http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Npbhatt&feedformat=atomstatwiki - User contributions [US]2022-01-23T09:54:18ZUser contributionsMediaWiki 1.28.3http://wiki.math.uwaterloo.ca/statwiki/index.php?title=conditional_neural_process&diff=42264conditional neural process2018-12-04T21:56:54Z<p>Npbhatt: /* Experimental Result II: Image Completion for Digits */ Technical Contribution: added details on latent variables</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 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 />
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 good example is given by the authors, consider a random 1-dimensional function <math>f ∼ P</math> defined on the real line (i.e., <math>X := R</math>, <math>Y := R</math>). <math>O</math> would constitute <math>n</math> observations of <math>f</math>’s value <math>y_i</math> at different locations <math>x_i</math> on the real line. Given these observations, we are interested in predicting <math>f</math>’s value at new locations on the real line. <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+m)^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 <math>m</math> 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 />
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 />
<br />
To generate a coherent sample,<br />
the authors compute the representation r from the observations,<br />
which parametrizes a Gaussian distribution over the latents z.<br />
Then z sampled once and used to generate the predictions<br />
for all targets. To get a different coherent sample they draw a<br />
new sample from the latents z and run the decoder again for<br />
all targets.<br />
<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 />
In order to generate a coherent sample,<br />
we compute the representation r from the observations,<br />
which parametrizes a Gaussian distribution over the latents z.<br />
z is then sampled once and used to generate the predictions<br />
for all targets. To get a different coherent sample we draw a<br />
new sample from the latents z and run the decoder again for<br />
all targets.<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 <math>0, ..., N − 1</math> 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 <math>O(n + m)</math><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 <math>O(n + m)</math> at test time<br />
as opposed to <math>O(nm)</math><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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DON%27T_DECAY_THE_LEARNING_RATE_,_INCREASE_THE_BATCH_SIZE&diff=42263DON'T DECAY THE LEARNING RATE , INCREASE THE BATCH SIZE2018-12-04T21:43:46Z<p>Npbhatt: /* EXPERIMENTS */ Techinical Contribution: Added some explanation on Figures 3 and 4 and some training details missed in the summary.</p>
<hr />
<div>Summary of the ICLR 2018 paper: '''Don't Decay the learning Rate, Increase the Batch Size ''' <br />
<br />
Link: [https://arxiv.org/pdf/1711.00489.pdf]<br />
<br />
Summarized by: Afify, Ahmed [ID: 20700841]<br />
<br />
==INTUITION==<br />
Nowadays, it is a common practice not to have a singular steady learning rate for the learning phase of neural network models. Instead, we use adaptive learning rates with the standard gradient descent method. The intuition behind this is that when we are far away from the minima, it is beneficial for us to take large steps towards the minima, as it would require a lesser number of steps to converge, but as we approach the minima, our step size should decrease, otherwise we may just keep oscillating around the minima. In practice, this is generally achieved by methods like SGD with momentum, Nesterov momentum, and Adam. However, the core claim of this paper is that the same effect can be achieved by increasing the batch size during the gradient descent process while keeping the learning rate constant throughout. In addition, the paper argues that such an approach also reduces the parameter updates required to reach the minima, thus leading to greater parallelism and shorter training times. The authors present conclusive experimental evidence to prove the empirical benefits of decaying learning rate can be achieved by increasing the batch size instead.<br />
<br />
== INTRODUCTION ==<br />
Stochastic gradient descent (SGD) is the most widely used optimization technique for training deep learning models. The reason for this is that the minima found using this process generalizes well to unseen data (Zhang et al., 2016; Wilson et al., 2017). However, the optimization process is slow and time consuming as each parameter update corresponds to a small step towards the goal. According to (Goyal et al., 2017; Hoffer et al., 2017; You et al., 2017a), this has motivated researchers to try to speed up this optimization process by taking bigger steps, and hence reduce the number of parameter updates in training a model. This can be achieved by using large batch training, which can be divided across many machines. <br />
<br />
