br />
===Meta Learning===<br />
<br />
Meta-Learning attempts to allow neural networks to learn more generalizable functions, as opposed to only approximating one function. This can be done by learning deep generative models which can do few-shot estimations of data. This can be implemented with attention mechanisms (Reed et al., 2017) or additional memory units in a VAE model (Bornschein et al., 2017). Another successful latent variable approach is to explicitly condition on some context during inference (J. Rezende et al., 2016). Given the generative nature of these models they are usually applied to image generation tasks, but models that include a conditioning class-variable can be used for classification as well. Recently meta-learning has also been applied to a wide range of tasks like RL (Wang et al., 2016; Finn et al., 2017) or program induction (Devlin et al., 2017).<br />
<br />
Classification is another common task in meta-learning, few-shot classification algorithms usually rely on some distance metric in feature space to compare target images and the observations (Koch et al., 2015), (Santoro et al., 2016).. Matching networks(Vinyals et al., 2016; Bartunov & Vetrov, 2016) are closely related to CNPs. In their case features of samples are compared with target features using an attention kernel. At a higher level one can interpret this model as a CNP where the aggregator is just the concatenation over all input samples and the decoder <math>g</math> contains an explicitly defined distance kernel. In this sense matching networks are closer to GPs than to CNPs, since they require the specification of a distance kernel that CNPs learn from the data instead. In addition, as MNs carry out all- to-all comparisons they scale with <math> O(n × m) </math>, although they can be modified to have the same complexity of <math>O(n + m)</math> as CNPs (Snell et al., 2017).<br />
<br />
Another field in the meta-learning field is Neural architecture search. It requires the search algorithm to define three things: the search space, search strategy, and performance evaluation strategy. It is one of the most popular trends in the meta-learning field now. The idea is we can define some search space, and let algorithms help us decide what architecture and hyperparameters would be best for a particular task. Also, since evaluating a neural network is expensive(needs train the neural network first), it needs a well designed performance evaluation strategy to lower down the computational cost<br />
<br />
A model that is conceptually very similar to CNPs (and in particular the latent variable version) is the “neural statistician” paper (Edwards & Storkey, 2016) and the related variational homoencoder (Hewitt et al., 2018). As with the<br />
other generative models the neural statistician learns to estimate the density of the observed data but does not allow for targeted sampling at what we have been referring to as input positions <math>x_i</math>. Instead, one can only generate i.i.d. samples from the estimated density. Finally, the latest variant of Conditional Neural Process can also be seen as an approximated amortized version of Bayesian DL(Gal & Ghahramani, 2016; Blundell et al., 2015; Louizos et al., 2017; Louizos & Welling, 2017). For example, Gal & Ghahramani 2016 develop a new theoretical framework casting dropout training in deep neural networks as approximate Bayesian inference in deep Gaussian processes. Their theory extracts information from existing models and gives us tools to model uncertainty.<br />
<br />
== Experimental Result I: Function Regression ==<br />
<br />
Classical 1D regression task that used as a common baseline for GP is the first example. <br />
They generated two different datasets that consisted of functions<br />
generated from a GP with an exponential kernel. In the first dataset they used a kernel with fixed parameters, and in the second dataset, the function switched at some random point. on the real line between two functions, each sampled with<br />
different kernel parameters. At every training step, they sampled a curve from the GP, select<br />
a subset of n points as observations, and a subset of t points as target points. Using the model, the observed points are encoded using a three-layer MLP encoder h with a 128-dimensional output representation. The representations are aggregated into a single representation<br />
<math display="inline">r = \frac{1}{n} \sum r_i</math><br />
, which is concatenated to <math display="inline">x_t</math> and passed to a decoder g consisting of a five layer<br />
MLP. The function outputs a Gaussian mean and variance for the target outputs. The model is trained to maximize the log-likelihood of the target points using the Adam optimizer. <br />
<br />
Two examples of the regression results obtained for each<br />
of the datasets are shown in the following figure.<br />
<br />
[[File:007.jpg|300px|center]]<br />
<br />
They compared the model to the predictions generated by a GP with the correct<br />
hyperparameters, which constitutes an upper bound on our<br />
performance. Although the prediction generated by the GP<br />
is smoother than the CNP's prediction both for the mean<br />
and variance, the model is able to learn to regress from a few<br />
context points for both the fixed kernels and switching kernels.<br />
As the number of context points grows, the accuracy<br />
of the model improves and the approximated uncertainty<br />
of the model decreases. Crucially, we see the model learns<br />
to estimate its own uncertainty given the observations very<br />
accurately. Nonetheless, it provides a good approximation<br />
that increases in accuracy as the number of context points<br />
increases.<br />
Furthermore, the model achieves similarly good performance<br />
on the switching kernel task. This type of regression task<br />
is not trivial for GPs whereas in our case we only have to<br />
change the dataset used for training<br />
<br />
== Experimental Result II: Image Completion for Digits ==<br />
<br />
[[File:002.jpg|600px|center]]<br />
<br />
They also tested CNP on the MNIST dataset and use the test<br />
set to evaluate its performance. As shown in the above figure the<br />
model learns to make good predictions of the underlying<br />
digit even for a small number of context points. Crucially,<br />
when conditioned only on one non-informative context point the model’s prediction corresponds<br />
to the average overall MNIST digits. As the number<br />
of context points increases the predictions become more<br />
similar to the underlying ground truth. This demonstrates<br />
the model’s capacity to extract dataset specific prior knowledge.<br />
It is worth mentioning that even with a complete set<br />
of observations, the model does not achieve pixel-perfect<br />
reconstruction, as we have a bottleneck at the representation<br />
level.<br />
Since this implementation of CNP returns factored outputs,<br />
the best prediction it can produce given limited context<br />
information is to average over all possible predictions that<br />
agree with the context. An alternative to this is to add<br />
latent variables in the model such that they can be sampled<br />
conditioned on the context to produce predictions with high<br />
probability in the data distribution. <br />
<br />
<br />
An important aspect of the model is its ability to estimate<br />
the uncertainty of the prediction. As shown in the bottom<br />
row of the above figure, as they added more observations, the variance<br />
shifts from being almost uniformly spread over the digit<br />
positions to being localized around areas that are specific<br />
to the underlying digit, specifically its edges. Being able to<br />
model the uncertainty given some context can be helpful for<br />
many tasks. One example is active exploration, where the<br />
model has a choice over where to observe.<br />
They tested this by<br />
comparing the predictions of CNP when the observations<br />
are chosen according to uncertainty, versus random pixels. This method is a very simple way of doing active<br />
exploration, but it already produces better prediction results<br />
then selecting the conditioning points at random.<br />
<br />
== Experimental Result III: Image Completion for Faces ==<br />
<br />
<br />
[[File:003.jpg|400px|center]]<br />
<br />
<br />
They also applied CNP to CelebA, a dataset of images of<br />
celebrity faces and reported performance obtained on the<br />
test set.<br />
<br />
As shown in the above figure our model is able to capture<br />
the complex shapes and colors of this dataset with predictions<br />
conditioned on less than 10% of the pixels being<br />
already close to the ground truth. As before, given a few contexts<br />
points the model averages over all possible faces, but as<br />
the number of context pairs increases the predictions capture<br />
image-specific details like face orientation and facial<br />
expression. Furthermore, as the number of context points<br />
increases the variance is shifted towards the edges in the<br />
image.<br />
<br />
[[File:004.jpg|400px|center]]<br />
<br />
An important aspect of CNPs demonstrated in the above figure is<br />
it's flexibility not only in the number of observations and<br />
targets it receives but also with regards to their input values.<br />
It is interesting to compare this property to GPs on one hand,<br />
and to trained generative models (van den Oord et al., 2016;<br />
Gregor et al., 2015) on the other hand.<br />
The first type of flexibility can be seen when conditioning on<br />
subsets that the model has not encountered during training.<br />
Consider conditioning the model on one half of the image,<br />
fox example. This forces the model to not only predict the pixel<br />
values according to some stationary smoothness property of<br />
the images, but also according to global spatial properties,<br />
e.g. symmetry and the relative location of different parts of<br />
faces. As seen in the first row of the figure, CNPs are able to<br />
capture those properties. A GP with a stationary kernel cannot<br />
capture this, and in the absence of observations would<br />
revert to its mean (the mean itself can be non-stationary but<br />
usually, this would not be enough to capture the interesting<br />
properties).<br />
<br />
In addition, the model is flexible with regards to the target<br />
input values. This means, e.g., we can query the model<br />
at resolutions it has not seen during training. We take a<br />
model that has only been trained using pixel coordinates of<br />
a specific resolution and predict at test time subpixel values<br />
for targets between the original coordinates. As shown in<br />
Figure 5, with one forward pass we can query the model at<br />
different resolutions. While GPs also exhibit this type of<br />
flexibility, it is not the case for trained generative models,<br />
which can only predict values for the pixel coordinates on<br />
which they were trained. In this sense, CNPs capture the best<br />
of both worlds – it is flexible in regards to the conditioning<br />
and prediction task and has the capacity to extract domain<br />
knowledge from a training set.<br />
<br />
[[File:010.jpg|400px|center]]<br />
<br />
<br />
They compared CNPs quantitatively to two related models:<br />
kNNs and GPs. As shown in the above table CNPs outperform<br />
the latter when a number of context points are small (empirically<br />
when half of the image or less is provided as context).<br />
When the majority of the image is given as context exact<br />
methods like GPs and kNN will perform better. From the table<br />
we can also see that the order in which the context points<br />
are provided is less important for CNPs, since providing the<br />
context points in order from top to bottom still results in<br />
good performance. Both insights point to the fact that CNPs<br />
learn a data-specific ‘prior’ that will generate good samples<br />
even when the number of context points is very small.<br />
<br />
== Experimental Result IV: Classification ==<br />
Finally, they applied the model to one-shot classification using the Omniglot dataset. This dataset consists of 1,623 classes of characters from 50 different alphabets. Each class has only 20 examples and as such this dataset is particularly suitable for few-shot learning algorithms. The authors used 1,200 randomly selected classes as their training set and the remainder as the testing data set.<br />
<br />
Additionally, to apply data augmentation the authors cropped the image from 32 × 32 to 28 × 28, applied small random<br />
translations and rotations to the inputs, and also increased<br />
the number of classes by rotating every character by 90<br />
degrees and defining that to be a new class. They generated<br />
the labels for an N-way classification task by choosing N<br />
random classes at each training step and arbitrarily assigning<br />
the labels 0, ..., N − 1 to each.<br />
<br />
<br />
[[File:008.jpg|400px|center]]<br />
<br />
Given that the input points are images, they modified the architecture<br />
of the encoder h to include convolution layers as<br />
mentioned in section 2. In addition, they only aggregated over<br />
inputs of the same class by using the information provided<br />
by the input label. The aggregated class-specific representations<br />
are then concatenated to form the final representation.<br />
Given that both the size of the class-specific representations<br />
and the number of classes is constant, the size of the final<br />
representation is still constant and thus the O(n + m)<br />
runtime still holds.<br />
The results of the classification are summarized in the following table<br />
CNPs achieve higher accuracy than models that are significantly<br />
more complex (like MANN). While CNPs do not<br />
beat state of the art for one-shot classification our accuracy<br />
values are comparable. Crucially, they reached those values<br />
using a significantly simpler architecture (three convolutional<br />
layers for the encoder and a three-layer MLP for the<br />
decoder) and with a lower runtime of O(n + m) at test time<br />
as opposed to O(nm)<br />
<br />
== Conclusion ==<br />
<br />
The paper introduced Conditional Neural Processes,<br />
a model that is both flexible at test time and has the<br />
capacity to extract prior knowledge from training data.<br />
<br />
The authors had demonstrated its ability to perform a variety of tasks<br />
including regression, classification and image completion.<br />
The paper compared CNP's to Gaussian Processes on one hand, and<br />
deep learning methods on the other, and also discussed the<br />
relation to meta-learning and few-shot learning.<br />
It is important to note that the specific CNP implementations<br />
described here are just simple proofs-of-concept and can<br />
be substantially extended, e.g. by including more elaborate<br />
architectures in line with modern deep learning advances.<br />
To summarize, this work can be seen as a step towards learning<br />
high-level abstractions, one of the grand challenges of<br />
contemporary machine learning. Functions learned by most<br />
Conditional Neural Processes<br />
conventional deep learning models are tied to a specific, constrained<br />
statistical context at any stage of training. A trained<br />
CNP is more general, in that it encapsulates the high-level<br />
statistics of a family of functions. As such it constitutes a<br />
high-level abstraction that can be reused for multiple tasks.<br />
In future work, they are going to explore how far these models can<br />
help in tackling the many key machine learning problems<br />
that seem to hinge on abstraction, such as transfer learning,<br />
meta-learning, and data efficiency.<br />
<br />
== Critiques ==<br />
<br />
This paper introduces a method, for reducing the computational complexity of the more famous Gaussian Processes model, but they have mentioned a complexity of O(n + m) which is almost the same order of RBF kernel GP. With respect to performances in a sequence of tasks, the authors have not made metric comparisons to GP methods to prove the superiority of their approach.<br />
<br />
It appears that the proposed model is effective in making accurate predictions using lower quality inputs. For example, a dataset with fewer data points or an image with fewer pixels. However, it is not clear whether the proposed algorithm can be trained with a smaller amount of input data.<br />
<br />
== Other Sources ==<br />
# Code for this model and a simpler explanation can be found at [https://github.com/deepmind/conditional-neural-process]<br />
# A newer version of the model is described in this paper [https://arxiv.org/pdf/1807.01622.pdf]<br />
# A good blog post on neural processes [https://kasparmartens.rbind.io/post/np/]<br />
<br />
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2013.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Learning_to_Teach&diff=42080Learning to Teach2018-11-30T16:33:20Z<p>R82zhang: [T] /*Add Critique about action space of teacher model and generalization */</p>
<hr />
<div><br />
<br />
=Introduction=<br />
<br />
This paper proposed the "learning to teach" (L2T) framework with two intelligent agents: a student model/agent, corresponding to the learner in traditional machine learning algorithms, and a teacher model/agent, determining the appropriate data, loss function, and hypothesis space to facilitate the learning of the student model.<br />
<br />
In modern human society, the role of teaching is heavily implicated in our education system; the goal is to equip students with the necessary knowledge and skills in an efficient manner. This is the fundamental ''student'' and ''teacher'' framework on which education stands. However, in the field of artificial intelligence (AI) and specifically machine learning, researchers have focused most of their efforts on the ''student'' (ie. designing various optimization algorithms to enhance the learning ability of intelligent agents). The paper argues that a formal study on the role of ‘teaching’ in AI is required. Analogous to teaching in human society, the teaching framework can: select training data that corresponds to the appropriate teaching materials (e.g. textbooks selected for the right difficulty), design loss functions that correspond to targeted examinations, and define the hypothesis space that corresponds to imparting the proper methodologies. Furthermore, an optimization framework (instead of heuristics) should be used to update the teaching skills based on the feedback from students, so as to achieve teacher-student co-evolution.<br />
<br />
Thus, the training phase of L2T would have several episodes of interactions between the teacher and the student model. Based on the state information in each step, the teacher model would update the teaching actions so that the student model could perform better on the Machine Learning problem. The student model would then provide reward signals back to the teacher model. These reward signals are used by the teacher model as part of the Reinforcement Learning process to update its parameters. This process is end-to-end trainable and the authors are convinced that once converged, the teacher model could be applied to new learning scenarios and even new students, without extra efforts on re-training.<br />
<br />
To demonstrate the practical value of the proposed approach, the '''training data scheduling''' problem is chosen as an example. The authors show that by using the proposed method to adaptively select the most<br />
suitable training data, they can significantly improve the accuracy and convergence speed of various neural networks including multi-layer perceptron (MLP), convolutional neural networks (CNNs)<br />
and recurrent neural networks (RNNs), for different applications including image classification and text understanding.<br />
Further more , the teacher model obtained by the paper from one task can be smoothly transferred to other tasks. As an example, the teacher model trained on MNIST with the MLP learner, one can achieve a satisfactory performance on CIFAR-10 only using roughly half<br />
of the training data to train a ResNet model as the student.<br />
<br />
=Related Work=<br />
The L2T framework connects with two emerging trends in machine learning. The first is the movement from simple to advanced learning. This includes meta-learning (Schmidhuber, 1987; Thrun & Pratt, 2012) which explores automatic learning by transferring learned knowledge from meta tasks [1]. This approach has been applied to few-shot learning scenarios and in designing general optimizers and neural network architectures. (Hochreiter et al., 2001; Andrychowicz et al., 2016; Li & Malik, 2016; Zoph & Le, 2017)<br />
<br />
The second is the teaching, which can be classified into either machine-teaching (Zhu, 2015) [2] or hardness based methods. The former seeks to construct a minimal training set for the student to learn a target model (ie. an oracle). The latter assumes an order of data from easy instances to hard ones, hardness being determined in different ways. In curriculum learning (CL) (Bengio et al, 2009; Spitkovsky et al. 2010; Tsvetkov et al, 2016) [3] measures hardness through heuristics of the data while self-paced learning (SPL) (Kumar et al., 2010; Lee & Grauman, 2011; Jiang et al., 2014; Supancic & Ramanan, 2013) [4] measures hardness by loss on data. <br />
<br />
The limitations of these works include the lack of a formally defined teaching problem, and the reliance on heuristics and fixed rules, which hinders generalization of the teaching task.<br />
<br />
=Learning to Teach=<br />
To introduce the problem and framework, without loss of generality, consider the setting of supervised learning.<br />
<br />
In supervised learning, each sample <math>x</math> is from a fixed but unknown distribution <math>P(x)</math>, and the corresponding label <math> y </math> is from a fixed but unknown distribution <math>P(y|x) </math>. The goal is to find a function <math>f_\omega(x)</math> with parameter vector <math>\omega</math> that minimizes the gap between the predicted label and the actual label.<br />
<br />
<br />
<br />
==Problem Definition==<br />
The student model, denoted &mu;(), takes the set of training data <math> D </math>, the function class <math> Ω </math>, and loss function <math> L </math> as input to output a function, <math> f(ω) </math>, with parameter <math>ω^*</math> which minimizes risk <math>R(ω)</math> as in:<br />
<br />
\begin{align*}<br />
ω^* = arg min_{w \in \Omega} \sum_{x,y \in D} L(y, f_ω(x)) =: \mu (D, L, \Omega)<br />
\end{align*}<br />
<br />
The teaching model, denoted φ, tries to provide <math> D </math>, <math> L </math>, and <math> Ω </math> (or any combination, denoted <math> A </math>) to the student model such that the student model either achieves lower risk R(ω) or progresses as fast as possible.<br />
In contrast to traditional machine learning, which is only concerned with the student model in the<br />
learning to teach framework, the problem in the paper is also concerned with a teacher model, which tries to provide<br />
appropriate inputs to the student model so that it can achieve low risk functional as efficiently<br />
as possible.<br />
<br />
<br />
::'''Training Data''': Outputting a good training set <math> D </math>, analogous to human teachers providing students with proper learning materials such as textbooks.<br />
::'''Loss Function''': Designing a good loss function <math> L </math> , analogous to providing useful assessment criteria for students.<br />
::'''Hypothesis Space''': Defining a good function class <math> Ω </math> which the student model can select from. This is analogous to human teachers providing appropriate context, eg. middle school students taught math with basic algebra while undergraduate students are taught with calculus. Different Ω leads to different errors and optimization problem (Mohri et al., 2012).<br />
<br />
==Framework==<br />
The training phase consists of the teacher providing the student with the subset <math> A_{train} </math> of <math> A </math> and then taking feedback to improve its own parameters.After the convergence of the training process,<br />
the teacher model can be used to teach either<br />
new student models, or the same student<br />
models in new learning scenarios such as another<br />
subset <math> A_{test} </math>is provided.Such a generalization is feasible as long as the state representations<br />
S are the same across different student<br />
models and different scenarios. The L2T process is outlined in figure below:<br />
<br />
[[File: L2T_process.png | 500px|center]]<br />
<br />
* <math> s_t &isin; S </math> represents information available to the teacher model at time <math> t </math>. <math> s_t </math> is typically constructed from the current student model <math> f_{t−1} </math> and the past teaching history of the teacher model. <math> S </math> represents the set of states.<br />
* <math> a_t &isin; A </math> represents action taken the teacher model at time <math> t </math>, given state <math>s_t</math>. <math> A </math> represents the set of actions, where the action(s) can be any combination of teaching tasks involving the training data, loss function, and hypothesis space. <br />
* <math> φ_θ : S → A </math> is policy used by the teacher model to generate its action <math> φ_θ(s_t) = a_t </math><br />
* Student model takes <math> a_t </math> as input and outputs function <math> f_t </math>, by using the conventional ML techniques.<br />
<br />
Once the training process converges, the teacher model may be utilized to teach a different subset of <math> A </math> or teach a different student model.<br />
<br />
=Application=<br />
<br />
There are different approaches to training the teacher model, this paper will apply reinforcement learning with <math> φ_θ </math> being the ''policy'' that interacts with <math> S </math>, the ''environment''. The paper applies data teaching to train a deep neural network student, <math> f </math>, for several classification tasks. Thus the student feedback measure will be classification accuracy. Its learning rule will be mini-batch stochastic gradient descent, where batches of data will arrive sequentially in random order. The teacher model is responsible for providing the training data, which in this case means it must determine which instances (subset) of the mini-batch of data will be fed to the student. In order to reach the convergence faster, the reward was set to relate to the speed the student model learns. <br />
<br />
The authors also designed a state feature vector <math> g(s) </math> in order to efficiently represent the current states which include arrived training data and the student model. Within the State Features, there are three categories including Data features, student model features and the combination of both data and learner model. This state feature will be computed when each mini-batch of data arrives.<br />
<br />
<br />
The optimizer for training the teacher model is the maximum expected reward: <br />
<br />
\begin{align} <br />
J(θ) = E_{φ_θ(a|s)}[R(s,a)]<br />
\end{align}<br />
<br />
Which is non-differentiable w.r.t. <math> θ </math>, thus a likelihood ratio policy gradient algorithm is used to optimize <math> J(θ) </math> (Williams, 1992) [4]<br />
<br />
==Experiments==<br />
<br />