However, increasing the batch size leads to decreasing the test set accuracy (Keskar et al., 2016; Goyal et al., 2017). Smith and Le (2017) believed that SGD has a scale of random fluctuations <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, <math> N </math> is the number of training samples, and <math> B </math> is the batch size. They concluded that there is an optimal batch size proportional to the learning rate when <math> B \ll N </math>, and optimum fluctuation scale <math>g</math> at constant learning rate which maximizes test set accuracy. This was observed empirically by Goyal et al., 2017 and used to train a ResNet-50 in under an hour with 76.3% validation accuracy on ImageNet dataset.<br />
<br />
In this paper, the authors' main goal is to provide evidence that increasing the batch size is quantitatively equivalent to decreasing the learning rate. They show that this approach achieves almost equivalent model performance on the test set with the same number of training epochs but with remarkably fewer number of parameter updates. The strategy of increasing the batch size during training is in effect decreasing the scale of random fluctuations. Moreover, an additional reduction in the number of parameter updates can be attained by increasing the learning rate and scaling <math> B \propto \epsilon </math> or even more reduction by increasing the momentum coefficient, <math> m </math>, and scaling <math> B \propto \frac{1}{1-m} </math>. Although the latter decreases the test accuracy. This has been demonstrated by several experiments on the ImageNet and CIFAR-10 datasets using ResNet-50 and Inception-ResNet-V2 architectures respectively.<br />
<br />
== STOCHASTIC GRADIENT DESCENT AND CONVEX OPTIMIZATION ==<br />
As mentioned in the previous section, the drawback of SGD when compared to full-batch training is the noise that it introduces that hinders optimization. According to (Robbins & Monro, 1951), there are two equations that govern how to reach the minimum of a convex function: (<math> \epsilon_i </math> denotes the learning rate at the <math> i^{th} </math> gradient update)<br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon_i = \infty </math>. This equation guarantees that we will reach the minimum. <br />
<br />
<math> \sum_{i=1}^{\infty} \epsilon^2_i < \infty </math>. This equation, which is valid only for a fixed batch size, guarantees that learning rate decays fast enough allowing us to reach the minimum rather than bouncing due to noise.<br />
<br />
These equations indicate that the learning rate must decay during training, and second equation is only available when the batch size is constant. To change the batch size, Smith and Le (2017) proposed to interpret SGD as integrating this stochastic differential equation <math> \frac{dw}{dt} = -\frac{dC}{dw} + \eta(t) </math>, where <math>C</math> represents cost function, <math>w</math> represents the parameters, and <math>\eta</math> represents the Gaussian random noise. Furthermore, they proved that noise scale <math>g</math> controls the magnitude of random fluctuations in the training dynamics by this formula: <math> g = \epsilon (\frac{N}{B}-1) </math>, where <math> \epsilon </math> is the learning rate, N is the training set size and <math>B</math> is the batch size. As we usually have <math> B \ll N </math>, we can define <math> g \approx \epsilon \frac{N}{B} </math>. This explains why when the learning rate decreases, noise <math>g</math> decreases, enabling us to converge to the minimum of the cost function. However, increasing the batch size has the same effect and makes <math>g</math> decays with constant learning rate. In this work, the batch size is increased until <math> B \approx \frac{N}{10} </math>, then the conventional way of decaying the learning rate is followed.<br />
<br />
== SIMULATED ANNEALING AND THE GENERALIZATION GAP ==<br />
'''Simulated Annealing:''' Decaying learning rates are empirically successful. To understand this, they note that introducing random fluctuations whose scale falls during training is also a well-established technique in non-convex optimization; simulated annealing. The initial noisy optimization phase allows exploring a larger fraction of the parameter space without becoming trapped in local minima. Once a promising region of parameter space is located, the noise is reduced to fine-tune the parameters.<br />
<br />
Simulated Annealing is a famous technique in non-convex optimization. Starting with noise in the training process helps us to explore a wide range of parameters. Once we are near the optimum value, noise is reduced to fine tune our final parameters. Nowadays researchers typically use sharp decay schedules like cosine decay or step-function drops. In physical sciences, slowly annealing (or decaying) the temperature (which is the noise scale in this situation) helps to converge to the global minimum, which is sharp. But decaying the temperature in discrete steps can make the system stuck in a local minimum, which leads to higher cost and lower curvature. The authors think that deep learning has the same intuition.<br />
<br />
'''Generalization Gap:''' Small batch data generalizes better to the test set than large batch data. Smith and Le (2017) found that there is an optimal batch size which corresponds to optimal noise scale <math> g </math> <math> (g \approx \epsilon \frac{N}{B}) </math>. They found an optimum batch size <math> B_{opt} \propto \epsilon N </math> that maximizes test set accuracies. This means that gradient noise is helpful as it makes SGD escape sharp minima which do not generalize well.<br />
<br />
== THE EFFECTIVE LEARNING RATE AND THE ACCUMULATION VARIABLE ==<br />
'''The Effective Learning Rate''' : <math> \epsilon_{eff} = \frac{\epsilon}{1-m} </math><br />
<br />
Smith and Le (2017) included momentum <math>m</math> to the vanilla SGD noise scale equation, <math> g = \frac{\epsilon}{1-m}(\frac{N}{B}-1)\approx \frac{\epsilon N}{B(1-m)} </math>. They found that by increasing the learning rate and the momentum while proportionally scaling <math> B \propto \frac{\epsilon }{1-m} </math>, further reduces the number of parameter updates needed during training. However, test accuracy decreases when the momentum coefficient is increased. <br />
<br />
To understand the reasons behind this, we need to analyze momentum update equations below:<br />
<br />
<center><math><br />
\Delta A = -(1-m)A + \frac{d\widehat{C}}{dw} <br />
</math><br />
<br />
<math><br />
\Delta w = -A\epsilon<br />
</math><br />
</center><br />
<br />
We can see that the accumulation variable <math> A </math>, starting at 0, increases exponentially until it reaches its steady state value during <math> \frac{B}{N(1-m)} </math> training epochs. If <math> \Delta w </math> is suppressed, it can reduce the rate of convergence. <br />
<br />
Moreover, at high momentum, we have four challenges:<br />
# Additional epochs are needed to catch up with the accumulation.<br />
# Accumulation needs more time <math> \frac{B}{N(1-m)} </math> to forget old gradients. <br />
# After this time, however, the accumulation cannot adapt to changes in the loss landscape.<br />
# In the early stage, a large batch size will lead to the instabilities.<br />
<br />
It is thus recommended to keep a reduced learning rate for the first few epochs of training.<br />
<br />
== EXPERIMENTS ==<br />
=== SIMULATED ANNEALING IN A WIDE RESNET ===<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Schedules used as in the below figure:''' . These demonstrate the equivalence between decreasing the learning rate and increasing the batch size.<br />
<br />
- Decaying learning rate: learning rate decays by a factor of 5 at a sequence of “steps”, and the batch size is constant<br />
<br />
- Increasing batch size: learning rate is constant, and the batch size is increased by a factor of 5 at every step.<br />
<br />
- Hybrid: At the beginning, the learning rate is constant and batch size is increased by a factor of 5. Then, the learning rate decays by a factor of 5 at each subsequent step, and the batch size is constant. This is the schedule that will be used if there is a hardware limit affecting a maximum batch size limit.<br />
<br />
If the learning rate itself must decay during training, then these schedules should show different learning curves (as a function of the number of training epochs) and reach different final test set accuracies. Meanwhile, if it is the noise scale which should decay, all three schedules should be indistinguishable.<br />
[[File:Paper_40_Fig_1.png | 800px|center]]<br />
<br />
As shown in the below figure: in the left figure (2a), we can observe that for the training set, the three learning curves are exactly the same while in figure 2b, increasing the batch size has a huge advantage of reducing the number of parameter updates.<br />
This concludes that noise scale is the one that needs to be decayed and not the learning rate itself<br />
[[File:Paper_40_Fig_2.png | 800px|center]] <br />
<br />
To make sure that these results are the same for the test set as well, in figure 3, we can see that the three learning curves are exactly the same for SGD with momentum, and Nesterov momentum. In figure 3b, the test set accuracy when training with Nesterov momentum parameter 0.9 is presented. <br />
[[File:Paper_40_Fig_3.png | 800px|center]]<br />
<br />
To check for other optimizers as well. the below figure shows the same experiment as in figure 3, which is the three learning curves for the test set, but for vanilla SGD and Adam, and showing<br />
[[File:Paper_40_Fig_4.png | 800px|center]]<br />
<br />
In figure 4a, the same experiment is repeated with vanilla SGD, again obtaining three similar curves. Finally in figure 4b the authors repeat the experiment with Adam. They also use the default parameter settings of TensorFlow, such that the initial base learning rate here is 0.01, β1 = 0.9 and β2 = 0.999.<br />
<br />