The L2T framework is tested on the following student models: multi-layer perceptron (MLP), ResNet (CNN), and Long-Short-Term-Memory network (RNN). <br />
<br />
The student tasks are Image classification for MNIST, for CIFAR-10, and sentiment classification for IMDB movie review dataset. <br />
<br />
The strategy will be benchmarked against the following teaching strategies:<br />
<br />
::'''NoTeach''': NoTeach removes the entire Teacher-Student paradigm and reverts back to the classical machine learning paradigm. In the context of data teaching, we consider the architecture fixed, and feed data in a pre-determined way. One would pre-define batch-size and cross-validation procedures as needed.<br />
::'''Self-Paced Learning (SPL)''': Teaching by ''hardness'' of data, defined as the loss. This strategy begins by filtering out data with larger loss value to train the student with "easy" data and gradually increases the hardness. Mathematically speaking, those training data <math>d </math> satisfying loss value <math>l(d) > \eta </math> will be filtered out, where the threshold <math> \eta </math> grows from smaller to larger during the training process. To improve the robustness of SPL, following the widely used trick in common SPL implementation (Jiang et al., 2014b), the authors filter training data using its loss rank in one mini-batch rather than the absolute loss value: they filter data instances with top <math>K </math>largest training loss values within a <math>M</math>-sized mini-batch, where <math>K</math> linearly drops from <math>M − 1 </math>to 0 during training.<br />
<br />
::'''L2T''': The Learning to Teach framework.<br />
::'''RandTeach''': Randomly filter data in each epoch according to the logged ratio of filtered data instances per epoch (as opposed to deliberate and dynamic filtering by L2T).<br />
<br />
For all teaching strategies, they make sure that the base neural network model will not be updated until <math>M </math> un-trained, yet selected data instances are accumulated. That is to guarantee that the convergence speed is only determined by the quality of taught data, not by different model updating frequencies. The model is implemented with Theano and run on one NVIDIA Tesla K40 GPU for each training/testing process.<br />
===Training a New Student===<br />
<br />
In the first set of experiments, the datasets or divided into two folds. The first folder is used to train the teacher; This is done by having the teacher train a student network on that half of the data, with a certain portion being used for computing rewards. After training, the teacher parameters are fixed, and used to train a new student network (with the same structure) on the second half of the dataset. When teaching a new student with the same model architecture, we observe that L2T achieves significantly faster convergence than other strategies across all tasks, especially compared to the NoTeach and RandTeach methods:<br />
<br />
[[File: L2T_speed.png | 1100px|center]]<br />
<br />
===Filtration Number===<br />
<br />
When investigating the details of filtered data instances per epoch, for the two image classification tasks, the L2T teacher filters an increasing amount of data as training goes on. The authors' intuition for the two image classification tasks is that the student model can learn from harder instances of data from the beginning, and thus the teacher can filter redundant data. In contrast, for training while for the natural language task, the student model must first learn from easy data instances.<br />
<br />
[[File: L2T_fig3.png | 1100px|center]]<br />
<br />
===Teaching New Student with Different Model Architecture===<br />
<br />
In this part, first a teacher model is trained by interacting with a student model. Then using the teacher model, another student model<br />
which has a different model architecture is taught.<br />
The results of Applying the teacher trained on ResNet32 to teach other architectures is shown below. The L2T algorithm can be seen to obtain higher accuracies earlier than the SPL, RandTeach, or NoTeach algorithms.<br />
<br />
[[File: L2T_fig4.png | 1100px|center]]<br />
<br />
===Training Time Analysis===<br />
<br />
The learning curves demonstrate the efficiency in accuracy achieved by the L2T over the other strategies. This is especially evident during the earlier training stages.<br />
<br />
[[File: L2T_fig5.png | 600px|center]]<br />
<br />
===Accuracy Improvement===<br />
<br />
When comparing training accuracy on the IMDB sentiment classification task, L2T improves on teaching policy over NoTeach and SPL.<br />
<br />
[[File: L2T_t1.png | 500px|center]]<br />
<br />
Table 1 shows that we boost the convergence speed, while the teacher model improves final accuracy. The student model is the LSTM network trained on IMDB. Prior to teaching the student model, we train the teacher model on half of the training data, and define the terminal reward as the set accuracy after the teacher model trains the student for 15 epochs. Then the teacher model is applied to train the student model on the full dataset till its convergence. The state features are kept the same as those in previous experiments. We can see that L2T achieves better classification accuracy for training LSTM network, surpassing the SPL baseline by more than 0.6 point (with p value < 0.001).<br />
<br />
=Future Work=<br />
<br />
There is some useful future work that can be extended from this work: <br />
<br />
1) Recent advances in multi-agent reinforcement learning could be tried on the Reinforcement Learning problem formulation of this paper. <br />
<br />
2) Some human in the loop architectures like CHAT and HAT (https://www.ijcai.org/proceedings/2017/0422.pdf) should give better results for the same framework. <br />
<br />
3) It would be interesting to try out the framework suggested in this paper (L2T) in Imperfect information and partially observable settings. <br />
<br />
4) As they have focused on data teaching exploring loss function teaching would be interesting.<br />
<br />
=Critique=<br />
<br />
While the conceptual framework of L2T is sound, the paper only experimentally demonstrates efficacy for ''data teaching'' which would seem to be the simplest to implement. The feasibility and effectiveness of teaching the loss function and hypothesis space are not explored in a real-world scenario. Also, this paper does not provide enough mathematical foundation to prove that this model can be generalized to other datasets and other general problems. The method presented here where the teacher model filters data does not seem to provide enough action space for the teacher model. Furthermore, the experimental results for data teaching suggest that the speed of convergence is the main improvement over other teaching strategies whereas the difference in accuracy less remarkable. The paper also assesses accuracy only by comparing L2T with NoTeach and SPL on the IMDB classification task, the improvement (or lack thereof) on the other classification tasks and teaching strategies is omitted. Again, this distinction is not possible to assess in loss function or hypothesis space teaching within the scope of this paper. They could have included larger datasets such as ImageNet and CIFAR100 in their experiments which would have provided some more insight.<br />
<br />
The idea of having a generalizable teacher model to enhance student learning is admirable. In fact, the L2T framework is similar to the reinforcement learning actor-critic model, which is known to be effective. In general, one expects an effective teacher model would facilitate transfer learning and can significantly reduce student model training time. However, the T2L framework seems to fall short of that goal. Consider the CIFAR10 training scenario, the L2T model achieve 85% accuracy after 2 million training data, which is only about 3% more accuracy than a no-teacher model. Perhaps in the future, the L2T framework can improve and produce better performance.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Pixels_to_Graphs_by_Associative_Embedding&diff=42078Pixels to Graphs by Associative Embedding2018-11-30T16:28:21Z<p>R82zhang: [E] Grammar fixes</p>
<hr />
<div>== Introduction == <br />
The paper presents a novel approach to generating a scene graph. A scene graph, as it relates to an image, is a graph with a vertex that represents each object identified in the image and an edge that represents relationships between the objects. <br />
<br />
An example of a scene graph:<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Scene Graph.PNG]]</div><br />
<br />
Current state-of-the-art techniques break down the construction of scene graphs by first identifying objects and then predicting the edges for any given pair of identified objects. By using this technique, reasoning over<br />
the full graph would be limited. On the other hand, this paper introduces an architecture that defines the entire graph directly from the image, enabling the network to reason across the entirety of the image to understand relationships, as opposed to only predicting relationships using object labels. <br />
<br />
A key concern, given that the new architecture produces both vertices (objects) and edges (relationships), is connecting the two. Specifically, the output of the network is some set of relationships E, and some set of vertices V. The network needs to also output the “source” and “destination” of each relationship, so that the final graph can be formed. In the image above, for example, the network would also need to tell us that “holding” comes from “person” and goes to “Frisbee”. To do this, the paper uses associative embeddings. Specifically, the network outputs a particular “embedding vector” for each vertex, as well as a “source embedding” and “destination embedding” for each relationship. A final post-processing step finds the vertex embedding closest to each of the source/destination embeddings of each relationship and in this way assigns the edges to pairs of vertices.<br />
<br />
== Previous Work == <br />
<br />
In the field of relationship detection, the following are the existing state of the art advances:<br />
<br />
1) Framing the task of identifying objects using localization from referential expressions, detection of human-object interactions, or the more general tasks of Visual Relationship Detection (VRD) and scene graph generation. <br />
<br />
2) Visual relationship detection methods like message passing RNNs and predicting over triplets of bounding boxes. <br />
<br />
In the field of associative embedding, the following are some interesting applications: <br />
<br />
1) Vector embeddings to group together body joints for multi-person pose estimation. <br />
<br />
2) Vector embeddings to detect body joints of the various people in an image.<br />
<br />
<br />
Reference Figure from the paper "Associative embedding: End-to-end learning for joint detection and grouping."<br />
<br />
[[File:Oct30_associative_embedding_appendix_fig2.jpg | center]]<br />
<br />
<br />
== Pixels To Graphs == <br />
The goal of the paper is to construct a graph from a set of pixels. In particular, to construct a graph<br />
grounded in the space of these pixels. Meaning that in addition to identifying vertices of the graph,<br />
we want to know their precise locations. A vertex, in this case, can refer to any object of interest in the<br />
scene including people, cars, clothing, and buildings. The relationships between these objects is then<br />
captured by the edges of the graph. These relationships may include verbs (eating, riding), spatial<br />
relations (on the left of, behind), and comparisons (smaller than, same color as).<br />
<br />
Formally we consider a directed graph G = (V, E). A given vertex vi ∈ V is grounded at a location (<math>xi</math><br />
,<math>yi</math>) and defined by its class and bounding box. Each edge e ∈ E takes the form<br />
ei = (<math>vs</math>,<math>vt</math> ,<math>ri</math>) defining a relationship of type <math>r_i</math> from <math>vs</math> to <math>vt</math> . We train a network to explicitly define V and E. This training is done end-to-end on a single network, allowing the network to reason fully over the image and all possible components of the graph when making its predictions<br />
<br />
== The Architecture: == <br />
: '''1. Detecting Graph Elements'''<br />
<br />
Given an image of dimensions h x w, a stacked hourglass (Appendix 2) is used to generate a h x w x f representation of the image. It should be noted that the dimension of the output (which is non-trainable), needs to fulfill certain criteria. Specifically, we need to have a resolution large enough to minimize the number of pixels with multiple detections while also being small enough to ensure that each 1 x 1 x f vector still contains the information needed for subsequent inference.<br />
<br />
A 1x1 convolution and sigmoid activation is performed on this result to generate a heat map (one for objects and one for relationships, using separately determined convolutions). The value at a given pixel can be interpreted as the likelihood of detection at that particular pixel in the original image. <br />
<br />
In order to claim that there is an element at some pixel, we need to have some likelihood threshold. Then, if a given pixel in the map has a value >= the threshold, we claim that there is an element at that pixel. This threshold is calculated by using binary cross-entropy loss on the final values in the heat map. Values with likelihoods greater than p-hat will be considered element detections. <br />
<br />
Finally, for each element that we detected, we extract the 1 x 1 x f feature vector. This is then used as an input to a set of Feed Forward Neural Networks (FFNNs), where we have a separate network for each characteristic of interest, and for each network, there's one hidden layer with f nodes. The object class and relationship (edges) could be supervised by softmax loss. Furthermore, in order to predict the bounding box of the object, we can use the approach proposed by the Faster-RCNN model[3]. The following image summarizes the process.<br />
<br />
<br />
[[File:Extraction Process.PNG|center]]<br />
<br />
:'''2. Connecting Elements with Associative Embeddings'''<br />
As explained earlier, to construct the scene graph, we need to know the source and destination of each edge. This is done through associative embeddings. <br />
<br />
First, let us define an embedding hi ϵ Rd produced for some vector i, and let us assume that we have n object detections in a particular image. Now, define hik, for k = 1 to Ki (where Ki is the number of edges in the graph with a vertex at vertex i) as the embedding associated with an edge that touches vertex i. We define two loss functions on these sets.<br />
<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Loss 1.PNG]]</div><br />
<br />
The goal of Lpull is to minimize the squared differences between the embedding of a given vertex and the embedding of an edge that references said vertex.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Loss 2.PNG]]</div><br />
<br />
On the other hand, minimizing Lpush implies assigning embeddings to vertices that are as far apart as possible. The further apart they are, the lower the output of max becomes until eventually, it reaches 0. Here, m is just a constant. In the paper, the values used were m = 8 and d = 8 (that is, 8D embeddings). Combining these two loss functions (and weighing them equally), accomplishes the task of predicting embeddings such that vertices are differentiated, but the embedding of a vertex is most similar to the vertex it references.<br />
<br />
:'''3. Support for Overlapping Detections'''<br />
An obvious concern is how the network would operate if there was more than one detection (be it object or relationship), in a given pixel. For example, detection of “shirt” and “person” may be centered at the exact same pixel. To account for this, the architecture is modified to allow for “slots” at each pixel. Specifically, so detections of objects are allowed at a particular pixel, while sr relationship detections are allowed at a given pixel. <br />
<br />
In order to allow for this, some changes are required after the feature extraction step. Specifically, we now use the 1x1xf vector as the input for so (or sr) different sets of 4 FFNNs, where the output (of the first three) is as shown in figure 2, and with the final FFNN outputting the probability of a detection existing in that particular slot, at that particular pixel. This new network is trained exclusively on whether or not a detection has been made in that slot, and, in prediction, is used to determine the number of slots to output at a given pixel. It is critical to note that this each of these so (or sr) sets of FFNNs share absolutely no weights. And each is trained for detection in its assigned slot.<br />
<br />
It is important to note that this implies a change in the training procedure. We now have so (or sr) different predictions (be it class, or class + bounding box), that we need to match with our set of ground truth detections at a given pixel. Without this step, we would not be able to assign a value to the error for that sample. To do this, we match a one-hot encoded vector of the ground-truth class and bounding box anchor (the reference vector), and then match them with the so (or sr) outputs provided at a given pixel. The Hungarian method is used to ensure maximum matching between the outputs and the reference method while ensuring we do not assign the same detection to multiple slots.<br />
<br />
==Results==<br />
A quick note on notation: R@50 indicates what percentage of ground-truth subject-predicate-object tuples appeared in a proposal of 50 such tuples. Since R@100 offers more possibilities, it will necessarily be higher. The 6.7, for example, indicates that 6.7% of the ground truth tuples appeared in the proposals of the network. <br />
<br />
The authors tested the network against two other architectures designed to develop a semantic understanding of images. For this, they used the Visual Genome dataset, with so = 3 and sr = 6. Overall, the new architecture vastly outperformed past models. The results were as follows:<br />
<br />
The table can be interpreted as follows:<br />
<br />
[[File:Results Table.PNG|center|600px]]<br />
<br />
::'''SGGen (no RPN)''': Given a particular image, without the use of Region Proposal networks, the accuracy of the proposed scene graph. No class predictions are provided.<br />
::'''SGGen (with RPN)''': Same as above, except the output of the Region Proposal Network, is used to enhance the input of a given image. No class predictions are provided.<br />
::'''SGCIs''': Ground-truth object bounding boxes are provided. The network is asked to classify them and determine relationships.<br />
::'''PredCIs''': As above, except the classes are also provided. The only goal is to predict relationships.<br />
<br />
Further analysis into the accuracy, when looking at predicates individually, shows that the architecture is very sensitive to over-represented relationship predicates.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Results - Part 2.PNG]]</div><br />
<br />
As shown in Figure 5, for many ground-truth predicates (those that do not appear often in the ground truth), the network does poorly. Even when allowed to propose 100 tuples, the network does not offer the predicate. Figure 4 simply observes the fact that certain sets of relationship predicates appear predominantly in a subset of slots. No general explanation has been offered for this behavior.<br />
<br />
== Conclusion ==<br />
In conclusion, the paper offers a novel approach that enables the extraction of image semantics while perpetually reasoning over the entire context of the image. Associative embeddings are used to connect object and predicate relationships, and parallel “slots” allow for multiple detections in one pixel. While this approach offers noticeable improvements in accuracy, it is clear that work needs to be done to account for the non-uniform distributions of relationships in the dataset.<br />
<br />
<br />
== Critiques ==<br />
<br />
The paper's contributions towards patterning unordered network outputs and using associative embeddings for connecting vertices and edges are commendable. However, it should be noted this paper is only an incremental improvement over existing well-studied architectures like the hourglass architecture. The modifications are not sufficiently supported by mathematical reasoning. The authors say that they make a slight modification to the hourglass design and double the number of features and weight all the loses equally. No scientific justification for why this is needed is given. Also the choice of constants to be 3 and 6 for <math display = "inline"> s_o</math> and <math display = "inline"> s_r</math> is not clear, as the authors leave out a fraction of the cases. I am not sure if the changes made are truly a critical advance as the experiments are conducted only on a single dataset and no generalizability arguments are made by the authors. So the methods might just work well only for this dataset and the changes may pertain to only this one. The theoretical analysis done in the paper comes directly from the hourglass literature and cannot be accounted for novelty.<br />
The paper could have identified the effect of their treatment by analyzing the structure of the network that they are presenting. However, there are lack of mathematical and structural analysis of each treatment that they are presenting in detailed levels.<br />
<br />
== Appendices ==<br />
<br />
'''Appendix 1: Sample Outputs'''<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Sample Pixel Graph Outputs.PNG]]</div><br />
<br />
'''Appendix 2: Stacked Hourglass Architecture'''<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Hourglass.PNG]]</div><br />
<br />
Although this goes beyond the focus of the paper, I would like to add a brief overview of the stacked hourglass architecture used to generate the heat map. This architecture is unique in that it allows cyclical top-down, bottom-up inference and recombination of features. While most architectures focus on optimizing the bottom-up portion (reducing dimensionality), the stacked-hourglass gives the network more flexibility in how it generates a representation by allowing it to learn a series of down-sampling / up-sampling steps.<br />
<br />
When you downsample and then upsample, a high amount of information is potentially lost on the upsampled reconstruction. Using the naive approach, this often results in poor reconstruction. This problem is accentuated when we stack multiple layers of downsampling and upsampling in the stacked hourglass architecture. To alleviate this issue, we add skip layers. Skip layers essentially allow earlier layers to send outputs into multiple later layers. The added information from the earlier layers ensures that the reconstructed embedding doesn't have its dimensionality reduced too much.<br />
<br />
[[File:skip+layers+Max+fusion+made+learning+difficult+due+to+gradient+switching..jpg|center|900px]]<br />
<br />
== References ==<br />
1. Alejandro Newell and Jia Deng, “Pixels to Graphs by Associative Embedding,” in NIPS, 2017<br />
<br />
2. Alejandro Newell, Kaiyu Yang, and Jia Deng. Stacked Hourglass Networks for Human Pose Estimation. ECCV, 2016<br />
<br />
3. Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. NIPS, pages 91–99, 2015.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fairness_Without_Demographics_in_Repeated_Loss_Minimization&diff=42071Fairness Without Demographics in Repeated Loss Minimization2018-11-30T16:19:54Z<p>R82zhang: [T] /*Add Related Works */</p>
<hr />
<div>This page contains the summary of the paper "[http://proceedings.mlr.press/v80/hashimoto18a.html Fairness Without Demographics in Repeated Loss Minimization]" by Hashimoto, T. B., Srivastava, M., Namkoong, H., & Liang, P. which was published at the International Conference of Machine Learning (ICML) in 2018. <br />
<br />
=Introduction=<br />
<br />
Usually, machine learning models are minimized in their average loss to achieve high overall accuracy. While this works well for the majority, minority groups that use the system suffer high error rates because they contribute fewer data to the model. For example, non-native speakers may contribute less to the speech recognizer machine learning model. This phenomenon is known as '''''representation disparity''''' and has been observed in many models that, for instance, recognize faces, or identify the language. This disparity further widens for minority users who suffer higher error rates, as they will lower usage of the system in the future. As a result, minority groups provide even less data for future optimization of the model. With less data points to work with, the disparity becomes even worse - a phenomenon referred to as '''''disparity amplification'''''. <br />
<br />
[[File:fairness_example.JPG|700px|center]]<br />
<br />
In this paper, Hashimoto et al. provide a strategy for controlling the worst case risk amongst all groups. They first show that standard '''''empirical risk minimization (ERM)''''' does not control the loss of minority groups, and thus causes representation disparity . This representation disparity is further amplified over time (even if the model is fair in the beginning). Second, the researchers try to mitigate this unfairness by proposing the use of '''''distributionally robust optimization (DRO)'''''. Indeed, Hashimoto et al. are able to show that DRO can bound the loss for minority groups at every step of time, and is fair for models that ERM turns unfair by applying it to Amazon Mechanical Turk task.<br />
<br />
===Note on Fairness===<br />
<br />
Hashimoto et al. follow the ''difference principle'' to achieve and measure fairness. It is defined as the maximization of the welfare of the worst-off group, rather than the whole group (cf. utilitarianism).<br />
<br />
===Related Works===<br />
The recent advancements on the topic of fairness in Machine learning can be classified into the following approaches:<br />
<br />
1. Rawls Difference principle (Rawls, 2001, p155) - Defines that maximizing the welfare of the worst-off group is fair and stable over time, which increases the chance that minorities will consent to status-quo. The current work builds on this as it sees predictive accuracy as a resource to be allocated.<br />
<br />
2. Labels of minorities present in the data:<br />
* Chouldechova, 2017: Use of race (a protected label) in recidivism protection. This study evaluated the likelihood for a criminal defendant to reoffend at a later time, which assisted with criminal justice decision-making. However, a risk assessment instrument called COMPAS was studied and discovered to be biased against black defendants. As the consequences for misclassification can be dire, fairness regarding using race as a label was studied.<br />
* Barocas & Selbst, 2016: Guaranteeing fairness for a protected label through constraints such as equalized odds, disparate impact, and calibration.<br />
In the case specific to this paper, this information is not present.<br />
<br />
3. Fairness when minority grouping are not present explicitly<br />
* Dwork et al., 2012 used Individual notions of fairness using fixed similarity function whereas Kearns et al., 2018; Hebert-Johnson et al., 2017 used subgroups of a set of protected labels.<br />
* Rawlsian Fairness for Machine Learning, Matthew Joseph, Michael Kearns, Jamie Morgenstern, Seth Neel †Aaron Roth November 1, 2016 <br />
* Kearns et al. (2018); Hebert-Johnson et al. (2017) consider subgroups of a set of protected features.<br />
Again for the specific case in this paper, this is not possible.<br />
<br />
4. Online settings<br />
* Joseph et al., 2016; Jabbari et al., 2017 looked at fairness in bandit learning using algorithms compatible with Rawls’ principle on equality of opportunity.<br />
* Liu et al. (2018) analyzed fairness temporally in the context of constraint-based fairness criteria. It showed that fairness is not ensured over time when static fairness constraints are enforced.<br />
<br />
=Representation Disparity=<br />
<br />
If a user makes a query <math display="inline">Z \sim P</math>, the model <math display="inline">\theta \in \Theta</math> makes a prediction, and the user experiences loss <math display="inline">\ell (\theta; Z)</math>. <br />
<br />
The expected loss of a model <math display="inline">\theta</math> is denoted as the risk <math display="inline">\mathcal{R}(\theta) = \mathbb{E}_{Z \sim P} [\ell (\theta; Z)] </math>. <br />
<br />
If input queries are made by users from <math display="inline">K</math> groups, then the distribution over all queries can be re-written as <math display="inline">Z \sim P := \sum_{k \in [K]} \alpha_kP_k</math>, where <math display="inline">\alpha_k</math> is the population portion of group <math display="inline">k</math> and <math display="inline">P_k</math> is its individual distribution, and we assume these two variables are unknown.<br />
<br />
The risk associated with group <math>k</math> can be written as, <math>\mathcal{R}_k(\theta) := \mathbb{E}_{P_k} [\ell (\theta; Z)]</math>.<br />
<br />
The worst-case risk over all groups can then be defined as,<br />
\begin{align}<br />
\mathcal{R}_{max}(\theta) := \underset{k \in [K]}{max} \mathcal{R}_k(\theta).<br />
\end{align}<br />
<br />
Minimizing this function is equivalent to minimizing the risk for the worst-off group. <br />
<br />
There is high representation disparity if the expected loss of the model <math display="inline">\mathcal{R}(\theta)</math> is low, but the worst-case risk <math display="inline">\mathcal{R}_{max}(\theta)</math> is high. A model with high representation disparity performs well on average (i.e. has low overall loss), but fails to represent some groups <math display="inline">k</math> (i.e. the risk for the worst-off group is high).<br />
<br />
Often, groups are latent and <math display="inline">k, P_k</math> are unknown and the worst-case risks are inaccessible. The technique proposed by Hashimoto et al does not require direct access to these.<br />
<br />
=Disparity Amplification=<br />
<br />
Representation disparity can amplify as time passes and loss is minimized. Over <math display="inline">t = 1, 2, ..., T</math> minimization rounds, the group proportions <math display="inline">\alpha_k^{(t)}</math> are not constant, but vary depending on past losses. <br />
<br />
At each round the expected number of users <math display="inline">\lambda_k^{(t+1)}</math> from group <math display="inline">k</math> is determined by <br />
\begin{align}<br />
\lambda_k^{(t+1)} := \lambda_k^{(t)} \nu(\mathcal{R}_k(\theta^{(t)})) + b_k<br />
\end{align}<br />
<br />
where <math display="inline">\lambda_k^{(t)} \nu(\mathcal{R}_k(\theta^{(t)}))</math> describes the fraction of retained users from the previous optimization, <math>\nu(x)</math> is a function that decreases as <math>x</math> increases, and <math display="inline">b_k</math> is the number of new users of group <math display="inline">k</math>. <br />
<br />
Furthermore, the group proportions <math display="inline">\alpha_k^{(t)}</math>, dependent on past losses is defined as:<br />
\begin{align}<br />
\alpha_k^{(t+1)} := \dfrac{\lambda_k^{(t+1)}}{\sum_{k'\in[K]} \lambda_{k'}^{(t+1)}}<br />
\end{align}<br />
<br />
To put simply, the number of expected users of a group depends on the number of new users of that group and the fraction of users that continue to use the system from the previous optimization step. If fewer users from minority groups return to the model (i.e. the model has a low retention rate of minority group users), Hashimoto et al. argue that the representation disparity amplifies. <br />
<br />
==Empirical Risk Minimization (ERM)==<br />
<br />
Without the knowledge of population proportions <math display="inline">\alpha_k^{(t)}</math>, the new user rate <math display="inline">b_k</math>, and the retention function <math display="inline">\nu</math> it is hard to control the worst-case risk over all time periods <math display="inline">\mathcal{R}_{max}^T</math>. That is why it is the standard approach to fit a sequence of models <math display="inline">\theta^{(t)}</math> by empirically approximating them. Using ERM, for instance, the optimal model is approached by minimizing the loss of the model:<br />
<br />
\begin{align}<br />
\theta^{(t)} = arg min_{\theta \in \Theta} \sum_i \ell(\theta; Z_i^{(t)})<br />
\end{align}<br />
<br />
However, ERM fails to prevent disparity amplification. By minimizing the expected loss of the model, minority groups experience higher loss (because the loss of the majority group is minimized), and do not return to use the system. In doing so, the population proportions <math display="inline">\alpha_k^{(t)}</math> shift, and certain minority groups contribute even less to the system. This is mirrored in the expected user count <math display="inline">\lambda^{(t)}</math> at each optimization point. In their paper Hashimoto et al. show that, if using ERM, <math display="inline">\lambda^{(t)}</math> is unstable because it loses its fair fixed point (i.e. the population fraction where risk minimization maintains the same population fraction over time). Therefore, ERM fails to control minority risk over time and is considered unfair.<br />
<br />
=Distributionally Robust Optimization (DRO)=<br />
<br />
To overcome the unfairness of ERM, Hashimoto et al. developed a distributionally robust optimization (DRO). At this point the goal is still to minimize the worst-case group risk over a single time-step <math display="inline">\mathcal{R}_{max} (\theta^{(t)}) </math> (time steps are omitted in this section's formulas). As previously mentioned, this is difficult to do because neither the population proportions <math display="inline">\alpha_k </math> nor group distributions <math display="inline">P_k </math> are known, which means the data was sampled from different unknown groups. Therefore, in order to improve the performance across different groups, Hashimoto et al. developed an optimization technique that is robust "against '''''all''''' directions around the data generating distribution". This refers to the notion that DRO is robust to any group distribution <math display="inline">P_k </math> whose loss other optimization techniques such as ERM might try to optimize. To create this distributionally robustness, the optimizations risk function <math display="inline">\mathcal{R}_{dro} </math> has to "up-weigh" data <math display="inline">Z</math> that cause high loss <math display="inline">\ell(\theta, Z)</math>. In other words, the risk function has to over-represent mixture components (i.e. group distributions <math display="inline">P_k </math>) in relation to their original mixture weights (i.e. the population proportions <math display="inline">\alpha_k </math>) for groups that suffer high loss. <br />
<br />
To do this Hashimoto et al. considered the worst-case loss (i.e. the highest risk) over all perturbations <math display="inline">P_k </math> around <math display="inline">P</math> within a certain limit (because obviously not every outlier should be up-weighed). This limit is described by the <math display="inline">\chi^2</math>-divergence (i.e. the distance, roughly speaking) between probability distributions. For two distributions <math display="inline">P</math> and <math display="inline">Q</math> the divergence is defined as <math display="inline">D_{\chi^2} (P || Q):= \int (\frac{dP}{dQ} - 1)^2</math>. If <math display="inline">P</math> is not absolutely continuous w.r.t <math display="inline">Q</math>, then <math display="inline">D_{\chi^2} (P || Q):= \infty</math>. With the help of the <math display="inline">\chi^2</math>-divergence, Hashimoto et al. defined the chi-squared ball <math display="inline">\mathcal{B}(P,r)</math> around the probability distribution P. This ball is defined so that <math display="inline">\mathcal{B}(P,r) := \{Q \ll P : D_{\chi^2} (Q || P) \leq r \}</math>. With the help of this ball the worst-case loss (i.e. the highest risk) over all perturbations <math display="inline">P_k </math> that lie inside the ball (i.e. within reasonable range) around the probability distribution <math display="inline">P</math> can be considered. This loss is given by<br />
<br />
\begin{align}<br />
\mathcal{R}_{dro}(\theta, r) := \underset{Q \in \mathcal{B}(P,r)}{sup} \mathbb{E}_Q [\ell(\theta;Z)]<br />
\end{align}<br />
<br />
which for <math display="inline">P:= \sum_{k \in [K]} \alpha_k P_k</math> for all models <math display="inline">\theta \in \Theta</math> where <math display="inline">r_k := (1/a_k -1)^2</math> bounds the risk <math display="inline">\mathcal{R}_k(\theta) \leq \mathcal{R}_{dro} (\theta; r_k)</math> for each group with risk <math display="inline">\mathcal{R}_k(\theta)</math>. Furthermore, if the lower bound on the group proportions <math display="inline">\alpha_{min} \leq min_{k \in [K]} \alpha_k</math> is specified, and the radius is defined as <math display="inline">r_{max} := (1/\alpha_{min} -1)^2</math>, the worst-case risk <math display="inline">\mathcal{R}_{max} (\theta) </math> can be controlled by <math display="inline">\mathcal{R}_{dro} (\theta; r_{max}) </math> by forming an upper bound that can be minimized.<br />
<br />
==Optimization of DRO==<br />
<br />
To minimize <math display="inline">\mathcal{R}_{dro}(\theta, r) := \underset{Q \in \mathcal{B}(P,r)}{sup} \mathbb{E}_Q [\ell(\theta;Z)]</math> Hashimoto et al. look at the dual of this maximization problem (i.e. every maximization problem can be transformed into a minimization problem and vice-versa). This dual is given by the minimization problem<br />
<br />
\begin{align}<br />
\mathcal{R}_{dro}(\theta, r) = \underset{\eta \in \mathbb{R}}{inf} \left\{ F(\theta; \eta):= C\left(\mathbb{E}_P \left[ [\ell(\theta;Z) - \eta]_+^2 \right] \right)^\frac{1}{2} + \eta \right\}<br />
\end{align}<br />
<br />
with <math display="inline">C = (2(1/a_{min} - 1)^2 + 1)^{1/2}</math>. <math display="inline">\eta</math> describes the dual variable (i.e. the variable that appears in creating the dual). Since <math display="inline">F(\theta; \eta)</math> involves an expectation <math display="inline">\mathbb{E}_P</math> over the data generating distribution <math display="inline">P</math>, <math display="inline">F(\theta; \eta)</math> can be directly minimized. For convex losses <math display="inline">\ell(\theta;Z)</math>, <math display="inline">F(\theta; \eta)</math> is convex, and can be minimized by performing a binary search over <math display="inline">\eta</math>. In their paper, Hashimoto et al. further show that optimizing <math display="inline">\mathcal{R}_{dro}(\theta, r_{max})</math> at each time step controls the ''future'' worst-case risk <math display="inline">\mathcal{R}_{max} (\theta) </math>, and therefore retention rates. That means if the initial group proportions satisfy <math display="inline">\alpha_k^{(0)} \geq a_{min}</math>, and <math display="inline">\mathcal{R}_{dro}(\theta, r_{max})</math> is optimized for every time step (and therefore <math display="inline">\mathcal{R}_{max} (\theta) </math> is minimized), <math display="inline">\mathcal{R}_{max}^T (\theta) </math> over all time steps is controlled. In other words, optimizing <math display="inline">\mathcal{R}_{dro}(\theta, r_{max})</math> every time step is enough to avoid disparity amplification.<br />
<br />
<br />
Pros of DRO: In many cases, the expected value is a good measure of performance<br />
Cons of DRO: One has to know the exact distribution of the underlying distribution to perform the stochastic optimization. Deviant from the assumed distribution may result in sub-optimal solutions. The paper makes strong assumptions on <math>\mathcal{P}</math> with respect to group allocations, and thus requires a high amount of data to optimize; when assumptions are violated, the algorithm fails to perform as intended.<br />
<br />
=Experiments=<br />
<br />
The paper demonstrate the effectiveness of DRO and human evaluation of a text autocomplete system on Amazon Mechanical Turk. In both cases, DRO controls the worst-case risk over time steps and improves minority retention.<br />
Below Figure gives Inferred dynamics from a Mechanical Turk based evaluation of autocomplete systems.DRO increases minority (a) user<br />
satisfaction and (b) retention, leading to a corresponding increase in (c) user count. Error bars indicates bootstrap quartiles.<br />
[[File:fig4999.png|thumb|center|600px|]].<br />
<br />
Below figure shows how Disparity amplification in corrected by DRO. Error bars indicate quartiles over 10 replicates.<br />
[[File:fig5999.png|thumb|center|400px|]].<br />
<br />
<br />
Below figure shows Classifier accuracy as a function of group imbalance.Dotted lines show accuracy on majority group.<br />
[[File:fig6999.png|thumb|center|400px|]].<br />
<br />
=Critiques=<br />
<br />
This paper works on representational disparity which is a critical problem to contribute to. The methods are well developed and the paper reads coherently. However, the authors have several limiting assumptions that are not very intuitive or scientifically suggestive. The first assumption is that the <math display="inline">\eta</math> function denoting the fraction of users retained is differentiable and strictly decreasing function. This assumption does not seem practical. The second assumption is that the learned parameters are having a Poisson distribution. There is no explanation of such an assumption and reasons hinted at are hand-wavy at best. Though the authors are building a case against the Empirical risk minimization method, this method is exactly solvable when the data is linearly separable. The DRO method is computationally more complex than ERM and is not entirely clear if it will always have an advantage for a different class of problems.<br />
<br />
Note: The first assumption about <math>\eta</math> can be weakened by introducing discrete yet smooth enough function for computational proposes only. Such function will be enough to mimic for differentiability.<br />
<br />
=Other Sources=<br />
# [https://blog.acolyer.org/2018/08/17/fairness-without-demographics-in-repeated-loss-minimization/] is a easy-to-read paper description.<br />
# [https://vimeo.com/295743125] a video of the authors explaining the paper in ICML 2018<br />
<br />
=References=<br />
Rawls, J. Justice as fairness: a restatement. Harvard University Press, 2001.<br />
<br />
Barocas, S. and Selbst, A. D. Big data’s disparate impact. 104 California Law Review, 3:671–732, 2016.<br />
<br />
Chouldechova, A. A study of bias in recidivism prediction instruments. Big Data, pp. 153–163, 2017<br />
<br />
Dwork, C., Hardt, M., Pitassi, T., Reingold, O., and Zemel, R. Fairness through awareness. In Innovations in Theoretical Computer Science (ITCS), pp. 214–226, 2012.<br />
<br />
Kearns, M., Neel, S., Roth, A., and Wu, Z. S. Preventing fairness gerrymandering: Auditing and learning for subgroup fairness. arXiv preprint arXiv:1711.05144, 2018.<br />
<br />
Hebert-Johnson, ´ U., Kim, M. P., Reingold, O., and Roth-blum, G. N. Calibration for the (computationally identifiable) masses. arXiv preprint arXiv:1711.08513, 2017.<br />
<br />
Joseph, M., Kearns, M., Morgenstern, J., Neel, S., and Roth, A. Rawlsian fairness for machine learning. In FATML, 2016.<br />
<br />
Jabbari, S., Joseph, M., Kearns, M., Morgenstern, J., and Roth, A. Fairness in reinforcement learning. In International Conference on Machine Learning (ICML), pp. 1617–1626, 2017.<br />
<br />
Liu, L. T., Dean, S., Rolf, E., Simchowitz, M., and Hardt, M. Delayed impact of fair machine learning. arXiv preprint arXiv:1803.04383, 2018.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=End_to_end_Active_Object_Tracking_via_Reinforcement_Learning&diff=42067End to end Active Object Tracking via Reinforcement Learning2018-11-30T16:12:33Z<p>R82zhang: /* Related Work */</p>
<hr />
<div>=Introduction=<br />
Object tracking has been a hot topic in recent years. It involves localization of an object in continuous video frames given an initial annotation in the first frame. <br />
The process normally consists of the following steps. <br />
<ol><br />
<li> Taking an initial set of object detections. </li><br />
<li> Creating and assigning a unique ID for each of the initial detections. </li><br />
<li> Tracking those objects as they move around in the video frames, maintaining the assignment of unique IDs. </li><br />
</ol><br />
There are two types of object tracking. <ol> <li>Passive tracking</li> <li> Active tracking </li> </ol><br />
<br />
[[File:active_tracking_pipeline.PNG|500px|center]]<br />
<br />
Passive tracking assumes that the object of interest is always in the image scene, meaning that there is no need for camera control during tracking. Although passive tracking is very useful and well-researched with existing works, it is not applicable in situations like tracking performed by a camera-mounted mobile robot or by a drone. <br />
On the other hand, active tracking involves two subtasks, including 1) Object Tracking and 2) Camera Control. It is difficult to jointly tune the pipeline between these two separate subtasks. Object Tracking may require human efforts for bounding box labeling. In addition, Camera Control is non-trivial, which can lead to many expensive trial-and-errors in the real world. <br />
<br />
To address these challenges, this paper presents an end-to-end active tracking solution via deep reinforcement learning. More specifically, the ConvNet-LSTM network takes raw video frames as input and outputs camera movement actions.<br />
The virtual environment is used to simulate active tracking. In a virtual environment, an agent (i.e. the tracker) observes a state (a visual frame) from a ﬁrst-person perspective and takes an action. Then, the environment returns the updated state (next visual frame). A3C, a modern Reinforcement Learning algorithm, is adopted to train the agent, where a customized reward function is designed to encourage the agent to be closely following the object.<br />
Environment augmentation technique is used to boost the tracker’s generalization ability. The tracker trained in the virtual environment is then tested on a real-world video dataset to assess the generalizability of the model. A video of the first version of this paper is available here[https://www.youtube.com/watch?v=C1Bn8WGtv0w].<br />
<br />
=Intuition=<br />
<br />
As in the case of the state of the art models, if the action module and the object tracking module are completely different, it is extremely difficult to train one or the other as it is impossible to know which is causing the error that is being observed at the end of the episode. The function of both these modules are the same at a high level as both are aiming for efficient navigation. So it makes sense to have a joint module that consists of both the observation and the action taking submodules. Now we can train the entire system together as the error needs to be propagated to the whole system. This is in line with the common practice in Deep Reinforcement Learning where the CNNs used to extract features in the case of Atari games are combined with the Q networks (in the case of DQN). The training of these CNN happens concurrently with the Q feedforward networks where the error function is the difference between the observed Q value and the target Q values. <br />
<br />
=Related Work= <br />
<br />
In the domain of object tracking, there are both active and passive approaches. The below summarize the advance passive object tracking approaches: <br />
<br />
1) Subspace learning was adopted to update the appearance model of an object. <br />
<br />
:Formerly, object tracking algorithms employ a fixed appearance model. Consequently, they often perform poorly when the target object changes in appearance or illumination. To overcome this problem, Ross et al. 2008 introduce a novel tracking method that incrementally adapts the appearance model according to new observations made during tracking [2].<br />
<br />
2) Multiple instance learning was employed to track an object. <br />
<br />
:Many researchers have shown that a tracking algorithm can achieve better performance by employing adaptive appearance models capable of separating an object from its background. However, the discriminative classifier in those models is often difficult to update. So, Babenko et al. 2009 introduce a novel algorithm that updates its appearance model using a “bag” of positive and negative examples. Subsequently, they show that tracking algorithms using weaker classifiers can still obtain superior performance [3].<br />
<br />
3) Correlation filter based object tracking has achieved success in real-time object tracking. <br />
<br />
:Correlation filter based object tracking algorithms attempt to “model the appearance of an object using filters”. At each frame, a small tracking window representing the target object is produced, and the tracker will correlate the windows over the image sequences, thus achieving object tracking. Bolme et al. 2010 validate this concept by creating a novel object tracking algorithm using an adaptive correlation filter called Minimum Output Sum of Squared Error (MOSSE) filter [4].<br />
<br />
4) Structured Output predicted was used to constrain object tracking and avoiding converting positions to labels of training samples. <br />
<br />
:Hare et al. 2016 argue the “sliding-window” approach use by popular object tracking algorithms is flawed because “the objective of the classifier (predicting labels for sliding-windows) is decoupled from the objective of the tracker (estimating object position).” Instead, they introduce a novel algorithm that uses “a kernelized structured output support vector machine (SVM) to avoid the need for intermediate classification”. Subsequently, they show the approach outperforms traditional trackers in various benchmarks [5].<br />
<br />
5) Tracking, learning, and Detection were integrated into one framework for long-term tracking, where a detection module was used to re-initialize the tracker once a missing object reappears. <br />
<br />
:Long-Term Tracking is the task to recognize and track an object as it “moves in and out of a camera’s field of view”. This task is made difficult by problems such as an object reappearing into the scene and changing its appearance, scale, or illumination. Kalal et al. 2012 proposed a unified tracking framework (TLD) that accomplishes long-term tracking by “decomposing the task into tracking, learning, and detection”. Specifically, “the tracker follows an object from frame-to-frame; the detector localizes the object’s appearances; and, the learner improves the detector by learning from errors.” Altogether, the TLD framework outperforms previous state-of-arts tracking approaches [6].<br />
<br />
6) Deep learning models like stacked autoencoder have been used to learn good representations for object tracking. <br />
<br />
:In recent year, Deep Learning approaches are gaining prominence in the field of object tracking. For example, Wang et al. 2013 obtain outstanding results using a deep-learning based algorithm that combines offline feature extraction and online tracking using stacked denoising autoencoders. Whereas, Wang et al. 2016 introduced a sequential training convolutional network that can efficiently transfer offline learned features for online visual tracking applications.<br />
<br />
7) Pixel-level image classification.<br />
<br />
:Object identification is essentially pixel level classification, where each pixel in the image is given a label. It is a more general form of image classification. In recent years, CNN has advanced many benchmarks in this field, and some AutoML methods, such as Neural Architecture Search has been applied in this field and achieved state of the art. <br />
<br />
For the active approaches, camera control and object tracking were considered as separate components. These approaches are difficult to tune. This paper tackles object tracking and camera control simultaneously in an end to end manner and is easy to tune. <br />
<br />
In the domain of domain of deep reinforcement learning, recent algorithms have achieved advanced gameplay in games like GO and Atari games. They have also been used in computer vision tasks like object localization, region proposal, and visual tracking. All advancements pertain to passive tracking but this paper focusses on active tracking using Deep RL, which has never been tried before.<br />
<br />
=Approach=<br />
Virtual tracking scenes are generated for both training and testing. An Asynchronous Actor-Critic Agents (A3C) model was used to train the tracker. For efficient training, data augmentation techniques and a customized reward function were used. An RGB screen frame of the first-person perspective was chosen as the state for the study. The tracker observes a visual state and takes one action <math>a_t</math> from the following set of 6 actions. <br />
<br />
\[A = \{\text{turn-left}, \text{turn-right}, \text{turn-left-and-move-forward},\\ \text{turn-right-and-move-forward}, \text{move-forward}, \text{no-op}\}\]<br />
<br />
The action is processed by the environment, which returns to the agent the current reward as well as the updated screen frame <math>(r_t, s_{t+1}) </math>.<br />
==Tracking Scenarios==<br />
It is impossible to train the desired end-to-end active tracker<br />
in real-world scenarios. Therefore, The following two Virtual environment engines are used for the simulated training.<br />
===ViZDoom=== <br />
ViZDoom[http://vizdoom.cs.put.edu.pl/] (Kempka et al., 2016; ViZ) is an RL research platform based on a 3D FPS video game called Doom. In ViZDoom, the game engine corresponds to the environment, while the video game player corresponds to the agent. The agent receives from the environment a state and a reward at each time step. In this study, customized ViZDoom maps are used. (see Fig. 4) composed of an object (a monster) and background (ceiling, ﬂoor, and wall). The monster walks along a pre-speciﬁed path programmed by the ACS script (Kempka et al., 2016), and the goal is to train the agent, i.e., the tracker, to follow closely the object. <br />
[[File:fig4.PNG|500px|center]]<br />
<br />
===Unreal Engine=== <br />
Though convenient for research, ViZDoom does not provide realistic scenarios. To this end, Unreal Engine (UE) is adopted to construct nearly real-world environments. UE is a popular game engine and has a broad inﬂuence in the game industry. It provides realistic scenarios which can mimic real-world scenes. UnrealCV (Qiu et al., 2017) is employed in this study, which provides convenient APIs, along with a wrapper (Zhong et al., 2017) compatible with OpenAI Gym (Brockman et al., 2016), for interactions between RL algorithms and the environments constructed based on UE.<br />
<br />
==A3C Algorithm==<br />