'''Conclusion:''' Decreasing the learning rate and increasing the batch size during training are equivalent<br />
<br />
=== INCREASING THE EFFECTIVE LEARNING RATE===<br />
<br />
Here, the focus is on minimizing the number of parameter updates required to train a model. As shown above, the first step is to replace decaying learning rates by increasing batch sizes. Now, the authors show here that we can also increase the effective learning rate <math>\epsilon_{eff} = \epsilon/(1 − m) </math> at the start of training, while scaling the initial batch size <math>B \propto \epsilon_{eff} </math> . All experiments are conducted using SGD with momentum. There are 50000 images in the CIFAR-10 training set, and since the scaling rules only hold when <math>B << N </math> , we decided to set a maximum batch size <math>B_{max} </math>= 5120 .<br />
<br />
'''Dataset:''' CIFAR-10 (50,000 training images)<br />
<br />
'''Network Architecture:''' “16-4” wide ResNet<br />
<br />
'''Training Parameters:''' Optimization Algorithm: SGD with momentum / Maximum batch size = 5120<br />
<br />
'''Training Schedules:''' <br />
<br />
The authors consider four training schedules, all of which decay the noise scale by a factor of five in a series of three steps with the same number of epochs.<br />
<br />
Original training schedule: initial learning rate of 0.1 which decays by a factor of 5 at each step, a momentum coefficient of 0.9, and a batch size of 128. Follows the implementation of Zagoruyko & Komodakis (2016).<br />
<br />
Increasing batch size: learning rate of 0.1, momentum coefficient of 0.9, initial batch size of 128 that increases by a factor of 5 at each step. <br />
<br />
Increased initial learning rate: initial learning rate of 0.5, initial batch size of 640 that increase during training.<br />
<br />
Increased momentum coefficient: increased initial learning rate of 0.5, initial batch size of 3200 that increase during training, and an increased momentum coefficient of 0.98.<br />
<br />
The results of all training schedules, which are presented in the below figure, are documented in the following table:<br />
<br />
[[File:Paper_40_Table_1.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_5.png | 800px|center]]<br />
<br />
<br />
<br />
'''Conclusion:''' Increasing the effective learning rate and scaling the batch size results in further reduction in the number of parameter updates<br />
<br />
=== TRAINING IMAGENET IN 2500 PARAMETER UPDATES===<br />
<br />
'''A) Experiment Goal:''' Control Batch Size<br />
<br />
'''Dataset:''' ImageNet (1.28 million training images)<br />
<br />
The paper modified the setup of Goyal et al. (2017), and used the following configuration:<br />
<br />
'''Network Architecture:''' Inception-ResNet-V2 <br />
<br />
'''Training Parameters:''' <br />
<br />
90 epochs / noise decayed at epoch 30, 60, and 80 by a factor of 10 / Initial ghost batch size = 32 / Learning rate = 3 / momentum coefficient = 0.9 / Initial batch size = 8192<br />
<br />
Two training schedules were used:<br />
<br />
“Decaying learning rate”, where batch size is fixed and the learning rate is decayed<br />
<br />
“Increasing batch size”, where batch size is increased to 81920 then the learning rate is decayed at two steps.<br />
<br />
[[File:Paper_40_Table_2.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_6.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the batch size resulted in reducing the number of parameter updates from 14,000 to 6,000.<br />
<br />
'''B) Experiment Goal:''' Control Batch Size and Momentum Coefficient<br />
<br />
'''Training Parameters:''' Ghost batch size = 64 / noise decayed at epoch 30, 60, and 80 by a factor of 10. <br />
<br />
The below table shows the number of parameter updates and accuracy for different sets of training parameters:<br />
<br />
[[File:Paper_40_Table_3.png | 800px|center]]<br />
<br />
[[File:Paper_40_Fig_7.png | 800px|center]]<br />
<br />
'''Conclusion:''' Increasing the momentum reduces the number of parameter updates, but leads to a drop in the test accuracy.<br />
<br />
=== TRAINING IMAGENET IN 30 MINUTES===<br />
<br />
'''Dataset:''' ImageNet (Already introduced in the previous section)<br />
<br />
'''Network Architecture:''' ResNet-50<br />
<br />
The paper replicated the setup of Goyal et al. (2017) while modifying the number of TPU devices, batch size, learning rate, and then calculating the time to complete 90 epochs, and measuring the accuracy, and performed the following experiments below:<br />
<br />
[[File:Paper_40_Table_4.png | 800px|center]]<br />
<br />
'''Conclusion:''' Model training times can be reduced by increasing the batch size during training.<br />
<br />
== RELATED WORK ==<br />
Main related work mentioned in the paper is as follows:<br />
<br />
- Smith & Le (2017) interpreted Stochastic gradient descent as stochastic differential equation; the paper built on this idea to include decaying learning rate.<br />
<br />
- Mandt et al. (2017) analyzed how to modify SGD for the task of Bayesian posterior sampling.<br />