This paper employs the Asynchronous Actor-Critic Agents (A3C) algorithm for training the tracker. <br />
At time step t, <math>s_{t} </math> denotes the observed state corresponding to the raw RGB frame. The action set is denoted by A of size K = |A|. An action, <math>a_{t} </math> ∈ A, is drawn from a policy function distribution: \[a_{t}\sim \pi\left ( . | s_{t} \right ) \in \mathbb{R}^{k} \] This is referred to as actor.<br />
The environment then returns a reward <math>r_{t} \in \mathbb{R} </math> , according to a reward function <math>r_{t} = g(s_{t})</math><br />
. The updated state <math>s_{t+1}</math> at next time step t+1 is subject to a certain but unknown state transition function <math> s_{t+1} = f(s_{t}, a_{t}) </math>, governed by the environment. <br />
Trace consisting of a sequence of triplets can be observed. \[\tau = \{\ldots, (s_{t}, a_{t}, r_{t}) , (s_{t+1}, a_{t+1}, r_{t+1}) , \ldots \}\]<br />
Meanwhile, <math>V(s_{t}) \in \mathbb{R} </math> denotes the expected accumulated reward in the future given state <math>s_{t}</math> (referred to as Critic). The policy function <math> \pi(.)</math> and the value function <math>V (·)</math> are then jointly modeled by a neural network. Rewriting these as <math>\pi(.|s_{t};\theta)</math> and <math>V(s_{t};{\theta}')</math> with parameters <math>\theta</math> and <math>{\theta}'</math> respectively. The parameters are learned over trace <math>\tau</math> by simultaneous stochastic policy gradient and value function regression.<br />
[[File:equation12.PNG|500px|center]]<br />
Where <math>R_{t} = \sum_{{t}'=t}^{t+T-1} \gamma^{{t}'-t}r_{{t}'}</math> is a discounted sum of future rewards up to <math>T</math> time steps with a factor <math>0 < \gamma \leq 1, \alpha</math> is the learning rate, <math>H (·)</math> is an entropy regularizer, and <math>\beta</math> is the regularizer factor.<br />
<br />
This is a multi-threaded training process where each thread maintains an independent environment-agent interaction. Nevertheless, the network parameters are shared among threads and are updated asynchronously every T-time step using eq 1 in a lock-free manner in each thread.<br />
<br />
[[File:A3C High Level Diagram.png|thumb|center|High-level diagram that depicts the A3C algorithm across <math>n</math> environments]]<br />
<br />
==Network Architecture==<br />
The tracker is a ConvNet-LSTM neural network as shown in Fig. 2, where the architecture speciﬁcation is given in the following table. The FC6 and FC1 correspond to the 6-action policy <math>\pi (·|s_{t})</math> and the value <math>V (s_{t})</math>, respectively. The screen is resized to 84 × 84 × 3 RGB images as the network input.<br />
[[File:network-architecture.PNG|500px|center]]<br />
[[File:table.PNG|500px|center]]<br />
==Reward Function==<br />
The reward function utilizes a two-dimensional local coordinate system (S). The x-axis points from the agent’s left shoulder to right shoulder and the y-axis points perpendicular to the x-axis and points to the agent’s front. The origin is where is the agent is. System S is parallel to the floor. The object’s local coordinate (x,y) and orientation a with regard to the system S.<br />
The reward function is defined as follows.<br />
[[File:reward_function.PNG|300px|center]]<br />
Where A>0, c>0, d>0 and λ>0 are tuning parameters. The reward equation states that the maximum reward A is achieved when the object stands perfectly in front of the agent with distanced and exhibits no rotation.<br />
==Environment Augmentation==<br />
To make the tracker generalize well, an environment augmentation technique is proposed for both virtual environments. <br />
<br />
For ViZDoom, (x,y, a) define the system state. For augmentation the initial system state is perturbed N times by editing the map with ACS script (Kempka et al., 2016), yielding a set of environments with varied initial positions and orientations <math>\{x_{i},y_{i},a_{i}\}_{i=1}^{N}</math>. Further ﬂipping left-right the screen frame (and accordingly the left-right action) is allowed. As a result, 2N environments are obtained out of one environment. During A3C training, one of the 2N environments is randomly sampled at the beginning of every episode. This makes the generalization ability of the tracker be improved.<br />
<br />
For UE, an environment with a character/target following a fixed path is constructed. To augment the environment, random background objects are chosen and making them invisible. Simultaneously, every episode starts from the position, where the agent fails at the last episode. This makes the environment and starting point different from episode to episode, so the variations of the environment during training are augmented.<br />
<br />
=Experimental Settings=<br />
==Environment Setup==<br />
A set of environments are produced for both training and testing. For ViZDoom, a training map as in Fig. 4, left column is adopted. This map is then augmented with N = 21, leading to 42 environments that can be sampled from during training. For testing, 9 maps are made, some of which are shown in Fig. 4, middle and right columns. In all maps, the path of the target is pre-speciﬁed, indicated by the blue lines. However, it is worth noting that the object does not strictly follow the planned path. Instead, it sometimes randomly moves in a “zig-zag” way during the course, which is a built-in game engine behavior. This poses an additional difﬁculty to the tracking problem. <br />
For UE, an environment named Square with random invisible background objects is generated and a target named Stefani walking along a ﬁxed path for training. For testing, another four environments named as Square1StefaniPath1 (S1SP1), Square1MalcomPath1 (S1MP1), Square1StefaniPath2 (S1SP2), and Square2MalcomPath2 (S2MP2) are made. As shown in Fig. 5, Square1 and Square2 are two different maps, Stefani and Malcom are two characters/targets, and Path1 and Path2 are different paths. Note that, the training environment Square is generated by hiding some background objects in Square1. <br />
For both ViZDoom and UE, an episode is terminated when either the accumulated reward drops below a threshold or the episode length reaches a maximum number. In these experiments, the reward threshold is set as -450 and the maximum length as 3000, respectively.<br />
==Metric==<br />
Two metrics are employed for the experiments. Accumulated Reward (AR) and Episode Length (EL). AR is like Precision in the conventional tracking literature. An AR that is too small leads to termination of the episode because it essentially means a failure of tracking. EL roughly measures the duration of good tracking and is analogous to the metric Successfully Tracked Frames in conventional tracking applications. The theoretical maximum for both AR and EL is 3000 when letting A = 1.0 in the reward function (because of the termination criterion).<br />
<br />
=Results=<br />
Two training protocols were followed namely RandomizedEnv(with augmentation) and SingleEnv(without the augmentation technique). However, only the results for RandomizedEnv are reported in the paper.<br />
There is only one table specifying the result from SingleEnv training which shows that it performs worse than the RandomizedEnv training. Compared to RandomizedEnv, SingleEnv does not exploit the capacity of the network better. The variability in the test results is very high for the non-augmented training case.<br />
[[File:table1.PNG|400px|center]] <br />
The testing environments results are reported in Tab. 2. These are 8 more challenging test environments that present different target appearances, different backgrounds, more varied paths and distracting targets comparing to the training environment.<br />
[[File:msm_table2.PNG|400px|center]]<br />
Following are the findings from the testing results:<br />
1. The tracker generalizes well in the case of target appearance changing (Zombie, Cacodemon).<br />
2. The tracker is insensitive to background variations such as changing the ceiling and ﬂoor (FloorCeiling) or placing additional walls in the map (Corridor).<br />
3. The tracker does not lose a target even when the target takes several sharp turns (SharpTurn). Note that in conventional tracking, the target is commonly assumed to move smoothly.<br />
4. The tracker is insensitive to a distracting object (Noise1) even when the “bait” is very close to the path (Noise2).<br />
<br />
The proposed tracker is compared against several of the conventional trackers with PID like module for camera control to simulate active tracking. The results are displayed in Tab. 3. <br />
<br />
[[File:table3.PNG|400px|center]]<br />
<br />
The camera control module is implemented such that in the first frame, a manual bounding box must be given to indicate the object to be tracked. For each subsequent frame, the passive tracker then predicts a bounding box which is passed to the Camera Control module. A comparison is made between the two subsequent bounding boxes as per the algorithm and action decision is made.<br />
The results show that the proposed solution outperforms the simulated active tracker. The simulated trackers lost their targets soon. The Meanshift tracker works well when there is no camera shift between continuous frames. Both KCF and Correlation trackers seem not capable of handling such a large camera shift, so they do not work as well as the case in passive tracking. The MIL tracker works reasonably in the active case, while it easily drifts when the object turns suddenly.<br />
<br />
Testing in the UE environment is tabulated in Table 5. Four different environments are tested and based on the long-term TLD tracker. <br />
[[File:table5.PNG|400px|center]]<br />
1. Comparison between S1SP1 and S1MP1 shows that the tracker generalizes well even when the model is trained with target Stefani, revealing that it does not overﬁt to a specialized appearance. <br />
2. The active tracker performs well when changing the path (S1SP1 versus S1SP2), demonstrating that it does not act by memorizing specialized path.<br />
3. When the map is changed, target, and path at the same time (S2MP2), though the tracker could not seize the target as accurately as in previous environments (the AR value drops), it can still track objects robustly (comparable EL value as in previous environments), proving its superior generalization potential. <br />
4. In most cases, the proposed tracker outperforms the simulated active tracker or achieves comparable results if it is not the best. The results of the simulated active tracker also suggest that it is difﬁcult to tune a uniﬁed camera-control module for them, even when a long-term tracker is adopted (see the results of TLD). <br />
<br />
Real world active tracking: To test and evaluate the tracker in real-world scenarios, the network trained on UE environment is tested on a few videos from the VOT dataset. <br />
<br />
[[File:fig7.PNG|400px|center]]<br />
<br />
Fig. 7 shows the output actions for two video clips named Woman and Sphere, respectively. The horizontal axis indicates the position of the target in the image, with a positive (negative) value meaning that a target in the right (left) part. The vertical axis indicates the size of the target, i.e., the area of the ground truth bounding box. Green and red dots indicate turn-left/turn-left-and-move-forward and turn-right/turn-right-and-move-forward actions, respectively. Yellow dots represent No-op action. As the ﬁgure shows, 1) When the target resides in the right (left) side, the tracker tends to turn right (left), trying to move the camera to “pull” the target to the center. 2) When the target size becomes bigger, which probably indicates that the tracker is too close to the target, the tracker outputs no-op actions more often, intending to stop and wait for the target to move farther.<br />
<br />
Video Link to the experimental results can be found below:<br />
[https://youtu.be/C1Bn8WGtv0w Video Demonstration of the Results]<br />
<br />
Supplementary Material for Further Experiments:<br />
[http://proceedings.mlr.press/v80/luo18a/luo18a-supp.zip Additional PDF and Video]<br />
<br />
Action Saliency Map: An input frame is fed into the tracker and forwarded to output the policy function. An action will be sampled subsequently. Then the gradient of this action is propagated backwards to the input layer, the saliency map is generated. According to the saliency map, how the input image affects the tracker's action can be observed. Fig. 8 shows the tracker indeed learns how to find the target, which improves the performance of the model.<br />
[[File:fig8.PNG|400px|center]]<br />
<br />
=Conclusion=<br />
In the paper, an end-to-end active tracker via deep reinforcement learning is proposed. Unlike conventional passive trackers, the proposed tracker is trained in simulators, saving the efforts of human labeling or trial-and-errors in real-world. It shows good generalization to unseen environments. The tracking ability can potentially transfer to real-world scenarios.<br />
=Critique=<br />
The paper presents a solution for active tracking using reinforcement learning. A ConvNet-LSTM network has been adopted. Environment augmentation has been proposed for training the network. The tracker trained using environment augmentation performs better than the one trained without it. This is true in both the ViZDoom and UE environment. The reward function looks intuitive for the task at hand which is object tracking. The virtual environment ViZDoom though used for training and testing, seems to have little or no generalization ability in real-world scenarios. The maps in ViZDoom itself are very simple. The comparison presented in the paper for the ViZDoom testing with changes in the environmental parameters look positive, but the relatively simple nature of the environment needs to be considered while looking at these results. Also, when the floor is replaced by the ceiling, the tracker performs worst in comparison to the other cases in the table, which seems to indicate that the floor and ceiling parameters are somewhat over-fitted in the model. The tracker trained in UE environment is tested against simulated trackers. The results show that the proposed solution performs better than the simulated trackers. However, since the trackers are simulated using the camera control algorithm written for this specific comparison, further testing is required for benchmarking. The real-world challenges of intensity variation, camera details, control signals through beyond the scope of the current paper, still need to be considered while discussing the generalization ability of the model to real-world scenarios. For example, the current action<br />
space includes only six discrete actions, which are inadequate for deployment in the real world because the tracker cannot adapt to the different moving speed of the target. It is also believed<br />
that training the tracker in UE simulator alone is sufficient for a successful real-world deployment. It is better to randomize more aspects of the environment during training, including the texture of each mesh, the illumination condition of the scene, the trajectory of the target as well as the speed of the target.<br />
The results on the real-world videos show a positive result towards the generalization ability of the models in real-world settings. The overall approach presented in the paper is intuitive and the results look promising.<br />
<br />
=Future Work=<br />
The authors did some future work for this paper in several ways. Basically, they implemented a successful robot. Moreover, they enhanced the system to deal with the virtual-to-real gap [1]. Specifically, 1) more advanced environment augmentation techniques have been proposed to boost the environment diversity, which improves the transferability tailored to the real world. 2) A more appropriate action space compared with the conference paper is developed, and using a continuous action space for active tracking is investigated. 3) A mapping from the neural network prediction to the robot control signal is established so as to successfully deliver the end-to-end tracking.<br />
<br />
=References=<br />
[https://arxiv.org/pdf/1808.03405.pdf 1] W. Luo, P. Sun, F. Zhong, W. Liu, T. Zhang, and Y. Wang, “End-to-end Active Object Tracking and Its Real-world Deployment via Reinforcement Learning”.<br />
<br />
[2] Ross, David A, Lim, Jongwoo, Lin, Ruei-Sung, and Yang, Ming- Hsuan. Incremental learning for robust visual tracking. International Journal of Computer Vision, 77(1-3):125–141, 2008.<br />
<br />
[3] Babenko, Boris, Yang, Ming-Hsuan, and Belongie, Serge. Visual tracking with online multiple instance learning. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 983–990, 2009.<br />
<br />
[4] Bolme, David S, Beveridge, J Ross, Draper, Bruce A, and Lui, Yui Man. Visual object tracking using adaptive correlation filters. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 2544–2550, 2010.<br />
<br />
[5] Hare, Sam, Golodetz, Stuart, Saffari, Amir, Vineet, Vibhav, Cheng, Ming-Ming, Hicks, Stephen L, and Torr, Philip HS. Struck: Structured output tracking with kernels. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(10):2096–2109, 2016.<br />
<br />
[6] Kalal, Zdenek, Mikolajczyk, Krystian, and Matas, Jiri. Tracking- learning-detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(7):1409–1422, 2012.<br />
<br />
[7] Wang, Naiyan and Yeung, Dit-Yan. Learning a deep compact image representation for visual tracking. In Advances in Neural Information Processing Systems, pp. 809–817, 2013.<br />
<br />
[8] Wang, Lijun, Ouyang, Wanli, Wang, Xiaogang, and Lu, Huchuan. Stct: Sequentially training convolutional networks for visual tracking. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 1373–1381, 2016.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=End_to_end_Active_Object_Tracking_via_Reinforcement_Learning&diff=42064End to end Active Object Tracking via Reinforcement Learning2018-11-30T16:12:09Z<p>R82zhang: [T] /* Related Work */</p>
<hr />
<div>=Introduction=<br />
Object tracking has been a hot topic in recent years. It involves localization of an object in continuous video frames given an initial annotation in the first frame. <br />
The process normally consists of the following steps. <br />
<ol><br />
<li> Taking an initial set of object detections. </li><br />
<li> Creating and assigning a unique ID for each of the initial detections. </li><br />
<li> Tracking those objects as they move around in the video frames, maintaining the assignment of unique IDs. </li><br />
</ol><br />
There are two types of object tracking. <ol> <li>Passive tracking</li> <li> Active tracking </li> </ol><br />
<br />
[[File:active_tracking_pipeline.PNG|500px|center]]<br />
<br />
Passive tracking assumes that the object of interest is always in the image scene, meaning that there is no need for camera control during tracking. Although passive tracking is very useful and well-researched with existing works, it is not applicable in situations like tracking performed by a camera-mounted mobile robot or by a drone. <br />
On the other hand, active tracking involves two subtasks, including 1) Object Tracking and 2) Camera Control. It is difficult to jointly tune the pipeline between these two separate subtasks. Object Tracking may require human efforts for bounding box labeling. In addition, Camera Control is non-trivial, which can lead to many expensive trial-and-errors in the real world. <br />
<br />
To address these challenges, this paper presents an end-to-end active tracking solution via deep reinforcement learning. More specifically, the ConvNet-LSTM network takes raw video frames as input and outputs camera movement actions.<br />
The virtual environment is used to simulate active tracking. In a virtual environment, an agent (i.e. the tracker) observes a state (a visual frame) from a ﬁrst-person perspective and takes an action. Then, the environment returns the updated state (next visual frame). A3C, a modern Reinforcement Learning algorithm, is adopted to train the agent, where a customized reward function is designed to encourage the agent to be closely following the object.<br />
Environment augmentation technique is used to boost the tracker’s generalization ability. The tracker trained in the virtual environment is then tested on a real-world video dataset to assess the generalizability of the model. A video of the first version of this paper is available here[https://www.youtube.com/watch?v=C1Bn8WGtv0w].<br />
<br />
=Intuition=<br />
<br />
As in the case of the state of the art models, if the action module and the object tracking module are completely different, it is extremely difficult to train one or the other as it is impossible to know which is causing the error that is being observed at the end of the episode. The function of both these modules are the same at a high level as both are aiming for efficient navigation. So it makes sense to have a joint module that consists of both the observation and the action taking submodules. Now we can train the entire system together as the error needs to be propagated to the whole system. This is in line with the common practice in Deep Reinforcement Learning where the CNNs used to extract features in the case of Atari games are combined with the Q networks (in the case of DQN). The training of these CNN happens concurrently with the Q feedforward networks where the error function is the difference between the observed Q value and the target Q values. <br />
<br />
=Related Work= <br />
<br />
In the domain of object tracking, there are both active and passive approaches. The below summarize the advance passive object tracking approaches: <br />
<br />
1) Subspace learning was adopted to update the appearance model of an object. <br />
<br />
:Formerly, object tracking algorithms employ a fixed appearance model. Consequently, they often perform poorly when the target object changes in appearance or illumination. To overcome this problem, Ross et al. 2008 introduce a novel tracking method that incrementally adapts the appearance model according to new observations made during tracking [2].<br />
<br />
2) Multiple instance learning was employed to track an object. <br />
<br />
:Many researchers have shown that a tracking algorithm can achieve better performance by employing adaptive appearance models capable of separating an object from its background. However, the discriminative classifier in those models is often difficult to update. So, Babenko et al. 2009 introduce a novel algorithm that updates its appearance model using a “bag” of positive and negative examples. Subsequently, they show that tracking algorithms using weaker classifiers can still obtain superior performance [3].<br />
<br />
3) Correlation filter based object tracking has achieved success in real-time object tracking. <br />
<br />
:Correlation filter based object tracking algorithms attempt to “model the appearance of an object using filters”. At each frame, a small tracking window representing the target object is produced, and the tracker will correlate the windows over the image sequences, thus achieving object tracking. Bolme et al. 2010 validate this concept by creating a novel object tracking algorithm using an adaptive correlation filter called Minimum Output Sum of Squared Error (MOSSE) filter [4].<br />
<br />
4) Structured Output predicted was used to constrain object tracking and avoiding converting positions to labels of training samples. <br />
<br />
:Hare et al. 2016 argue the “sliding-window” approach use by popular object tracking algorithms is flawed because “the objective of the classifier (predicting labels for sliding-windows) is decoupled from the objective of the tracker (estimating object position).” Instead, they introduce a novel algorithm that uses “a kernelized structured output support vector machine (SVM) to avoid the need for intermediate classification”. Subsequently, they show the approach outperforms traditional trackers in various benchmarks [5].<br />
<br />
5) Tracking, learning, and Detection were integrated into one framework for long-term tracking, where a detection module was used to re-initialize the tracker once a missing object reappears. <br />
<br />
:Long-Term Tracking is the task to recognize and track an object as it “moves in and out of a camera’s field of view”. This task is made difficult by problems such as an object reappearing into the scene and changing its appearance, scale, or illumination. Kalal et al. 2012 proposed a unified tracking framework (TLD) that accomplishes long-term tracking by “decomposing the task into tracking, learning, and detection”. Specifically, “the tracker follows an object from frame-to-frame; the detector localizes the object’s appearances; and, the learner improves the detector by learning from errors.” Altogether, the TLD framework outperforms previous state-of-arts tracking approaches [6].<br />
<br />
6) Deep learning models like stacked autoencoder have been used to learn good representations for object tracking. <br />
<br />
:In recent year, Deep Learning approaches are gaining prominence in the field of object tracking. For example, Wang et al. 2013 obtain outstanding results using a deep-learning based algorithm that combines offline feature extraction and online tracking using stacked denoising autoencoders. Whereas, Wang et al. 2016 introduced a sequential training convolutional network that can efficiently transfer offline learned features for online visual tracking applications.<br />
<br />
7) Pixel-level image classification.<br />
Object identification is essentially pixel level classification, where each pixel in the image is given a label. It is a more general form of image classification. In recent years, CNN has advanced many benchmarks in this field, and some AutoML methods, such as Neural Architecture Search has been applied in this field and achieved state of the art. <br />
<br />
For the active approaches, camera control and object tracking were considered as separate components. These approaches are difficult to tune. This paper tackles object tracking and camera control simultaneously in an end to end manner and is easy to tune. <br />
<br />
In the domain of domain of deep reinforcement learning, recent algorithms have achieved advanced gameplay in games like GO and Atari games. They have also been used in computer vision tasks like object localization, region proposal, and visual tracking. All advancements pertain to passive tracking but this paper focusses on active tracking using Deep RL, which has never been tried before.<br />
<br />
=Approach=<br />
Virtual tracking scenes are generated for both training and testing. An Asynchronous Actor-Critic Agents (A3C) model was used to train the tracker. For efficient training, data augmentation techniques and a customized reward function were used. An RGB screen frame of the first-person perspective was chosen as the state for the study. The tracker observes a visual state and takes one action <math>a_t</math> from the following set of 6 actions. <br />
<br />
\[A = \{\text{turn-left}, \text{turn-right}, \text{turn-left-and-move-forward},\\ \text{turn-right-and-move-forward}, \text{move-forward}, \text{no-op}\}\]<br />
<br />
The action is processed by the environment, which returns to the agent the current reward as well as the updated screen frame <math>(r_t, s_{t+1}) </math>.<br />
==Tracking Scenarios==<br />
It is impossible to train the desired end-to-end active tracker<br />