<br />
- Keskar et al. (2016) focused on the analysis of noise once the training is started.<br />
<br />
- Moreover, the proportional relationship between batch size and learning rate was first discovered by Goyal et al. (2017) and successfully trained ResNet-50 on ImageNet in one hour after discovering the proportionality relationship between batch size and learning rate.<br />
<br />
- Furthermore, You et al. (2017a) presented Layer-wise Adaptive Rate Scaling (LARS), which is applying different learning rates to train ImageNet in 14 minutes and 74.9% accuracy. <br />
<br />
- Wilson et al. (2017) argued that adaptive optimization methods tend to generalize less well than SGD and SGD with momentum (although<br />
they did not include K-FAC in their study), while the authors' work reduces the gap in convergence speed.<br />
<br />
- Finally, another strategy called Asynchronous-SGD that allowed (Recht et al., 2011; Dean et al., 2012) to use multiple GPUs even with small batch sizes.<br />
<br />
== CONCLUSIONS ==<br />
Increasing the batch size during training has the same benefits of decaying the learning rate in addition to reducing the number of parameter updates, which corresponds to faster training time. Experiments were performed on different image datasets and various optimizers with different training schedules to prove this result. The paper proposed to increase the learning rate and momentum parameter <math>m</math>, while scaling <math> B \propto \frac{\epsilon}{1-m} </math>, which achieves fewer parameter updates, but slightly less test set accuracy as mentioned in detail in the experiments’ section. In summary, on ImageNet dataset, Inception-ResNet-V2 achieved 77% validation accuracy in under 2500 parameter updates, and ResNet-50 achieved 76.1% validation set accuracy on TPU in less than 30 minutes. One of the great findings of this paper is that all the methods use the hyper-parameters directly from previous works in the literature, and no additional hyper-parameter tuning was performed.<br />
<br />
== CRITIQUE ==<br />
'''Pros:'''<br />
<br />
- The paper showed empirically that increasing batch size and decaying learning rate are equivalent.<br />
<br />
- Several experiments were performed on different optimizers such as SGD and Adam.<br />
<br />
- Had several comparisons with previous experimental setups.<br />
<br />
'''Cons:'''<br />
<br />
<br />
- All datasets used are image datasets. Other experiments should have been done on datasets from different domains to ensure generalization. <br />
<br />
- The number of parameter updates was used as a comparison criterion, but wall-clock times could have provided additional measurable judgment although they depend on the hardware used.<br />
<br />
- Special hardware is needed for large batch training, which is not always feasible. As batch-size increases, we generally need more RAM to train the same model. However, if the learning rate is decreased, the RAM use remains constant. As a result, learning rate decay will allow us to train bigger models.<br />
<br />
- In section 5.2 (Increasing the Effective Learning rate), the authors did not test a range of learning rate values and used only (0.1 and 0.5). Additional results from varying the initial learning rate values from 0.1 to 3.2 are provided in the appendix, which indicates that the test accuracy begins to fall for initial learning rates greater than ~0.4. The appended results do not show validation set accuracy curves like in Figure 6, however. It would be beneficial to see if they were similar to the original 0.1 and 0.5 initial learning rate baselines.<br />
<br />
- Although the main idea of the paper is interesting, its results do not seem to be too surprising in comparison with other recent papers in the subject.<br />
<br />
- The paper could benefit from using some other models to demonstrate its claim and generalize its idea by adding some comparisons with other models as well as other recent methods to increase batch size.<br />
<br />
- The paper presents interesting ideas. However, it lacks mathematical and theoretical analysis beyond the idea. Since the experiment is primary on image dataset and it does not provide sufficient theories, the paper itself presents limited applicability to other types. <br />
<br />
- Also, in an experimental setting, only single training runs from one random initialization is used. It would be better to take the best of many runs or to show confidence intervals.<br />
<br />
- It is proposed that we should compare learning rate decay with batch-size increase under the setting that total budget / number of training samples is fixed.<br />
<br />
- While the paper demonstrated the proposed solution can decrease training time, it is not an entirely fair comparison because computations were distributed on a TPU POD. Suppose computing resource remains the same, the purposed method may possibly train slower.<br />
<br />