in real-world scenarios. Therefore, The following two Virtual environment engines are used for the simulated training.<br />
===ViZDoom=== <br />
ViZDoom[http://vizdoom.cs.put.edu.pl/] (Kempka et al., 2016; ViZ) is an RL research platform based on a 3D FPS video game called Doom. In ViZDoom, the game engine corresponds to the environment, while the video game player corresponds to the agent. The agent receives from the environment a state and a reward at each time step. In this study, customized ViZDoom maps are used. (see Fig. 4) composed of an object (a monster) and background (ceiling, ﬂoor, and wall). The monster walks along a pre-speciﬁed path programmed by the ACS script (Kempka et al., 2016), and the goal is to train the agent, i.e., the tracker, to follow closely the object. <br />
[[File:fig4.PNG|500px|center]]<br />
<br />
===Unreal Engine=== <br />
Though convenient for research, ViZDoom does not provide realistic scenarios. To this end, Unreal Engine (UE) is adopted to construct nearly real-world environments. UE is a popular game engine and has a broad inﬂuence in the game industry. It provides realistic scenarios which can mimic real-world scenes. UnrealCV (Qiu et al., 2017) is employed in this study, which provides convenient APIs, along with a wrapper (Zhong et al., 2017) compatible with OpenAI Gym (Brockman et al., 2016), for interactions between RL algorithms and the environments constructed based on UE.<br />
<br />
==A3C Algorithm==<br />
This paper employs the Asynchronous Actor-Critic Agents (A3C) algorithm for training the tracker. <br />
At time step t, <math>s_{t} </math> denotes the observed state corresponding to the raw RGB frame. The action set is denoted by A of size K = |A|. An action, <math>a_{t} </math> ∈ A, is drawn from a policy function distribution: \[a_{t}\sim \pi\left ( . | s_{t} \right ) \in \mathbb{R}^{k} \] This is referred to as actor.<br />
The environment then returns a reward <math>r_{t} \in \mathbb{R} </math> , according to a reward function <math>r_{t} = g(s_{t})</math><br />
. The updated state <math>s_{t+1}</math> at next time step t+1 is subject to a certain but unknown state transition function <math> s_{t+1} = f(s_{t}, a_{t}) </math>, governed by the environment. <br />
Trace consisting of a sequence of triplets can be observed. \[\tau = \{\ldots, (s_{t}, a_{t}, r_{t}) , (s_{t+1}, a_{t+1}, r_{t+1}) , \ldots \}\]<br />
Meanwhile, <math>V(s_{t}) \in \mathbb{R} </math> denotes the expected accumulated reward in the future given state <math>s_{t}</math> (referred to as Critic). The policy function <math> \pi(.)</math> and the value function <math>V (·)</math> are then jointly modeled by a neural network. Rewriting these as <math>\pi(.|s_{t};\theta)</math> and <math>V(s_{t};{\theta}')</math> with parameters <math>\theta</math> and <math>{\theta}'</math> respectively. The parameters are learned over trace <math>\tau</math> by simultaneous stochastic policy gradient and value function regression.<br />
[[File:equation12.PNG|500px|center]]<br />
Where <math>R_{t} = \sum_{{t}'=t}^{t+T-1} \gamma^{{t}'-t}r_{{t}'}</math> is a discounted sum of future rewards up to <math>T</math> time steps with a factor <math>0 < \gamma \leq 1, \alpha</math> is the learning rate, <math>H (·)</math> is an entropy regularizer, and <math>\beta</math> is the regularizer factor.<br />
<br />
This is a multi-threaded training process where each thread maintains an independent environment-agent interaction. Nevertheless, the network parameters are shared among threads and are updated asynchronously every T-time step using eq 1 in a lock-free manner in each thread.<br />
<br />
[[File:A3C High Level Diagram.png|thumb|center|High-level diagram that depicts the A3C algorithm across <math>n</math> environments]]<br />
<br />
==Network Architecture==<br />
The tracker is a ConvNet-LSTM neural network as shown in Fig. 2, where the architecture speciﬁcation is given in the following table. The FC6 and FC1 correspond to the 6-action policy <math>\pi (·|s_{t})</math> and the value <math>V (s_{t})</math>, respectively. The screen is resized to 84 × 84 × 3 RGB images as the network input.<br />
[[File:network-architecture.PNG|500px|center]]<br />
[[File:table.PNG|500px|center]]<br />
==Reward Function==<br />
The reward function utilizes a two-dimensional local coordinate system (S). The x-axis points from the agent’s left shoulder to right shoulder and the y-axis points perpendicular to the x-axis and points to the agent’s front. The origin is where is the agent is. System S is parallel to the floor. The object’s local coordinate (x,y) and orientation a with regard to the system S.<br />
The reward function is defined as follows.<br />
[[File:reward_function.PNG|300px|center]]<br />
Where A>0, c>0, d>0 and λ>0 are tuning parameters. The reward equation states that the maximum reward A is achieved when the object stands perfectly in front of the agent with distanced and exhibits no rotation.<br />
==Environment Augmentation==<br />
To make the tracker generalize well, an environment augmentation technique is proposed for both virtual environments. <br />
<br />
For ViZDoom, (x,y, a) define the system state. For augmentation the initial system state is perturbed N times by editing the map with ACS script (Kempka et al., 2016), yielding a set of environments with varied initial positions and orientations <math>\{x_{i},y_{i},a_{i}\}_{i=1}^{N}</math>. Further ﬂipping left-right the screen frame (and accordingly the left-right action) is allowed. As a result, 2N environments are obtained out of one environment. During A3C training, one of the 2N environments is randomly sampled at the beginning of every episode. This makes the generalization ability of the tracker be improved.<br />
<br />
For UE, an environment with a character/target following a fixed path is constructed. To augment the environment, random background objects are chosen and making them invisible. Simultaneously, every episode starts from the position, where the agent fails at the last episode. This makes the environment and starting point different from episode to episode, so the variations of the environment during training are augmented.<br />
<br />
=Experimental Settings=<br />
==Environment Setup==<br />
A set of environments are produced for both training and testing. For ViZDoom, a training map as in Fig. 4, left column is adopted. This map is then augmented with N = 21, leading to 42 environments that can be sampled from during training. For testing, 9 maps are made, some of which are shown in Fig. 4, middle and right columns. In all maps, the path of the target is pre-speciﬁed, indicated by the blue lines. However, it is worth noting that the object does not strictly follow the planned path. Instead, it sometimes randomly moves in a “zig-zag” way during the course, which is a built-in game engine behavior. This poses an additional difﬁculty to the tracking problem. <br />
For UE, an environment named Square with random invisible background objects is generated and a target named Stefani walking along a ﬁxed path for training. For testing, another four environments named as Square1StefaniPath1 (S1SP1), Square1MalcomPath1 (S1MP1), Square1StefaniPath2 (S1SP2), and Square2MalcomPath2 (S2MP2) are made. As shown in Fig. 5, Square1 and Square2 are two different maps, Stefani and Malcom are two characters/targets, and Path1 and Path2 are different paths. Note that, the training environment Square is generated by hiding some background objects in Square1. <br />
For both ViZDoom and UE, an episode is terminated when either the accumulated reward drops below a threshold or the episode length reaches a maximum number. In these experiments, the reward threshold is set as -450 and the maximum length as 3000, respectively.<br />
==Metric==<br />
Two metrics are employed for the experiments. Accumulated Reward (AR) and Episode Length (EL). AR is like Precision in the conventional tracking literature. An AR that is too small leads to termination of the episode because it essentially means a failure of tracking. EL roughly measures the duration of good tracking and is analogous to the metric Successfully Tracked Frames in conventional tracking applications. The theoretical maximum for both AR and EL is 3000 when letting A = 1.0 in the reward function (because of the termination criterion).<br />
<br />
=Results=<br />
Two training protocols were followed namely RandomizedEnv(with augmentation) and SingleEnv(without the augmentation technique). However, only the results for RandomizedEnv are reported in the paper.<br />
There is only one table specifying the result from SingleEnv training which shows that it performs worse than the RandomizedEnv training. Compared to RandomizedEnv, SingleEnv does not exploit the capacity of the network better. The variability in the test results is very high for the non-augmented training case.<br />
[[File:table1.PNG|400px|center]] <br />
The testing environments results are reported in Tab. 2. These are 8 more challenging test environments that present different target appearances, different backgrounds, more varied paths and distracting targets comparing to the training environment.<br />
[[File:msm_table2.PNG|400px|center]]<br />
Following are the findings from the testing results:<br />
1. The tracker generalizes well in the case of target appearance changing (Zombie, Cacodemon).<br />
2. The tracker is insensitive to background variations such as changing the ceiling and ﬂoor (FloorCeiling) or placing additional walls in the map (Corridor).<br />
3. The tracker does not lose a target even when the target takes several sharp turns (SharpTurn). Note that in conventional tracking, the target is commonly assumed to move smoothly.<br />
4. The tracker is insensitive to a distracting object (Noise1) even when the “bait” is very close to the path (Noise2).<br />
<br />
The proposed tracker is compared against several of the conventional trackers with PID like module for camera control to simulate active tracking. The results are displayed in Tab. 3. <br />
<br />
[[File:table3.PNG|400px|center]]<br />
<br />
The camera control module is implemented such that in the first frame, a manual bounding box must be given to indicate the object to be tracked. For each subsequent frame, the passive tracker then predicts a bounding box which is passed to the Camera Control module. A comparison is made between the two subsequent bounding boxes as per the algorithm and action decision is made.<br />
The results show that the proposed solution outperforms the simulated active tracker. The simulated trackers lost their targets soon. The Meanshift tracker works well when there is no camera shift between continuous frames. Both KCF and Correlation trackers seem not capable of handling such a large camera shift, so they do not work as well as the case in passive tracking. The MIL tracker works reasonably in the active case, while it easily drifts when the object turns suddenly.<br />
<br />
Testing in the UE environment is tabulated in Table 5. Four different environments are tested and based on the long-term TLD tracker. <br />
[[File:table5.PNG|400px|center]]<br />
1. Comparison between S1SP1 and S1MP1 shows that the tracker generalizes well even when the model is trained with target Stefani, revealing that it does not overﬁt to a specialized appearance. <br />
2. The active tracker performs well when changing the path (S1SP1 versus S1SP2), demonstrating that it does not act by memorizing specialized path.<br />
3. When the map is changed, target, and path at the same time (S2MP2), though the tracker could not seize the target as accurately as in previous environments (the AR value drops), it can still track objects robustly (comparable EL value as in previous environments), proving its superior generalization potential. <br />
4. In most cases, the proposed tracker outperforms the simulated active tracker or achieves comparable results if it is not the best. The results of the simulated active tracker also suggest that it is difﬁcult to tune a uniﬁed camera-control module for them, even when a long-term tracker is adopted (see the results of TLD). <br />
<br />
Real world active tracking: To test and evaluate the tracker in real-world scenarios, the network trained on UE environment is tested on a few videos from the VOT dataset. <br />
<br />
[[File:fig7.PNG|400px|center]]<br />
<br />
Fig. 7 shows the output actions for two video clips named Woman and Sphere, respectively. The horizontal axis indicates the position of the target in the image, with a positive (negative) value meaning that a target in the right (left) part. The vertical axis indicates the size of the target, i.e., the area of the ground truth bounding box. Green and red dots indicate turn-left/turn-left-and-move-forward and turn-right/turn-right-and-move-forward actions, respectively. Yellow dots represent No-op action. As the ﬁgure shows, 1) When the target resides in the right (left) side, the tracker tends to turn right (left), trying to move the camera to “pull” the target to the center. 2) When the target size becomes bigger, which probably indicates that the tracker is too close to the target, the tracker outputs no-op actions more often, intending to stop and wait for the target to move farther.<br />
<br />
Video Link to the experimental results can be found below:<br />
[https://youtu.be/C1Bn8WGtv0w Video Demonstration of the Results]<br />
<br />
Supplementary Material for Further Experiments:<br />
[http://proceedings.mlr.press/v80/luo18a/luo18a-supp.zip Additional PDF and Video]<br />
<br />
Action Saliency Map: An input frame is fed into the tracker and forwarded to output the policy function. An action will be sampled subsequently. Then the gradient of this action is propagated backwards to the input layer, the saliency map is generated. According to the saliency map, how the input image affects the tracker's action can be observed. Fig. 8 shows the tracker indeed learns how to find the target, which improves the performance of the model.<br />
[[File:fig8.PNG|400px|center]]<br />
<br />
=Conclusion=<br />
In the paper, an end-to-end active tracker via deep reinforcement learning is proposed. Unlike conventional passive trackers, the proposed tracker is trained in simulators, saving the efforts of human labeling or trial-and-errors in real-world. It shows good generalization to unseen environments. The tracking ability can potentially transfer to real-world scenarios.<br />
=Critique=<br />
The paper presents a solution for active tracking using reinforcement learning. A ConvNet-LSTM network has been adopted. Environment augmentation has been proposed for training the network. The tracker trained using environment augmentation performs better than the one trained without it. This is true in both the ViZDoom and UE environment. The reward function looks intuitive for the task at hand which is object tracking. The virtual environment ViZDoom though used for training and testing, seems to have little or no generalization ability in real-world scenarios. The maps in ViZDoom itself are very simple. The comparison presented in the paper for the ViZDoom testing with changes in the environmental parameters look positive, but the relatively simple nature of the environment needs to be considered while looking at these results. Also, when the floor is replaced by the ceiling, the tracker performs worst in comparison to the other cases in the table, which seems to indicate that the floor and ceiling parameters are somewhat over-fitted in the model. The tracker trained in UE environment is tested against simulated trackers. The results show that the proposed solution performs better than the simulated trackers. However, since the trackers are simulated using the camera control algorithm written for this specific comparison, further testing is required for benchmarking. The real-world challenges of intensity variation, camera details, control signals through beyond the scope of the current paper, still need to be considered while discussing the generalization ability of the model to real-world scenarios. For example, the current action<br />
space includes only six discrete actions, which are inadequate for deployment in the real world because the tracker cannot adapt to the different moving speed of the target. It is also believed<br />
that training the tracker in UE simulator alone is sufficient for a successful real-world deployment. It is better to randomize more aspects of the environment during training, including the texture of each mesh, the illumination condition of the scene, the trajectory of the target as well as the speed of the target.<br />
The results on the real-world videos show a positive result towards the generalization ability of the models in real-world settings. The overall approach presented in the paper is intuitive and the results look promising.<br />
<br />
=Future Work=<br />
The authors did some future work for this paper in several ways. Basically, they implemented a successful robot. Moreover, they enhanced the system to deal with the virtual-to-real gap [1]. Specifically, 1) more advanced environment augmentation techniques have been proposed to boost the environment diversity, which improves the transferability tailored to the real world. 2) A more appropriate action space compared with the conference paper is developed, and using a continuous action space for active tracking is investigated. 3) A mapping from the neural network prediction to the robot control signal is established so as to successfully deliver the end-to-end tracking.<br />
<br />
=References=<br />
[https://arxiv.org/pdf/1808.03405.pdf 1] W. Luo, P. Sun, F. Zhong, W. Liu, T. Zhang, and Y. Wang, “End-to-end Active Object Tracking and Its Real-world Deployment via Reinforcement Learning”.<br />
<br />
[2] Ross, David A, Lim, Jongwoo, Lin, Ruei-Sung, and Yang, Ming- Hsuan. Incremental learning for robust visual tracking. International Journal of Computer Vision, 77(1-3):125–141, 2008.<br />
<br />
[3] Babenko, Boris, Yang, Ming-Hsuan, and Belongie, Serge. Visual tracking with online multiple instance learning. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 983–990, 2009.<br />
<br />
[4] Bolme, David S, Beveridge, J Ross, Draper, Bruce A, and Lui, Yui Man. Visual object tracking using adaptive correlation filters. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 2544–2550, 2010.<br />
<br />
[5] Hare, Sam, Golodetz, Stuart, Saffari, Amir, Vineet, Vibhav, Cheng, Ming-Ming, Hicks, Stephen L, and Torr, Philip HS. Struck: Structured output tracking with kernels. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(10):2096–2109, 2016.<br />
<br />
[6] Kalal, Zdenek, Mikolajczyk, Krystian, and Matas, Jiri. Tracking- learning-detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(7):1409–1422, 2012.<br />
<br />
[7] Wang, Naiyan and Yeung, Dit-Yan. Learning a deep compact image representation for visual tracking. In Advances in Neural Information Processing Systems, pp. 809–817, 2013.<br />
<br />
[8] Wang, Lijun, Ouyang, Wanli, Wang, Xiaogang, and Lu, Huchuan. Stct: Sequentially training convolutional networks for visual tracking. In The IEEE Conference on Computer Vision and Pattern Recognition, pp. 1373–1381, 2016.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Attend_and_Predict:_Understanding_Gene_Regulation_by_Selective_Attention_on_Chromatin&diff=39193Attend and Predict: Understanding Gene Regulation by Selective Attention on Chromatin2018-11-14T23:48:08Z<p>R82zhang: [T] Attention-based Deep Models</p>
<hr />
<div>This page contains a summary of the paper [https://arxiv.org/abs/1708.00339 "Attend and Predict: Understanding Gene Regulation by Selective Attention on Chromatin."] by Singh, Ritambhara, et al. It was published at the Advances in Neural Information Processing Systems (NIPS) in 2017. <br />
<br />
<br />
= Background =<br />
<br />
Gene regulation is the process of controlling which genes in a cell's DNA are turned 'on' (expressed) or 'off' (not expressed). By this process, a functional product such as a protein is created. Even though all the cells of a multicellular organism (e.g., humans) contain the same DNA, different types of cells in that organism may express very different sets of genes. As a result, each cell types have distinct functionality. In other words how a cell operates depends upon the genes expressed in that cell. Many factors including ‘Chromatin modification marks’ influence which genes are abundant in that cell.<br />
<br />
The function of chromatin is to efficiently wraps DNA around bead-like structures of histones into a condensed volume to fit into the nucleus of a cell, and protect the DNA structure and sequence during cell division and replication. Different chemical modifications in the histones of the chromatin, known as histone marks, change spatial arrangement of the condensed DNA structure. Which in turn affects the gene’s expression of the histone mark’s neighboring region. Histone marks can promote (obstruct) the gene to be turned on by making the gene region accessible (restricted). This section of the DNA, where histone marks can potentially have an impact, is known as DNA flanking region or ‘gene region’ which is considered to cover 10k base pair centered at the transcription start site (TSS) (i.e., a 5k base pair in each direction). Unlike genetic mutations, histone modifications are reversible [1]. Therefore, understanding the influence of histone marks in determining gene regulation can assist in developing drugs for genetic diseases.<br />
<br />
= Introduction = <br />
<br />
Revolution in genomic technologies now enables us to profile genome-wide chromatin mark signals. Therefore, biologists can now measure gene expressions and chromatin signals of the ‘gene region’ for different cell types covering whole human genome. The Roadmap Epigenome Project (REMC, publicly available) [2] recently released 2,804 genome-wide datasets of 100 separate “normal” (not diseased) human cells/tissues, among which 166 datasets are gene expression reads and the rest are signal reads of various histone marks. The goal is to understand which histone marks are the most important and how they interact together in gene regulation for each cell type.<br />
<br />
Signal reads for histone marks are high-dimensional and spatially structured. Influence of a histone modification mark can be anywhere in the gene region (covering 10k base pairs centered around the Transcription Start Site of each gene). It is important to understand how the impact of the mark on gene expression varies over the gene region. In other words, how histone signals over the gene region impacts the gene expression. There are different types of histone marks in human chromatin that can have an influence on gene regulation. Researchers have found five standard histone proteins. These five histone proteins can be altered in different combinations with different chemical modifications resulting in a large number of distinct histone modification marks. Different histone modification marks can act as a module to interact with each other and influence the gene expression.<br />
<br />
<br />
This paper proposes an attention-based deep learning model to find how this chromatin factors/ histone modification marks contributes to the gene expression of a particular cell. AttentiveChrome[3] utilizes a hierarchy of multiple LSTM to discover interactions between signals of each histone marks, and learn dependencies among the marks on expressing a gene. The authors included two levels of soft attention mechanism, (1) to attend to the most relevant signals of a histone mark, and (2) to attend to the important marks and their interactions. In this context, ''attention'' refers to weighting the importance of different items differently.<br />
<br />
== Main Contributions ==<br />
The contributions of this work can be summarized as follows:<br />
<br />
* More accurate predictions than the state-of-the-art baselines. This is measured using datasets from REMC on 56 different cell types.<br />
* Better interpretation than the state-of-the-art methods for visualizing deep learning model. They compute the correlation of the attention scores of the model with the mark signal from REMC. <br />
* Like the application of attention models previously in indirectly hinting the parts of the input that the model deemed important, AttentiveChrome can too explain it's decisions by hinting at “what” and “where” it has focused.<br />
* This is the first time that the attention based deep learning approach is applied to a problem in molecular biology.<br />
* Ability to deal with highly modular inputs<br />
<br />
= Previous Works = <br />
<br />
Machine learning algorithms to classify gene expression from histone modification signals have been surveyed by [15]. These algorithms vary from linear regression, support vector machine, and random forests to rule-based learning, and CNNs. To accommodate the spatially structured, high dimensional input data (histone modification signals) these studies applied different feature selection strategies. The preceding research study, DeepChrome [4], by the authors incorporated the best position selection strategy. The positions that are highly correlated to the gene expression are considered as the best positions. This model can learn the relationship between the histone marks. This CNN based DeepChrome model outperforms all the previous works. However, these approaches either (1) failed to model the spatial dependencies among the marks, or (2) required additional feature analysis. Only AttentiveChrome is reported to satisfy all of the eight desirable metrics of a model.<br />
<br />
= AttentiveChrome: Model Formulation =<br />
<br />
The authors proposed an end-to-end architecture which has the ability to simultaneously attend and predict. This method incorporates recurrent neural networks (RNN) composed of LSTM units to model the sequential spatial dependencies of the gene regions and predict gene expression level from The embedding vector, <math> h_t </math>, output of an LSTM module encodes the learned representation of the feature dependencies from the time step 0 to <math> t </math>. For this task, each bin position of the gene region is considered as a time step.<br />
<br />
The proposed AttentiveChrome framework contains following 5 important modules:<br />
<br />
* Bin-level LSTM encoder encoding the bin positions of the gene region (one for each HM mark)<br />
* Bin-level <math> \alpha </math>-Attention across all bin positions (one for each HM mark)<br />
* HM-level LSTM encoder (one encoder encoding all HM marks)<br />
* HM-level <math> \beta </math>-Attention among all HM marks (one)<br />
* The final classification module<br />
<br />
Figure 1 (Supplementary Figure 2) presents an overview of the proposed AttentiveChrome framework.<br />
<br />
<br />
[[File:supplemntary_figure_2.png|thumb|center| 800px |Figure 1: Overview of the all five modules of the proposed AttentiveChrome framework]]<br />
<br />
<br />
<br />
== Input and Output ==<br />
<br />
Each dataset contains the gene expression labels and the histone signal reads for one specific cell type. The authors evaluated AttentiveChrome on 56 different cell types. For each mark, we have a feature/input vector containing the signals reads surrounding the gene’s TSS position (gene region) for the histone mark. The label of this input vector denotes the gene expression of the specific gene. This study considers binary labeling where <math> +1 </math> denotes gene is expressed (on) and <math> -1 </math> denotes that the gene is not expressed (off). Each histone marks will have one feature vector for each gene. The authors integrates the feature inputs and outputs of their previous work DeepChrome [4] into this research. The input feature is represented by a matrix <math> \textbf{X} </math> of size <math> M \times T </math>, where <math> M </math> is the number of HM marks considered in the input, and <math> T </math> is the number of bin positions taken into account to represent the gene region. The <math> j^{th} </math> row of the vector <math> \textbf{X} </math>, <math> x_j</math>, represents sequentially structured signals from the <math> j^{th} </math> HM mark, where <math> j\in \{1, \cdots, M\} </math>. Therefore, <math> x_j^t</math>, in the matrix <math> \textbf{X} </math> represents the value from the <math> t^{th}</math> bin belonging to the <math> j^{th} </math> HM mark, where <math> t\in \{1, \cdots, T\} </math>. If the training set contains <math>N_{tr} </math> labeled pairs, the <math> n^{th} </math> is specified as <math>( X^n, y^n)</math>, where <math> X^n </math> is a matrix of size <math> M \times T </math> and <math> y^n \in \{ -1, +1 \} </math> is the binary label, and <math> n \in \{ 1, \cdots, N_{tr} \} </math>.<br />
<br />
Figure 2 (also refer to Figure 1 (a), and 1(b) for better understanding) exhibits the input feature, and the output of AttentiveChrome for a particular gene (one sample).<br />
<br />
[[File:input-output-attentivechrome.png|center|thumb| 700px | Figure 2: Input and Output of the AttentiveChrome model]]<br />
<br />
== Bin-Level Encoder (one LSTM for each HM) ==<br />
The sequentially ordered elements (each element actually is a bin position) of the gene region of <math> n^{th} </math> gene is represented by the <math> j_{th} </math> row vector <math> x^j </math>. The authors considered each bin position as a time step for LSTM. This study incorporates bidirectional LSTM to model the overall dependencies among a total of <math> T </math> bin positions in the gene region. The bidirectional LSTM contains two LSTMs<br />
* A forward LSTM, <math> \overrightarrow{LSTM_j} </math>, to model <math> x^j </math> from <math> x_1^j </math> to <math> x_T^j </math>, which outputs the embedding vector <math> \overrightarrow{h^t_j} </math>, of size <math> d </math> for each bin <math> t </math><br />
* A reverse LSTM, <math> \overleftarrow{LSTM_j} </math>, to model <math> x^j </math> from <math> x_T^j </math> to <math> x_1^j </math>, which outputs the embedding vector <math> \overleftarrow{h^j_t} </math>, of size <math> d </math> for each bin <math> t </math><br />
<br />
The final output of this layer, embedding vector at <math> t^{th} </math> bin for the <math> j^{th} </math> HM, <math> h^j_t </math>, of size <math> d </math>, is obtained by concatenating the two vectors from the both directions. Therefore, <math> h^j_t = [ \overrightarrow{h^j_t}, \overleftarrow{h^j_t}]</math>. Figure 1 (c) illustrates the module for <math> j=2 </math>.<br />
<br />
== Bin-Level <math> \alpha</math>-attention ==<br />
<br />
Each bin contributes differently in the encoding of the entire <math> j^{th} </math> mark. To highlight the most important bins for prediction a soft attention weight vector <math> \alpha^j </math> of size <math> T </math> is learned for each <math> j </math>. To calculated the soft weight <math> \alpha^j_t </math>, for each <math> t </math>, the embedding vectors <math> \{h^j_1, \cdots, h^j_t \} </math> of all the bins are utilized. The following equation is used:<br />
<br />
<math> \alpha^j_t = \frac{exp(\textbf{W}_b h^j_t)}{\sum_{i=1}^T{exp(\textbf{W}_b h^j_i)}} </math><br />
<br />
<br />
The parameter <math> W_b </math> is learned alongside during the process. Therefore, the <math> j^{th} </math> HM mark can be represented by <math> m^j = \sum_{t=1}^T{\alpha^j_t \times h^j_t}</math>. Here, <math> h^j_t</math> is the embedding vector and <math> \alpha^t_j </math> is the importance weight of the <math> t^{th} </math> bin in the representation of the <math> j^{th} </math> HM mark. Intuitively <math> \textbf{W}_b </math> will learn the cell type. Figure 1(d) shows this module for <math> HM_2 </math>.<br />
<br />
== HM-level Encoder (one LSTM) ==<br />
<br />
Studies observed that HMs work cooperatively to provoke or subdue gene expression [5]. The HM-level encoder (not in the fFgure 1) utilizes one bidirectional LSTM to capture this relationship between the HMs. To formulate the sequential dependency a random sequence is imagined as the authors did not find influence of any specific ordering of the HMs. The representation <math> m_j </math>of the <math> j^{th} </math> HM, <math> HM_j </math>, which is calculated from the bin-level attention layer, is the input of this step. This set based encoder outputs an embedding vector <math> s^j </math> of size <math> d’ </math>, which is the encoding for the <math> j^{th} </math> HM.<br />
<br />
<math> s^j = [ \overrightarrow{LSTM_s}(m_j), \overleftarrow{LSTM_s}(m_j) ] </math><br />
<br />
The dependencies between <math> j^{th} </math> HM and the other HM marks are encoded in <math> s^j </math>, whereas <math> m^j </math> from the previous step encodes the bin dependencies of the <math> j^{th} </math> HM.<br />
<br />
<br />
== HM-Level <math> \beta</math>-attention ==<br />
This second soft attention level (Figure 1(e)) finds the important HM marks for classifying a gene’s expression by learning the importance weights, <math> \beta_j </math>, for each <math> HM_j </math>, where <math> j \in \{ 1, \cdots, M \} </math>. The equation is <br />
<br />
<math> \beta^j = \frac{exp(\textbf{W}_s s^j)}{\sum_{i=1}^M{exp(\textbf{W}_s s^j)}} </math><br />
<br />
The HM-level context parameter <math> \textbf{W}_s </math> is trained jointly in the process. Intuitively <math> \textbf{W}_s </math> learns how the HMs are significant for a cell type. Finally the entire gene region is encoded in a hidden representation <math> \textbf{v} </math>, using the weighted sum of the embedding of all HM marks. <br />
<br />
<br />
<math> \textbf{v} = \sum_{j=1}^MT{\beta^j \times s^j}</math><br />
<br />
<br />
<br />
<br />
<br />
<math> \textbf{v} = \sum_{j=1}^MT{\beta^j \times s^j}</math><br />
<br />
== End-to-end training ==<br />
<br />
The embedding vector <math> \textbf{v} </math> is fed to a simple classification module, <math> f(\textbf{v}) = </math>softmax<math> (\textbf{W}_c\textbf{v}+b_c) </math>, where <math> \textbf{W}_c </math>, and <math> b_c </math> are learnable parameters. The output is the probability of gene expression being high (expressed) or low (suppressed).<br />
The whole model including the attention modules is differentiable. Thus backpropagation can perform end-to-end learning trivially. The negative log-likelihood loss function is minimized in the learning.<br />
<br />
= Experimental Settings =<br />
<br />
This work make use of the REMC dataset. AttentiveChrome is evaluated on 56 different cell types. Similar to DeepChrome, this study considered the following five core HM marks (<math> M=5 </math>). Because these selected marks are uniformly profiled across all 56 cell types in the REMC study.<br />
<br />
[[File:HM.png|center|thumb| 700px | Table 2: Fve core HM marks and their attributes considered in this paper]]<br />
<br />
<br />
<br />
For a gene region 10k base pairs centred at the TSS site (5k bp in each direction) are taken into account. These 10k base pairs are divided into 100 bins, each bin consisting of <math> T=100 </math> continuous bp). Therefore, for each gene in a particular cell type, the input matrix will be of size <math> 5 \times 100 </math>. The gene expression labels are normalized and discretized to represent binary labelling. The sample dataset is divided into three equal sized folds for training, validation, and testing.<br />
<br />
== Model Variations and Two Baselines ==<br />
To evaluate the performance of the proposed model the authors considered RNN method (direct LSTM without any attention), and their prior work DeepChrome as baselines. The results obtained from multiple variations of the AttentiveChrome model are compared with the baselines. The authors considered five variant of AttentiveChrome during performance evaluation. The variants are:<br />
<br />
* LSTM-Attn: one LSTM with attention on the input matrix (does not consider the modular nature of HM marks)<br />
* CNN-Attn: DeepChrome [4] with one attention mechanism incorporated. <br />
* LSTM-<math>\alpha , \beta</math>: the proposed architecture.<br />
* CNN-<math>\alpha , \beta</math>: LSTM module of the proposed architecture replaced with CNN. This variation includes two attention mechanisms. First attention mechanism contains one <math>\alpha</math>-attention on top of a CNN module per HM mark. And, the second -<math>\beta</math>- attention mechanism is used to combine HMs.<br />
* LSTM-<math>\alpha</math>: one LSTM and <math>\alpha</math>-attention per HM mark.<br />
<br />
== Hyperparameters ==<br />
<br />
For all the variants of AttentiveChrome the bin-level LSTM embedding size <math> d</math> is set to 32, and the HM-level LSTM embedding size <math>d’</math> is set to 16. Because of bidirectional LSTM, the size of the embedding vector <math> h_t</math>, and <math>m_j</math> will be 64, and 32 respectively. Size of the context vectors are set accordingly.<br />
<br />
= Performance Evaluation =<br />
<br />
== AUC Scores ==<br />
<br />
This study summarizes AUC scores across all 56 cell types on the test set to compare the methods.<br />
<br />
TABLE 2<br />
<br />
Overall the LSTM-attention models perform better than the DeepChrome (CNN-based) and LSTM baselines. The authors argue that the proposed AttentiveChrome model is a good choice because of its interpretability, even though the performance improvement from DeepChrome is insignificant.<br />
<br />
== Evaluation of Attention Scores for Interpretation ==<br />
<br />
To understand if the model is focusing on the right regions, the authors make use of additional study results from REMC database. To validate the bin attention,signal data of a new histone mark, H3K27ac, referred to as <math>H_{active}</math> in this article, from REMC database is utilized. This particular histone mark is known to mark active region when the gene is expressed (ON). Genome-wide read of this HM mark is available for three important cell types: stem cell (H1-hESC), blood cell (GM12878), and leukemia cell (K562). This particular HM mark is used to analyze the visualization results only and not applied in the learning phase. The authors discussed performance of both the attention mechanisms in this section. <br />
<br />
=== Correlation of Importance Weight of <math>H_{prom}</math> with <math>H_{active}</math> ===<br />
<br />
Average read count of <math>H_{active}</math> across all 100 bins for all the active genes (ON or labeled as <math>+1</math>) in the three selected cell types is calculated. The proposed AttentiveChrome and LSTM-<math>\alpha</math> methods are compared with two widely used visualization techniques, (1) class based, and (2) saliency map applied on the baseline DeepChrome model (CNN-based prior work). Using these visualization methods, the authors calculate the importance weights for <math>H_{prom}</math> (promoter HM mark used in training) across the 100 bins. The Pearson Correlation score between these importance weights and the read count of the <math>H_{active}</math> (HM mark for validation) across the same 100 bins is computed. The <math>H_{active}</math> read counts indicates the actual active regions of those cells. <br />
<br />
TABLE 3<br />
<br />
The results indicate that the proposed models consistently gained highest correlation with <math>H_{active}</math> for all three cell types. Thus, the proposed method is successful to capture the important signals.<br />
<br />
=== Visualization of Attention Weight of bins for each HM or a specific cell type GM12878===<br />
<br />
To visualize bin level attention weights, the authors plotted the average bin-level attention weights for each HM for a specific cell type GM12878 (blood cell) for expressed (ON) genes and suppressed (OFF) genes separately. <br />
<br />
FIGURE 2 (a)<br />
<br />
For the “ON” genes, the attention profiles are well defined for the HM marks, <math>H_{prom}</math>, <math>H_{enhc}</math>, <math>H_{struct}</math>. On the other hand, the weights are low for <math>H_{reprA}</math> and <math>H_{reprB}</math>. The average trend reverses for the “OFF” genes, where the repressor HM marks have more influence than the <math>H_{prom}</math>, <math>H_{enhc}</math>, <math>H_{struct}</math>. This observation agrees with the biologist finding that <math>H_{prom}</math>, <math>H_{enhc}</math>, <math>H_{struct}</math> marks stimulates gene activation and, <math>H_{reprA}</math> and <math>H_{reprB}</math> mark restrains the genes. <br />
<br />
=== Attention Weight of bins with <math>H_{active}</math>===<br />
<br />
The average read counts of <math>H_{active}</math> for the same 100 bins across all the active (ON) genes for the cell type GM12878 is plotted. Besides, for AttentiveChrome the plot of bin-level attention weights of averaged over all the genes that are PREDICTED ON for GM12878 is also provided. The plots exhibit that the <math>H_{prom}</math> profile is similar to <math>H_{active}</math>.<br />
<br />
FIGURE 2(b)<br />
<br />
=== Visualization of HM-level Attention Weight for Gene PAX5 ===<br />
<br />
To visualize HM-level attention weight the authors produces a heatmap for a differentially regulated gene, PAX5, for the three aforementioned cell types. PAX5 plays significant role in gene regulation when stem cells convert to blood cells. This gene is OFF in stem cells (H1-hESC), however it becomes activated when the stem cell is transformed into blood cell (GM12878). The <math>\beta_j</math> weight for <math>H_{repr}</math> is high when the gene is OFF in H1-hESC, and the weight decreases when the gene is ON in GM12878. On the contrary, for <math>H_{prom}</math> mark the <math>\beta_j</math> weight increases from H1-hESC to GM12878 as the gene becomes activated. This information extracted by the deep learning model is also supported by biological literature [16]. <br />
<br />
FIGURE 2(c)<br />
<br />
= Related Works/Studies =<br />
<br />
In the last few years, deep learning models obtained models obtained unprecedented success in diverse research fields. Though as not rapidly as other fields, deep learning based algorithms are gaining popularity among bioinformaticians.<br />
<br />
== Attention-based Deep Models ==<br />
<br />
The idea of attention technique in deep learning is adapted from the human visual perception system. Humans tend to focus over some parts more than the others while perceiving a scene. This mechanism augmented with deep neural networks achieved an excellent outcome in several research topics, such as machine translation. Various types of attention models e.,g., soft [6], or location-aware [7], or hard [8, 9] attentions have been proposed in the literature. In the soft attention model, a soft weight vector is calculated for the overall feature vectors. The extent of the weight is correlated with the degree of importance of the feature in the prediction. In practice, RNN is often used to help implement such models.<br />
<br />
== Visualization and Apprehension of Deep Models ==<br />
<br />
Prior studies mostly focused on interpreting convolutional neural networks (CNN) for image classification. Deconvulation approaches [10] attempt to map hidden layer representations back to an input space. Saliency maps, [11, 12], attempt to use taylor expansion to approximate the network, and identify the most relevant input features. Class optimization [12] based visualisation techniques attempt to find the best example member of each class. Some recent research works [13, 14] tried to understand recurrent neural networks (RNN) for text-based problems. By looking into the features the model attends to, we can interpret the output of a deep model.<br />
<br />
= Conclusion = <br />
<br />
The paper has introduced an attention-based approach called "AttentiveChrome" that deals with both understanding and prediction with several advantages on previous architectures including higher accuracy from state-of-the-art baselines, clearer interpretation than saliency map and class optimization. Finally, according to the authors, this is the first implementation of deep attention to understand gene regulation. AttentiveChrome is claimed to be the first attention based model applied on a molecular biology dataset. The authors expect that through this deep attention mechanism the biologists can have a better understanding of epigenomic data. This model can handle understanding and prediction of hard to interpret biological data. <br />
<br />
= Critiques =<br />
<br />
This paper does not give a considerable algorithmic contribution. They have only used existing methods for this application. This deep learning based method is shown to perform better than simple machine learning models like linear regression and SVMs but this is considerably harder to implement and has many more hyperparameters to tune. The training time is considerably higher, especially because all the parameters are learned together. The dataset considered in the application here also seems to have only a limited number of samples for a study of high complexity. Model hyperparameters have been chosen randomly without any explanation of intuition for them. The authors have also not cited any relevant literature to understand where these numbers came from. <br />
<br />
Discussion about attention scores for interpretation does not provide any clear definition or mention previous literature using them. Reference of literature about H3K27ac, and how its read counts represent active region of a cell should be included. No reasoning given for why only one specific cell type is used to visualize bin level attention weights. Example of some other real world problems where this model can be useful should be provided. <br />
<br />
<br />
<br />
= Additional Resources =<br />
<br />
# [https://qdata.github.io/deep4biomed-web/ Official DeepChrome Website]<br />
# [http://papers.nips.cc/paper/7255-attend-and-predict-understanding-gene-regulation-by-selective-attention-on-chromatin-supplemental.zip Supplemental]<br />
# [https://github.com/QData/AttentiveChrome/blob/master/NIPS%20poster.pdf Poster]<br />
# [https://www.youtube.com/watch?v=tfgmXvSgsQE&feature=youtu.be Video Presentation]<br />
<br />
= Reference =<br />
<br />
[1] Andrew J Bannister and Tony Kouzarides. Regulation of chromatin by histone modifications. Cell Research, 21(3):381–395, 2011.<br />
<br />
[2] Anshul Kundaje, Wouter Meuleman, Jason Ernst, Misha Bilenky, Angela Yen, Alireza Heravi-Moussavi, Pouya Kheradpour, Zhizhuo Zhang, Jianrong Wang, Michael J Ziller, et al. Integrative analysis of 111 reference human epigenomes. Nature, 518(7539):317–330, 2015.<br />
<br />
[3] Singh, Ritambhara, et al. "Attend and Predict: Understanding Gene Regulation by Selective Attention on Chromatin." Advances in Neural Information Processing Systems. 2017.<br />
<br />
[4] Ritambhara Singh, Jack Lanchantin, Gabriel Robins, and Yanjun Qi. Deepchrome: deep-learning for predicting gene expression from histone modifications. Bioinformatics, 32(17):i639–i648, 2016.<br />
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[5] Joanna Boros, Nausica Arnoult, Vincent Stroobant, Jean-François Collet, and Anabelle Decottignies. Polycomb repressive complex 2 and h3k27me3 cooperate with h3k9 methylation to maintain heterochromatin protein 1α at chromatin. Molecular and cellular biology, 34(19):3662–3674, 2014.<br />
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[6] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014.<br />
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[7] Jan K Chorowski, Dzmitry Bahdanau, Dmitriy Serdyuk, Kyunghyun Cho, and Yoshua Bengio. Attention-based models for speech recognition. In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems 28, pages 577–585. Curran Associates, Inc., 2015.<br />
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[8] Minh-Thang Luong, Hieu Pham, and Christopher D. Manning. Effective approaches to attention-based neural machine translation. In Empirical Methods in Natural Language Processing (EMNLP), pages 1412–1421, Lisbon, Portugal, September 2015. Association for Computational Linguistics.<br />
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[9] Huijuan Xu and Kate Saenko. Ask, attend and answer: Exploring question-guided spatial attention for visual question answering. In ECCV, 2016.<br />
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[10] Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In Computer Vision–ECCV 2014, pages 818–833. Springer, 2014.<br />
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[11] David Baehrens, Timon Schroeter, Stefan Harmeling, Motoaki Kawanabe, Katja Hansen, and Klaus-Robert MÃžller. How to explain individual classification decisions. volume 11, pages 1803–1831, 2010.<br />
<br />
[12] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Visualising image classification models and saliency maps. 2013.<br />
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[13] Andrej Karpathy, Justin Johnson, and Fei-Fei Li. Visualizing and understanding recurrent networks. 2015.<br />
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[14] Jiwei Li, Xinlei Chen, Eduard Hovy, and Dan Jurafsky. Visualizing and understanding neural models in nlp. 2015.<br />
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[15] Xianjun Dong and Zhiping Weng. The correlation between histone modifications and gene expression. Epigenomics, 5(2):113–116, 2013.<br />
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[16] Shane McManus, Anja Ebert, Giorgia Salvagiotto, Jasna Medvedovic, Qiong Sun, Ido Tamir, Markus Jaritz, Hiromi Tagoh, and Meinrad Busslinger. The transcription factor pax5 regulates its target genes by recruiting chromatin-modifying proteins in committed b cells. The EMBO journal, 30(12):2388–2404, 2011.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=MULTI-VIEW_DATA_GENERATION_WITHOUT_VIEW_SUPERVISION&diff=39187MULTI-VIEW DATA GENERATION WITHOUT VIEW SUPERVISION2018-11-14T23:30:48Z<p>R82zhang: [T] add common evaluation metrics for generative models</p>
<hr />
<div>This page contains a summary of the paper "[https://openreview.net/forum?id=ryRh0bb0Z Multi-View Data Generation without Supervision]" by Mickael Chen, Ludovic Denoyer, Thierry Artieres. It was published at the International Conference on Learning Representations (ICLR) in 2018. <br />
<br />
==Introduction==<br />
<br />
===Motivation===<br />
High Dimensional Generative models have seen a surge of interest of late with the introduction of Variational Auto-Encoders and Generative Adversarial Networks. This paper focuses on a particular problem where one aims at generating samples corresponding to a number of objects under various views. The distribution of the data is assumed to be driven by two independent latent factors: the content, which represents the intrinsic features of an object, and the view, which stands for the settings of a particular observation of that object (for example, the different angles of the same object). The paper proposes two models using this disentanglement of latent space - a generative model and a conditional variant of the same.<br />
<br />
===Related Work===<br />
<br />
The problem of handling multi-view inputs has mainly been studied from the predictive point of view where one wants, for example, to learn a model able to predict/classify over multiple views of the same object (Su et al. (2015); Qi et al. (2016)). These approaches generally involve (early or late) fusion of the different views at a particular level of a deep architecture. Recent studies have focused on identifying factors of variations from multiview datasets. The underlying idea is to consider that a particular data sample may be thought as the mix of a content information (e.g. related to its class label like a given person in a face dataset) and of a side information, the view, which accounts for factors of variability (e.g. exposure, viewpoint, with/wo glasses...). So, all the samples of the same class contain the same content but different view. A number of approaches have been proposed to disentangle the content from the view, also referred as the style in some papers (Mathieu et al. (2016); Denton & Birodkar (2017)). The two common limitations the earlier approaches pose - as claimed by the paper - are that (i) they usually<br />
consider discrete views that are characterized by a domain or a set of discrete (binary/categorical) attributes (e.g. face with/wo glasses, the color of the hair, etc.) and could not easily scale to a large number of attributes or to continuous views. (ii) most models are trained using view supervision (e.g. the view attributes), which of course greatly helps in the learning of such model, yet prevents their use on many datasets where this information is not available. <br />
<br />
===Contributions===<br />
<br />
The contributions that authors claim are the following: (i) A new generative model able to generate data with various content and high view diversity using a supervision on the content information only. (ii) Extend the generative model to a conditional model that allows generating new views over any input sample. (iii) Report experimental results on four different images datasets to prove that the models can generate realistic samples and capture (and generate with) the diversity of views.<br />
<br />
==Paper Overview==<br />
<br />
===Background===<br />
<br />
The paper uses the concept of the popular GAN (Generative Adverserial Networks) proposed by Goodfellow et al.(2014).<br />
<br />
GENERATIVE ADVERSARIAL NETWORK:<br />
<br />
Generative adversarial networks (GANs) are deep neural net architectures comprised of two nets, pitting one against the other (thus the “adversarial”). GANs was introduced in a paper by Ian Goodfellow and other researchers at the University of Montreal, including Yoshua Bengio, in 2014. Referring to GANs, Facebook’s AI research director Yann LeCun called adversarial training “the most interesting idea in the last 10 years in ML.”<br />
<br />
Let us denote <math>X</math> an input space composed of multidimensional samples x e.g. vector, matrix or tensor. Given a latent space <math>R^n</math> and a prior distribution <math>p_z(z)</math> over this latent space, any generator function <math>G : R^n → X</math> defines a distribution <math>p_G </math> on <math> X</math> which is the distribution of samples G(z) where <math>z ∼ p_z</math>. A GAN defines, in addition to G, a discriminator function D : X → [0; 1] which aims at differentiating between real inputs sampled from the training set and fake inputs sampled following <math>p_G</math>, while the generator is learned to fool the discriminator D. Usually both G and D are implemented with neural networks. The objective function is based on the following adversarial criterion:<br />
<br />
<div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{p_x}[log D(x)] + Ep_z[log(1 − D(G(z)))]</math></div><br />
<br />
where <math>p_x</math> is the empirical data distribution on X .<br />