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<hr />
<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 (<math>10^{172}</math>), which is more than the number of atoms in the universe, and it is much larger than the game states in Chess (<math>10^{47}</math>). 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 applied to Trees (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. This formula serves the purpose of balance exploitation (first term) and exploration (second term) in Monte Carlo Tree Search. The philosophy is that nodes with high rewards and nodes poorly explored should both be explored more often.<br />
<br />
Note that the Upper Confidence Bound (UCB) formula can achieve the optimal solution of the multi-arm bandit problem theoretically.<br />
<br />
<math><math> \frac{w_i}{n_i} + c \sqrt{\frac{\ln t}{n_i}} </math></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 />
The selection of the final action, the algorithm computes the most visited node and<br />
selects the corresponding action.<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 />
Also, the neccessity to discretize state and action in the CNN is disputable. With careful design maybe we can incorporate continuous inputs.<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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=a_neural_representation_of_sketch_drawings&diff=42261a neural representation of sketch drawings2018-12-04T21:18:23Z<p>Npbhatt: /* Critique */ Technical Contribution: Added a critique that wasn't mentioned in the summary, but is important.</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 />
Neural Network-based approaches are able to generate latent space representation of vector images, which follows a Gaussian distribution. The generated output of these networks is trained to match the Gaussian distribution by minimizing a given loss function. Using this idea, previous works attempted to generate a sequence-to-Sequence model 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 />
* The authors have not mentioned details on training details such as learning rate, training time, parameter size, and so on. <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 />
* As they said their model can become increasingly difficult to train on with increased size.<br />
<br />
== References == <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 />
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# 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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# 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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Wasserstein_Auto-encoders&diff=42260Wasserstein Auto-encoders2018-12-04T21:10:33Z<p>Npbhatt: /* Experiments */ Techinical Contribution: Added missing details on training details</p>
<hr />
<div>The first version of this work was published in 2017 and this version (which is the third revision) is presented in ICLR 2018. Source code for the first version is available [https://github.com/tolstikhin/wae here]<br />
<br />
=Introduction=<br />
Early successes in the field of representation learning were based on supervised approaches, which used large labeled datasets to achieve impressive results. On the other hand, popular unsupervised generative modeling methods mainly consisted of probabilistic approaches focusing on low dimensional data. In recent years, there have been models proposed which try to combine these two approaches. One such popular method is called variational auto-encoders (VAEs). VAEs are theoretically elegant but have a major drawback of generating blurry sample images when used for modeling natural images. In comparison, generative adversarial networks (GANs) produce much sharper sample images but have their own list of problems which include a lack of encoder, harder to train, and the "mode collapse" problem. Mode collapse problem refers to the inability of the model to capture all the variability in the true data distribution. Currently, there has been a lot of activities around finding and evaluating numerous GANs architectures and combining VAEs and GANs, but a model which combines the best of both GANs and VAEs is yet to be discovered.<br />
<br />
The work done in this paper builds upon the theoretical work done in Bousquet et al.[2017] [4]. The authors tackle generative modeling using optimal transport (OT). The OT cost is defined as the measure of distance between probability distributions.<br />
<br />
To be more specific on the OT:<br />
<br />
Given a function <math>c : X × Y → R</math>, they seek a minimizer of <math> C(µ, ν) := \underset{π ∈ Π(µ, ν)}{inf} \int_{X×Y}{c(x, y)dπ(x, y)}</math><br />
<br />