It has been shown in Goodfellow et al. (2014) that if G∗ and D∗ are optimal for the above criterion, the Jensen-Shannon divergence between <math>p_{G∗}</math> and the empirical distribution of the data <math>p_x</math> in the dataset is minimized, making GAN able to estimate complex continuous data distributions.<br />
<br />
CONDITIONAL GENERATIVE ADVERSARIAL NETWORK:<br />
<br />
In the Conditional GAN (CGAN), the generator learns to generate a fake sample with a specific condition or characteristics (such as a label associated with an image or more detailed tag) rather than a generic sample from unknown noise distribution. Now, to add such a condition to both generator and discriminator, we will simply feed some vector y, into both networks. Hence, both the discriminator D(X,y) and generator G(z,y) are jointly distributed with y. <br />
<br />
Now, the objective function of CGAN is:<br />
<br />
<div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{p_x}[log D(x,y)] + Ep_z[log(1 − D(G(y,z)))]</math></div><br />
<br />
The paper also suggests that many studies have reported that when dealing with high-dimensional input spaces, CGAN tends to collapse the modes of the data distribution, mostly ignoring the latent factor z and generating x only based on the condition y, exhibiting an almost deterministic behavior. At this point, the CGAN also fails to produce a satisfying amount of diversity in generated samples.<br />
<br />
===Generative Multi-View Model===<br />
<br />
''' Objective and Notations: ''' The distribution of the data x ∈ X is assumed to be driven by two latent factors: a content factor denoted c which corresponds to the invariant proprieties of the object and a view factor denoted v which corresponds to the factor of variations. Typically, if X is the space of people’s faces, c stands for the intrinsic features of a person’s face while v stands for the transient features and the viewpoint of a particular photo of the face, including the photo exposure<br />
and additional elements like a hat, glasses, etc.... These two factors c and v are assumed to be independent and these are the factors needed to learn.<br />
<br />
The paper defines two tasks here to be done: <br />
(i) '''Multi View Generation''': we want to be able to sample over X by controlling the two factors c and v. Given two priors, p(c) and p(v), this sampling will be possible if we are able to estimate p(x|c, v) from a training set.<br />
(ii) '''Conditional Multi-View Generation''': the second objective is to be able to sample different views of a given object. Given a prior p(v), this sampling will be achieved by learning the probability p(c|x), in addition to p(x|c, v). Ability to learn generative models able to generate from a disentangled latent space would allow controlling the sampling on the two different axes,<br />
the content and the view. The authors claim the originality of work is to learn such generative models without using any view labeling information.<br />
<br />
The paper introduces the vectors '''c''' and '''v''' to represent latent vectors in R<sup>c</sup> and R<sup>v</sup><br />
<br />
<br />
''' Generative Multi-view Model: '''<br />
<br />
Consider two prior distributions over the content and view factors denoted as <math>p_c</math> and <math>p_v</math>, corresponding to the prior distribution over content and latent factors. Moreover, we consider a generator G that implements a distribution over samples x, denoted as <math>p_G</math> by computing G(c, v) with <math>c ∼ p_c</math> and <math>v ∼ p_v</math>. The objective is to learn this generator so that its first input c corresponds to the content of the generated sample while its second input v, captures the underlying view of the sample. Doing so would allow one to control the output sample of the generator by tuning its content or its view (i.e. c and v).<br />
<br />
The key idea that authors propose is to focus on the distribution of pairs of inputs rather than on the distribution over individual samples. When no view supervision is available the only valuable pairs of samples that one may build from the dataset consist of two samples of a given object under two different views. When we choose any two samples randomly from the dataset from the same object, it is most likely that we get two different views. The paper explains that there are three goals here, (i) As in regular GAN, each sample generated by G needs to look realistic. (ii) As real pairs are composed of two views of the same object, the generator should generate pairs of the same object. Since the two sampled view factors v1 and v2 are different, the only way this can be achieved is by encoding the content vector c which is invariant. (iii) It is expected that the discriminator should easily discriminate between a pair of samples corresponding to the same object under different views from a pair of samples corresponding to a same object under the same view. Because the pair shares the same content factor c, this should force the generator to use the view factors v1 and v2 to produce diversity in the generated pair.<br />
<br />
Now, the objective function of GMV Model is:<br />
<br />
<div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{x_1,x_2}[log D(x_1,x_2)] + E_{v_1,v_2}[log(1 − D(G(c,v_1),G(c,v_2)))]</math></div><br />
<br />
Once the model is learned, generator G that generates single samples by first sampling c and v following <math>p_c</math> and <math>p_v</math>, then by computing G(c, v). By freezing c or v, one may then generate samples corresponding to multiple views of any particular content, or corresponding to many contents under a particular view. One can also make interpolations between two given views over a particular content, or between two contents using a particular view<br />
<br />
<div style="text-align: center;font-size:100%">[[File:GMV.png]]</div><br />
<br />
===Conditional Generative Model (C-GMV)===<br />
<br />
C-GMV is proposed by the authors to be able to change the view of a given object that would be provided as an input to the model. This model extends the generative model's the ability to extract the content factor from any given input and to use this extracted content in order to generate new views of the corresponding object. To achieve such a goal, we must add to our generative model an encoder function denoted <math>E : X → R^C</math> that will map any input in X to the content space <math>R^C</math><br />
<br />
Input sample x is encoded in the content space using an encoder function, noted E (implemented as a neural network).<br />
This encoder serves to generate a content vector c = E(x) that will be combined with a randomly sampled view <math>v ∼ p_v</math> to generate an artificial example. The artificial sample is then combined with the original input x to form a negative pair. The issue with this approach is that CGAN is known to easily miss modes of the underlying distribution. The generator enters in a state where it ignores the noisy component v. To overcome this phenomenon, we use the same idea as in GMV. We build negative pairs <math>(G(c, v_1), G(c, v_2))</math> by randomly sampling two views <math>v_1</math> and <math>v_2</math> that are combined to get a unique content c. c is computed from a sample x using the encoder E, i.e. c= E(x). By doing so, the ability of our approach to generating pairs with view diversity is preserved. Since this diversity can only be captured by taking into account the two different view vectors provided to the model (<math>v_1</math> and <math>v_2</math>), this will encourage G(c, v) to generate samples containing both the content information c, and the view v. Positive pairs are sampled from the training set and correspond to two views of a given object.<br />
<br />
The Objective function for C-GMV will be:<br />
<br />
<div style="text-align: center;font-size:100%"><math>\underset{G}{min} \ \underset{D}{max}</math> <math>E_{x_1,x_2 ~ p_x|l(x_1)=l(x_2)}[log D(x_1,x_2)] + E_{v_1,v_2 ~ p_v,x~p_x}[log(1 − D(G(E(x),v_1),G(E(x),v_2)))]+E_{v∼p_v,x∼p_x}[log(1 − D(G(E(x), v), x))] </math></div><br />
<br />
<div style="text-align: center;font-size:100%">[[File:CGMV.png]]</div><br />
<br />
==Experiments and Results==<br />
<br />
The authors have given an exhaustive set of results and experiments.<br />
<br />
Datasets: The two models were evaluated by performing experiments over four image datasets of various domains. Note that when supervision is available on the views (like CelebA for example where images are labeled with attributes) it is not used for learning models. The only supervision that is used is if two samples correspond to the same object or not.<br />
<br />
<div style="text-align: center;font-size:100%">[[File:table_data.png]]</div><br />
<br />
<br />
Model Architecture: Same architectures for every dataset. The images were rescaled to 3×64×64 tensors. The generator G and the discriminator D follow that of the DCGAN implementation proposed in Radford et al. (2015). The Adam optimiser was used, with a batch size of 128. the learning rates for G and D were set to 1*10<sup>-3</sup> and 2*10<sup>-4</sup> respectively for the GMV experiments. In the C-GMV experiments, learning rates of 5*10<sup>-5</sup> were used. Alternating gradient descent was used to optimize the different objectives of the network components.<br />
<br />
Baselines: Most existing methods are learned on datasets with view labeling. To fairly compare with alternative models, authors have built baselines working in the same conditions as the models in this paper. In addition, models are compared with the model from Mathieu et al. (2016). Results gained with two implementations are reported, the first one based on the implementation provided by the authors2 (denoted Mathieu et al. (2016)), and the second one (denoted Mathieu et al. (2016) (DCGAN) ) that implements the same model using architectures inspired from DCGAN Radford et al. (2015), which is more stable and that was tuned to allow a fair comparison with our approach. For pure multi-view generative setting, generative model(GMV) is compared with standard GANs that are learned to approximate the joint generation of multiple samples: DCGANx2 is learned to output pairs of views over the same object, DCGANx4 is trained on quadruplets, and DCGANx8 on eight different views. <br />
<br />
===Generating Multiple Contents and Views===<br />
<br />
Figure 1 shows examples of generated images by our model and Figure 4 shows images sampled by the DCGAN based models (DCGANx2, DCGANx4, and DCGANx8) on 3DChairs and CelebA datasets.<br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig1_gmv.png]]</div><br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig4_gmv.png]]</div><br />
<br />
<br />
Figure 5 shows additional results, using the same presentation, for the GMV model only on two other datasets<br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig5_gmv.png]]</div><br />
<br />
Figure 6 shows generated samples obtained by interpolation between two different view factors (left) or two content factors (right). It allows us to have a better idea of the underlying view/content structure captured by GMV. We can see that our approach is able to smoothly move from one content/view to another content/view while keeping the other factor constant. This also illustrates that content and view factors are well independently handled by the generator i.e. changing the view<br />
does not modify the content and vice versa.<br />
<br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig6_gmv.png]]</div><br />
<br />
===Generating Multiple Views of a Given Object===<br />
<br />
The second set of experiments evaluates the ability of C-GMV to capture a particular content from an input sample and to use this content to generate multiple views of the same object. Figure 7 and 8 illustrate the diversity of views in samples generated by our model and compare our results with those obtained with the CGAN model and to models from Mathieu et al. (2016). For each row, the input sample is shown in the left column. New views are generated from that input and shown to the right, with those generated from C_GMV in the centre, and those generated from CGAN on the far right.<br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig7_gmv.png]]</div><br />
<br />
<br />
<div style="text-align: center;font-size:100%">[[File:fig8_gmv.png]]</div><br />
<br />
=== Evaluation of the Quality of Generated Samples ===<br />
<br />
There are usually several metrics to evaluate generative models. Some of them are: <br />
<ol><br />
<li>Inception Score</li><br />
<li>Latent Space Interpolation</li><br />
<li>log-likelihood (LL) score</li><br />
<li> minimum description length (MDL) score</li><br />
<li>minimum message length (MML) score</li><br />
<li>Akaike Information Criterion (AIC) score</li><br />
<li>Bayesian Information Criterion (BIC) score</li><br />
</ol><br />
<br />
<br />
<br />
<br />
<br />
The authors did sets of experiments aimed at evaluating the quality of the generated samples. They have been made on the CelebA dataset and evaluate (i) the ability of the models to preserve the identity of a person in multiple generated views, (ii) to generate realistic samples, (iii) to preserve the diversity in the generated views and (iv) to capture the view distributions of the original dataset.<br />
<br />
<div style="text-align: center;font-size:100%">[[File:tab3.png]]</div><br />
<br />
<br />
<div style="text-align: center;font-size:100%">[[File:tab4.png]]</div><br />
<br />
==Conclusion==<br />
<br />
The paper proposed a generative model, which can be learnt from multi-view data without any supervision. Moreover, it introduced a conditional version that allows generating new views of an input image. Using experiments, they proved that the model can capture content and view factors. Here, the paper showed that the application of architecture search to dense image prediction was achieved through a) The construction of a recursive search space leveraging innovation in the dense prediction literature b) construction of a fast proxy predictive of a large task. The learned architecture was shown to surpass human invented architectures across three dense image prediction tasks i.e scene parsing, person part segmentation and semantic segmentation. <br />
<br />
==Future Work==<br />
The authors of the papers mentioned that they plan to explore using their model for data augmentation, as it can produce other data views for training, in both semi-supervised and one-shot/few-shot learning settings. <br />
<br />
==Critique==<br />
<br />
The main idea is to train the model with pairs of images with different views. It is not that clear as to what defines a view in particular. The algorithms are largely based on earlier concepts of GAN and CGAN The authors give reference to the previous papers tackling the same problem and clearly define that the novelty in this approach is not making use of view labels. The authors give a very thorough list of experiments which clearly establish the superiority of the proposed models to baselines.<br />
<br />
However, this paper only tested the model on rather constrained examples. As was observed in the results the proposed approach seems to have a high sample complexity relying on training samples covering the full range of variations for both specified and unspecified variations. Also, the proposed model does not attempt to disentangle variations within the specified and unspecified components.<br />
<br />
==References==<br />
<br />
[1] Mickael Chen, Ludovic Denoyer, Thierry Artieres. MULTI-VIEW DATA GENERATION WITHOUT VIEW SUPERVISION. Published as a conference paper at ICLR 2018<br />
<br />
[2] Michael F Mathieu, Junbo Jake Zhao, Junbo Zhao, Aditya Ramesh, Pablo Sprechmann, and Yann LeCun. Disentangling factors of variation in deep representation using adversarial training. In Advances in Neural Information Processing Systems, pp. 5040–5048, 2016.<br />
<br />
[3] Mathieu Aubry, Daniel Maturana, Alexei Efros, Bryan Russell, and Josef Sivic. Seeing 3d chairs: exemplar part-based 2d-3d alignment using a large dataset of cad models. In CVPR, 2014.<br />
<br />
[4] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pp. 2672–2680, 2014.<br />
<br />
[5] Emily Denton and Vighnesh Birodkar. Unsupervised learning of disentangled representations from video. arXiv preprint arXiv:1705.10915, 2017.</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Reinforcement_Learning_of_Theorem_Proving&diff=39183Reinforcement Learning of Theorem Proving2018-11-14T23:16:49Z<p>R82zhang: [T]Add more information about MCTS.</p>
<hr />
<div>== Introduction ==<br />
Automated reasoning over mathematical proof was a major motivation for the development of computer science. Automated theorem provers (ATP) can in principle be used to attack any formally stated mathematical problem and is a research area that has been present since the early 20th century [1]. As of today, state-of-art ATP systems rely on the fast implementation of complete proof calculi. such as resolution and tableau. However, they are still far weaker than trained mathematicians. Within current ATP systems, many heuristics are essential for their performance. As a result, <br />
in recent years machine learning has been used to replace such heuristics and improve the performance of ATPs.<br />
<br />
In this paper, the authors propose a reinforcement learning based ATP, rlCoP. The proposed ATP reasons within first-order logic. The underlying proof calculi are the connection calculi [2], and the reinforcement learning method is Monte Carlo tree search along with policy and value learning. It is shown that reinforcement learning results in a 42.1% performance increase compared to the base prover (without learning).<br />
<br />
== Related Work ==<br />
C. Kalizyk and J. Urban proposed a supervised learning based ATP, FEMaLeCoP, whose underlying proof calculi is the same as this paper in 2015 [3]. Their algorithm learns from existing proofs to choose the next tableau extension step. Such systems are known to only learn a high-level selection of relevant facts from a large knowledge base and delegate the internal proof search to standard ATP systems. S. Loos, et al. developed an supervised learning ATP system in 2017 [4], with superposition as their proof calculi. However, they chose deep neural network (CNNs and RNNs) as feature extractor. These systems are treated as black boxes in literature with not much understanding of their performances possible. <br />
<br />
Some other works add Monte Carlo tree search to connection tableau, without reinforcement learning iterations, with complete backtracking and without learned value. This is closest to the authors' approach but the performance is poorer than this paper. <br />
<br />
On a different note, A. Alemi, et al. proposed a deep sequence model for premise selection in 2016 [5], and they claim to be the first team to involve deep neural networks in ATPs. Although premise selection is not directly linked to automated reasoning, it is still an important component in ATPs, and their paper provides some insights into how to process datasets of formally stated mathematical problems.<br />
<br />
== First Order Logic and Connection Calculi ==<br />
Here we assume basic first-order logic and theorem proving terminology, and we will offer a brief introduction of the bare prover and connection calculi. Let us try to prove the following first-order sentence.<br />
<br />
[[file:fof_sentence.png|frameless|center]]<br />
<br />
This sentence can be transformed into a formula in Skolemized Disjunctive Normal Form (DNF), which is referred to as the "matrix".<br />
<br />
[[file:skolemized_dnf.png|frameless|center]] <br />
[[file:matrix.png|frameless|center]] <br />
<br />
The original first-order sentence is valid if and only if the Skolemized DNF formula is a tautology. The connection calculi attempt to show that the Skolemized DNF formula is a tautology by constructing a tableau. We will start at the special node, root, which is an open leaf. At each step, we select a clause (for example, clause <math display="inline">P \wedge R</math> is selected in the first step), and add the literals as children for an existing open leaf. For every open leaf, examine the path from the root to this leaf. If two literals on this path are unifiable (for example, <math display="inline">Qx'</math> is unifiable with <math display="inline">\neg Qc</math>), this leaf is then closed. In standard terminology, it states that a connection is found on this branch.<br />
<br />
[[file:tableaux_example.png|thumb|center|Figure 1. An example of closed tableaux. Adapted from [2]]]<br />
<br />
The paper's goal is to close every leaf, i.e. on every branch, there exists a connection. If such state is reached, the paper has shown that the Skolemized DNF formula is a tautology, thus proving the original first-order sentence. As we can see from the constructed tableaux, the example sentence is indeed valid.<br />
<br />
In formal terms, the rules of connection calculi is shown in Figure 2, and the formal tableaux for the example sentence is shown in Figure 3. Each leaf is denoted as <math display="inline">subgoal, M, path</math> where <math display="inline">subgoal</math> is a list of literals that we need to find connection later, <math display="inline">M</math> stands for the matrix, and <math display="inline">path</math> stands for the path leading to this leaf.<br />
<br />
[[file:formal_calculi.png|thumb|center|Figure 2. Formal connection calculi. Adapted from [2].]]<br />
[[file:formal_tableaux.png|thumb|center|Figure 3. Formal tableaux constructed from the example sentence. Adapted from [2].]]<br />
<br />
To sum up, the bare prover follows a very simple algorithm. given a matrix, a non-negated clause is chosen as the first subgoal. The function ''prove(subgoal, M, path)'' is stated as follows:<br />
* If ''subgoal'' is empty<br />
** return ''TRUE''<br />
* If reduction is possible<br />
** Perform reduction, generating ''new_subgoal'', ''new_path''<br />
** return ''prove(new_subgoal, M, new_path)''<br />
* For all clauses in ''M''<br />
** If a clause can do extension with ''subgoal''<br />
** Perform extension, generating ''new_subgoal1'', ''new_path'', ''new_subgoal2''<br />
** return ''prove(new_subgoal1, M, new_path)'' and ''prove(new_subgoal2, M, path)''<br />
* return ''FALSE''<br />
<br />
It is important to note that the bare prover implemented in this paper is incomplete. Here is a pathological example. Suppose the following matrix (which is trivially a tautology) is feed into the bare prover. Let clause <math display="inline">P(0)</math> be the first subgoal. Clearly choosing <math display="inline">\neg P(0)</math> to extend will complete the proof.<br />
<br />
[[file:pathological.png|frameless|center]] <br />
<br />
However, if we choose <math display="inline">\neg P(x) \lor P(s(x))</math> to do extension, the algorithm will generate an infinite branch <math display="inline">P(0), P(s(0)), P(s(s(0))) ...</math>. It is the task of reinforcement learning to guide the prover in such scenarios towards a successful proof.<br />
<br />
In addition, the provability of first-order sentences is generally undecidable (this result is named the Church-Turing Thesis), which sheds light on the difficulty of automated theorem proving.<br />
<br />
== Mizar Math Library ==<br />
Mizar Math Library (MML) is a library of mathematical theories. The axioms behind the library is the Tarski-Grothendieck set theory, written in first-order logic. The library contains 57,000+ theorems and their proofs, along with many other lemmas, as well as unproven conjectures. Figure 4 shows a Mizar article of the theorem "If <math display="inline"> p </math> is prime, then <math display="inline"> \sqrt p </math> is irrational."<br />
<br />
[[file:mizar_article.png|thumb|center|Figure 3. An article from MML. Adapted from [6].]]<br />
<br />
The training and testing data for this paper is a subset of MML, the Mizar40, which is 32,524 theorems proved by automated theorem provers. Below is an example from the Mizar40 library, it states that with ''d3_xboole_0'' and ''t3_xboole_0'' as premises, we can prove ''t5_xboole_0''.<br />
<br />
[[file:mizar40_0.png|frameless|center]]<br />
[[file:mizar40_1.png|frameless|center]]<br />
[[file:mizar40_2.png|frameless|center]]<br />
[[file:mizar40_3.png|frameless|center]]<br />
<br />
== Monte Carlo Guidance ==<br />
<br />
Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes. The focus of Monte Carlo tree search is on the analysis of the most promising moves, expanding the search tree based on random sampling of the search space. Then the expansion will then be used to weight the node in the search tree.<br />
<br />
In the reinforcement learning setting, the action is defined as one inference (either reduction or extension). The proof state is defined as the whole tableaux. To implement Monte-Carlo tree search, each proof state <math display="inline"> i </math> needs to maintain three parameters, its prior probability <math display="inline"> p_i </math>, its total reward <math display="inline"> w_i </math>, and number of its visits <math display="inline"> n_i </math>. If no policy learning is used, the prior probabilities are all equal to one. <br />
<br />
A simple heuristic is used to estimate the future reward of leaf states: suppose leaf state <math display="inline"> i </math> has <math display="inline"> G_i </math> open subgoals, the reward is computed as <math display="inline"> 0.95 ^ {G_i} </math>. This will be replaced once value learning is implemented.<br />
<br />
The standard UCT formula is chosen to select the next actions in the playouts<br />
\begin{align}<br />
{\frac{w_i}{n_i}} + 2 \cdot p_i \cdot {\sqrt{\frac{\log N}{n_i}}}<br />
\end{align}<br />
where <math display="inline"> N </math> stands for the total number of visits of the parent node.<br />
<br />
The bare prover is asked to play <math display="inline"> b </math> playouts of length <math display="inline"> d </math> from the empty tableaux, each playout backpropagates the values of proof states it visits. After these <math display="inline"> b </math> playouts a special action (inference) is made, corresponding to an actual move, resulting in a new bigstep tableaux. The next <math display="inline"> b </math> playouts will start from this tableaux, followed by another bigstep, etc.<br />
<br />
== Policy Learning and Guidance ==<br />
<br />
From many runs of MCT, we will know the prior probability of actions in particular proof states, we can extract the frequency of each action <math display="inline"> a </math>, and normalize it by dividing with the average action frequency at that state, resulting in a relative proportion <math display="inline"> r_a \in (0, \infty) </math>. We characterize the proof states for policy learning by extracting human-engineered features. Also, we characterize actions by extracting features from the clause chosen and literal chosen as well. Thus we will have a feature vector <math display="inline"> (f_s, f_a) </math>. <br />
<br />
The feature vector <math display="inline"> (f_s, f_a) </math> is regressed against the associated <math display="inline"> r_a </math>.<br />
<br />
During the proof search, the prior probabilities <math display="inline"> p_i </math> of available actions <math display="inline"> a_i </math> in a state <math display="inline"> s </math> is computed as the softmax of their predictions.<br />
<br />
Training examples are only extracted from big step states, making the amount of training data manageable.<br />
<br />
== Value Learning and Guidance ==<br />
<br />
Bigstep states are also used for proof state evaluation. For a proof state <math display="inline"> s </math>, if it corresponds to a successful proof, the value is assigned as <math display="inline"> v_s = 1 </math>. If it corresponds to a failed proof, the value is assigned as <math display="inline"> v_s = 0 </math>. For other scenarios, denote the distance between state <math display="inline"> s </math> and a successful state as <math display="inline"> d_s </math>, then the value is assigned as <math display="inline"> v_s = 0.99^{d_s} </math> <br />
<br />
Proof state feature <math display="inline"> f_s </math> is regressed against the value <math display="inline"> v_s </math>. During the proof search, the reward of leaf states are computed from this prediction.<br />
<br />
== Features and Learners ==<br />
For proof states, features are collected from the whole tableaux (subgoals, matrix, and paths). Each unique symbol is represented by an integer, and the tableaux can be represented as a sequence of integers. Term walk is implemented to combine a sequence of integers into a single integer by multiplying components by a fixed large prime and adding them up. Then the resulting integer is reduced to a smaller feature space by taking modulo by a large prime.<br />
<br />
For actions the feature extraction process is similar, but the term walk is over the chosen literal and the chosen clause.<br />
<br />
In addition to the term walks, they also added several common features: number of goals, total symbol size of all goals, length of active paths, number of current variable instantiations, most common symbols.<br />
<br />
The whole project is implemented in OCaml, and XGBoost is ported into OCaml as the learner.<br />
<br />
== Experimental Results ==<br />
The authors split Mizar40 dataset into 90% training examples and 10% testing examples. 200,000 inferences are allowed for each problem. 10 iterations of policy and value learning are performed (based on MCT). The training and testing results are shown as follows. In the table, ''mlCoP'' represents for the bare prover with iterative deepening (i.e. a complete automated theorem prover with connection calculi), and ''bare prover'' stands for the prover implemented in this paper, without MCT guidance.<br />
<br />
[[file:atp_result0.jpg|frane|center]]<br />
[[file:atp_result1.jpg|frame|center|Figure 4. Experimental result on Mizar40 dataset]]<br />
<br />
As shown by these results, reinforcement learning leads to a significant performance increase for automated theorem proving, the 42.1% performance improvement is unusually high, since the published improvement in this field is typically between 3% and 10%. [1]<br />
<br />
== Conclusions ==<br />
In this work, the authors developed an automated theorem prover that uses no domain engineering and instead replies on MCT guided by reinforcement learning. The resulting system is more than 40% stronger than the baseline system. The authors believe that this is a landmark in the field of automated reasoning, demonstrating that building general problem solvers by reinforcement learning is a viable approach. [1]<br />
<br />
== Critiques ==<br />
Until now, automated reasoning is relatively new to the field of machine learning, and this paper shows a lot of promise in this research area.<br />
<br />
The feature extraction part of this paper is less than optimal. It is my opinion that with proper neural network architecture, deep learning extracted features will be superior to human-engineered features, which is also shown in [4, 5].<br />
<br />
Also, the policy-value learning iteration is quite inefficient. The learning loop is:<br />
* Loop <br />
** Run MCT with the previous model on an entire dataset<br />
** Collect MCT data<br />
** Train a new model<br />
If we adopt this to an online learning scheme by learning as soon as MCT generates new data, and update the model immediately, there might be some performance increase.<br />
<br />
The experimental design of this paper has some flaws. The authors compare the performance of ''mlCoP'' and ''rlCoP'' by limiting them to the same number of inference steps. However, every inference step of ''rlCoP'' requires additional machine learning prediction, which costs more time. A better way to compare their performance is to set a time limit.<br />
<br />
It would also be interesting to study automated theorem proving in another logic system, like high order logic.<br />
<br />
== References ==<br />
[1] C. Kaliszyk, et al. Reinforcement Learning of Theorem Proving. NIPS 2018.<br />
<br />
[2] J. Otten and W. Bibel. leanCoP: Lean Connection-Based Theorem Proving. Journal of Symbolic Computation, vol. 36, pp. 139-161, 2003.<br />
<br />
[3] C. Kaliszyk and J. Urban. FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover. Lecture Notes in Computer Science. vol. 9450. pp. 88-96, 2015.<br />
<br />
[4] S. Loos, et al. Deep Network Guided Proof Search. LPAR-21, 2017.<br />
<br />
[5] A. Alemi, et al. DeepMath-Deep Sequence Models for Premise Selection. NIPS 2016.<br />
<br />
[6] Mizar Math Library. http://mizar.org/library/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38711Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T19:03:47Z<p>R82zhang: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] <br />
<br />
Goal:<br />
This paper presents a method of let computers searching for a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. In theory, the search space consists of what they choose for the network backbone and the internal structure of the DPC. In practice, they just used MobileNet and Modified Xception net as the backbone. So the search space only consists of the internal structure of the DPC cell.<br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38710Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:58:31Z<p>R82zhang: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] <br />
<br />
Goal:<br />
This paper presents a method of let computers searching for a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the Cell/Block approach above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38709Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:57:32Z<p>R82zhang: /* Introduction */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] <br />
<br />
Goal:<br />
This paper presents a method of let computers searching for a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38708Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:55:08Z<p>R82zhang: /* Result */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
As we can see, the searched DPC model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38707Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:54:39Z<p>R82zhang: /* Result */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
As we can see, the search model achieves better performance (measured by mIOU) with less than half of the computational resources(parameters), and 37% less of operations (add and multiply).<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38706Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:51:03Z<p>R82zhang: /* References */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]<br />
<br />
9. AutoML: https://cloud.google.com/automl/ <br />
<br />
10. Custom-vision: https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38705Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:50:16Z<p>R82zhang: /* Critique */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than hire data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers. <br />
<br />
There are some real-world applications that already deploy NAS techniques in production. Two good examples are Google AutoML and Microsoft Custom Vision AI.<br />
[9, 10]<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38704Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:47:36Z<p>R82zhang: /* Result */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
=Future work=<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than higher data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38703Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:44:09Z<p>R82zhang: /* Critique */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than higher data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38702Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:43:40Z<p>R82zhang: /* Critique */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of computational power. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. <br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans, and we define these operations based on previous experience. That also prevents the search algorithm to find something revolutionary.<br />
<br />
4. May have the potential to take away entry-level data science jobs.<br />
If there is a significant reduction in the search cost, it will be more cost effective to apply NAS rather than higher data scientists. Once matured, this technology will have the potential to take away entry-level data science jobs and make data science jobs only possessed by high-level researchers.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38701Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:37:51Z<p>R82zhang: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] <br />
In the implementation, they used Google's black box optimization tool Google vizier. It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38700Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:36:14Z<p>R82zhang: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|500px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38699Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:36:04Z<p>R82zhang: </p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network architecture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:search_strategy.png|200px]]<br />
</div><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:search_strategy.png&diff=38697File:search strategy.png2018-11-12T18:32:20Z<p>R82zhang: </p>
<hr />
<div></div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38696Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:26:31Z<p>R82zhang: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm, and Grid Search.<br />
<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that are close to the current observed best point. Intuitively it makes sense because it combines exploration and exploitation. When you sample points close to the current<br />
optimal point, you are doing exploitation. And when you sample points randomly, you are doing exploration.<br />
<br />
<br />
They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38694Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:19:38Z<p>R82zhang: /* References */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]<br />
<br />
8. Github implementation of Google Vizer, a black-box optimization tool [https://github.com/tobegit3hub/advisor.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38693Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:18:30Z<p>R82zhang: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it [8]<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38692Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:18:11Z<p>R82zhang: /* References */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]<br />
<br />
7. .J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for black-box optimization. In SIGKDD, 2017.]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38691Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:17:48Z<p>R82zhang: /* Search Strategy */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques. [7] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38690Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:10:58Z<p>R82zhang: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [8].J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In<br />
CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for<br />
black-box optimization. In SIGKDD, 2017.] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
<br />
<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38689Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:10:17Z<p>R82zhang: /* Result */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [8].J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In<br />
CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for<br />
black-box optimization. In SIGKDD, 2017.] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
<br />
<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 400px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|400px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38688Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:09:22Z<p>R82zhang: /* What they used in this paper */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|500px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [8].J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In<br />
CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for<br />
black-box optimization. In SIGKDD, 2017.] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
<br />
<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 200px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|200px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38687Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T18:09:01Z<p>R82zhang: [P] formatting</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.50.04 PM.png|200px]]<br />
</div><br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is a supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [8].J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In<br />
CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for<br />
black-box optimization. In SIGKDD, 2017.] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
<br />
<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.51.14 PM.png| 200px]]<br />
</div><br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-12 at 12.32.05 PM.png|200px]]<br />
</div><br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38686Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T17:59:47Z<p>R82zhang: /* Multi-branch networks */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
[pic]<br />
[1]<br />
This paper's approach is very close to the number 3 above<br />
<br />
The paper defines two components: The "network backbone" and a cell unit called "DPC". The network backbone's job is to take input image as a tensor and return a feature map f that is supposedly good abstraction of the image. The DPC is what they introduced in this paper, short for Dense Prediction Cell. The search space consists of what they choose for the network backbone and the internal<br />
structure of the DPC. <br />
<br />
For the network backbone, they simply choose from existing mature architecture. They used networks like Mobile-Net-v2, Inception-Net, and e.t.c. For the structure of DPC, they define a smaller unit of called branch. A branch is a triple of (Xi, OP, Yi), where Xi is an input tensor, and OP is the operation that can be done on the tensor, and Yi is the resulting after the Operation. <br />
<br />
In the paper, they set each DPC consists of 5 cells for the balance expressivity and computational tractability.<br />
<br />
The operator space, OP, is defined as the following set of functions:<br />
<ol><br />
<li>Convolution with a 1 × 1 kernel.</li><br />
<li>3×3 atrous separable convolution with rate rh×rw, where rh and rw ∈ {1, 3, 6, 9, . . . , 21}. </li><br />
<li>Average spatial pyramid pooling with grid size gh × gw, where gh and gw ∈ {1, 2, 4, 8}. </li><br />
</ol><br />
<br />
<br />
The operation spae has 1 + 8×8 + 4×4 = 81 functions in the operator space, resulting in i × 81 possible options. Therefore, for B = 5,<br />
the search space size is B! × 81^B ≈ 4.2 × 10^11 configurations.<br />
<br />
<br />
<br />
=Search Strategy=<br />
<br />
<!-- spatial pooling layer[8] https://arxiv.org/pdf/1406.4729.pdf --><br />
<br />
There are some common search strategies used in the field of NAS, such as Reinforcement learning, Random search, Evolution algorithm.<br />
The one they used in the paper is Random Search. It basically samples points from the search space uniformly at random as well as sampling<br />
some points that is close to the current observed best point. They quoted from another paper that claims random search performs the random search is competitive with reinforcement learning and other learning techniques [8].J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In<br />
CVPR, 2015.<br />
In the implementation wise, they used a Google vizier, which is a search tool for black box optimization. [D. Golovin, B. Solnik, S. Moitra, G. Kochanski, J. Karro, and D. Sculley. Google vizier: A service for<br />
black-box optimization. In SIGKDD, 2017.] It is not open source, but there is an open source implementation of it https://github.com/tobegit3hub/advisor.<br />
<br />
<br />
<br />
<br />
=Performance Evaluation Strategy=<br />
<br />
The evaluation in this particular task is very tricky. The reason is we are evaluating neural network here. In order to evaluate it, we need to train it first. And we are doing pixel level classification on images with high resolutions, so the naive approach would require a tremendous amount of computational resources. <br />
<br />
The way they solve it in the paper is defining a proxy task. The proxy task is a task that requires sufficient less computational <br />
resources, while can still give a good estimate of the performance of the network. In most image classical tasks of NAS, the proxy<br />
task is to train the network on images of lower resolution. The assumption is, if the network performs well on images with lower density, it should reasonably perform well on images with higher resolution.<br />
<br />
However, the above approach does not work on this case. The reason is that the dense prediction tasks innately require high-resolution images as training data. The approach used in the paper is the flowing:<br />
<ol><br />
<li> Use a smaller backbone for proxy task</li><br />
<li> caching the feature maps produced by the network backbone on the training set and directly building a single DPC on top of it </li><br />
<li> Early stopping train for 30k iterations with a batch size of 8</li><br />
</ol><br />
<br />
If training on the large-scale backbone without fixing the weights of the backbone, they would need one week to train a network on a P100 GPU, but now they cut down the proxy task to be run 90 min. Then they rank the selected architectures, choosing the top 50 and do <br />
a full evaluation on it.<br />
<br />
The evaluation metric they used is called mIOU, which is pixel level intersection over union. Which just the area of the intersection<br />
of the ground truth and the prediction over the area of the union of the ground truth and the prediction.<br />
<br />
=Result=<br />
<br />
This method achieves state of art performances in many datasets. The following table quantifies the gain on performance on many datasets.<br />
<br />
[pic]<br />
The chose to train on modified Xception network as a backbone, and the following are the resulting architecture for the DPC.<br />
<br />
[pic]<br />
<br />
<br />
= Future work and real-world applications<br />
The author suggests that when increasing the number of branches in the DPC, there might be a further gain on the performance on the<br />
image segmentation task. However, although the random search in an exponentially growing space may become more challenging. There may need more intelligent search strategy.<br />
<br />
<br />
There are some real-world applications that already deploy NAS techniques in production. The search technique described in this paper may be deployed in production if the cost can be driven down. <br />
Two good examples are Google AutoML and<br />
Microsoft Custom Vision AI.<br />
[9, 10] https://cloud.google.com/automl/ https://azure.microsoft.com/en-us/services/cognitive-services/custom-vision-service/<br />
<br />
=Critique=<br />
<br />
1. Rich man's game<br />
<br />
The technique described in the paper can only be applied by parties with abundant computational resources, like Google, Facebook, Microsoft, and e.t.c. For small research groups and companies, this method is not that useful due to the lack of the computational power<br />
one process. Future improvement will be needed on the design an even more efficient proxy task that can tell whether a network will perform<br />
well that requires fewer computations. But here is the irony, if we can tell whether a network will perform well or not without training it, we would<br />
not need a search technique in the first place. So everything comes back to the fact that there is no guiding theory on deep learning.<br />
<br />
2. Benefit/Cost ratio<br />
<br />
The technique here does outperform human designed network in many cases, but the gain is not huge. In Cityscapes dataset, the performance gain is 0.7%, wherein PASCAL-Person-Part dataset, the gain is 3.7%, and the PASCAL VOC 2012 dataset, it does not outperform human experts. (All measured by mIOU) Even though the push of the state-of-the-art is always something that worth celebrating, <br />
but in practice, one would argue after spending so many resources doing the search, the computer should achieve superhuman performance level. (Like Chess Engine vs Chess Grand Master). In practice, one may simply go with the current state-of-the-art model to avoid the<br />
expensive search cost.<br />
<br />
3. Still Heavily influenced by Human Bias<br />
When we define the search space, we introduced human bias. Firstly, the network backbone is chosen from previous matured architectures, which may not actually be optimal. Secondly, the internal branches in the DPC also consist with layers whose operations are defined by us humans. That also limits the search algorithm to find something revolutionary.<br />
<br />
=References=<br />
1. # Searching For Efficient Multi-Scale Architectures For Dense Image Prediction, [[https://arxiv.org/abs/1809.04184]].<br />
<br />
2. # E. Real, A. Aggarwal, Y. Huang, and Q. V. Le. Regularized evolution for image classifier architecture search. arXiv:1802.01548, 2018.<br />
<br />
3. #C. Liu, B. Zoph, M. Neumann, J. Shlens, W. Hua, L.-J. Li, L. Fei-Fei, A. Yuille, J. Huang, and K. Murphy. Progressive neural architecture search. In ECCV, 2018.<br />
<br />
4. #B. Zoph, V. Vasudevan, J. Shlens, and Q. V. Le. Learning transferable architectures for scalable image recognition. In CVPR, 2018.<br />
<br />
5. #Neural Architecture Search: A Survey [[https://arxiv.org/abs/1808.05377]]<br />
<br />
6. #Deep Residual Learning for Image Recognition [[https://arxiv.org/pdf/1512.03385.pdf]]</div>R82zhanghttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Searching_For_Efficient_Multi_Scale_Architectures_For_Dense_Image_Prediction&diff=38685Searching For Efficient Multi Scale Architectures For Dense Image Prediction2018-11-12T17:59:17Z<p>R82zhang: /* Chain-structured neural networks */</p>
<hr />
<div><br />
[Need add more pics and references]<br />
=Introduction=<br />
<br />
The design of neural network architectures is an important component for the success of machine learning and data science projects. In recent years, the field of Neural Architecture Search(NAS) has emerged, which is the study of automatically finding an optimal neural architecture in a given task in a well-defined architecture space. Often, the resulting architecture has outperformed human experts designed network in many tasks such as image classification and natural language processing.[2,3,4] This paper presents a method in finding a neural architecture that performs well in the task of Dense image segmentation.<br />
<br />
=Motivation=<br />
<br />
Deep Neural network's success is largely due to the fact that it greatly reduces the work in Feature Engineering, as DNN has the ability to automatically extract useful features given the raw input. However, it created a<br />
new type of engineering work - network engineering. In order to successfully extract features, you need to have the corresponding network architecture. So what really happened is the engineering work is shifted from feature engineering to how to design the network so that it can better abstract useful features.<br />
<br />
The motivation for NAS is that since there is no guiding theory on how to design the optimal network archtichture, given that we have <br />
abundant computational resources, one intuitive solution is to define a finite search space and let the computers do the dirty work of searching for structures and hyperparameters.<br />
<br />
<br />
=NAS Overview=<br />
<br />
NAS essentially turns a design problem into a search problem. As a search problem in general, we need a clear definition of three things:<br />
<ol><br />
<li> Search space</li><br />
<li> Search strategy</li><br />
<li> Performance Estimation Strategy</li><br />
</ol> <br />
[5]<br />
<br />
<br />
The search space is very intuitive to understand. In what hyperparameter space we should look for our optimal solution. In the field of NAS, the search space is heavily dependent on the assumption we make on the neural architecture. The search<br />
strategy details how to look explore the search space. The evaluation strategy is when we find a set of hyperparameters, how should we evaluate our model. In the field of NAS, it is typically to find architectures that achieve high predictive performance on unseen data. [5]<br />
<br />
We will take a deep dive into the above three dimensions of NAS in the following sections<br />
<br />
=Search Space=<br />
There are typically three ways of defining the search space.<br />
==Chain-structured neural networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen_Shot_2018-11-10_at_6.03.00_PM.png|100px]]<br />
</div><br />
[5]<br />
The chain structed network can be viewd as sequence of n layers, where the layer <math> i</math> recives input from <math> i-1</math> layer and the output serves<br />
the input to layer <math> i+1</math>.<br />
<br />
The search space is then parametrized by:<br />
1) Number of layers n<br />
2) Type of operations can be executed on each layer<br />
3) Hyperparameters associated with each layer<br />
<br />
==Multi-branch networks ==<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.08 PM.png|200px]]</div><br />
<br />
[5]<br />
This architecture allows significantly more degrees of freedom. It allows shortcuts and parallel branches. Some of the ideas are inspired by human hand-crafted networks. For example, the shortcut from shallow layers directly to the deep layers are coming from networks like ResNet [6]<br />
<br />
The search space includes the search space of chain-structured networks, with added additional freedom of adding shortcut connections and allowing parallel branches to exist.<br />
<br />
==Cell/Block ==<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">[[File:Screen Shot 2018-11-10 at 6.03.31 PM.png|300px]]</div><br />
<br />
[6]<br />
This architecture defines a cell which is used as the building block of the neural network. A good analogy here is to think a cell as a lego piece, and you can define different types of cells as different<br />
lego pieces. And then you can combine them together to form a new neural structure. <br />
<br />
<br />
The search space includes the internal structure of the cell and how to combine these blocks to form the resulting architecture.<br />
<br />
==What they used in this paper ==<br />
[pic]<br />
[1]<br />
This paper's appro