The measures <math>π ∈ Π(µ, ν)</math> are called transport plans or transference plans. The measures <math>π ∈ Π(µ, ν)</math> achieving the infimum are called optimal transport plans. The classical interpretation of this problem is the problem of minimizing the total cost <math>C(µ, ν)</math> of transporting the mass distribution <math>µ</math> to the mass distribution <math>ν</math>, where the cost of transporting one unit of mass at the point <math>x ∈ X</math> to one unit of mass at the point <math>y ∈ Y</math> is given by the cost function <math>c(x, y)</math>.<br />
<br />
One of the features of OT cost which is beneficial is that it provides much weaker topology when compared to other costs, including f-divergences which are associated with the original GAN algorithms. <br />
This particular feature is crucial in applications where the data is usually supported on low dimensional manifolds in the input space. This result in a problem with the stronger notions of distances such as f-divergences as they often max out and provide no useful gradients for training. In comparison, the OT cost has been claimed to behave much more nicely [5, 8]. Despite the preceding claim, the implementation, which is similar to GANs, still requires the addition of a constraint or a regularization term into the objective function.<br />
<br />
==Original Contributions==<br />
Let <math>P_X</math> be the true but unknown data distribution, <math>P_G</math> be the latent variable model specified by the prior distribution <math>P_Z</math> of latent codes <math>Z \in \mathcal{Z}</math> and the generative model <math>P_G(X|Z)</math> of the data points <math>X \in \mathcal{X}</math> given <math>Z</math>. The goal in this paper is to minimize <math>OT\ W_c(P_X, P_G)</math>.<br />
<br />
The main contributions are given below:<br />
<br />
* A new class of auto-encoders called Wasserstein Auto-Encoders (WAE). WAEs minimize the optimal transport <math>W_c(P_X, P_G)</math> for any cost function <math>c</math>. As is the case with VAEs, WAE objective function is also made up of two terms: the c-reconstruction cost and a regularizer term <math>\mathcal{D}_Z(P_Z, Q_Z)</math> which penalizes the discrepancy between two distributions in <math>\mathcal{Z}: P_Z\ and\ Q_Z</math>. <math>Q_Z</math> is a distribution of encoded points, i.e. <math>Q_Z := \mathbb{E}_{P_X}[Q(Z|X)]</math>. Note that when <math>c</math> is the squared cost and the regularizer term is the GAN objective, WAE is equivalent to the adversarial auto-encoders described in [2].<br />
<br />
* Experimental results of using WAE on MNIST and CelebA datasets with squared cost <math>c(x, y) = ||x - y||_2^2</math>. The results of these experiments show that WAEs have the good features of VAEs such as stable training, encoder-decoder architecture, and a nice latent manifold structure while simultaneously improving the quality of the generated samples.<br />
<br />
* Two different regularizers. One based on GANs and adversarial training in the latent space <math>\mathcal{Z}</math>. The other one is based on something called "Maximum Mean Discrepancy" which known to have high performance when matching high dimensional standard normal distributions. The second regularizer also makes the problem fully adversary-free min-min optimization problem, and gets rid of the problem of tuning the GAN. During GAN training, the mode can often collapse, the model is sensitive to hyper parameters, and the loss is uninterpretable since it fluctuates during training. WAE solves such problems, and is much more developer-friendly. Most important of all, the loss in WAE is interpretable, making is easier to decide when to terminate the training.<br />
<br />
* The final contribution is the mathematical analysis used to derive the WAE objective function. In particular, the mathematical analysis shows that in the case of generative models, the primal form of <math>W_c(P_X, P_G)</math> is equivalent to a problem which deals with the optimization of a probabilistic encoder <math>Q(Z|X)</math><br />
<br />
The paper provides an ostensibly simple recipe to implement a non-blurry VAE (it is generative) It provides what looks like an elegant and logical way to cast the Wasserstein distance metric to setup the VAE/GAN problem.<br />
<br />
The paper gives three instructive VAEGAN model comparisons, unifying them thematically – Adversarial Autoencoders (AAE), Adversarial Variational Bayes (AVB), and the original Variational Autoencoders (VAE). These generalizations arise for the case with random decoders – the paper introduces the idea with deterministic decodes, and then extends it to random decoders – with play on the regularizer of the VAE which these papers replace with a GAN.<br />
<br />
=Proposed Method=<br />
<br />
The method proposed by the authors uses a novel auto-encoder architecture to minimize the optimal transport cost <math>W_c(P_X, P_G)</math>. In the optimization problem that follows, the decoder tries to accurately reconstruct the data points as measured by the cost function <math>c</math>. The encoder tries to achieve the following two conflicting goals at the same time: (1) try to match the distribution of the encoded data points <math>Q_Z := \mathbb{E}_{P_X}[Q(Z|X)]</math> to the prior distribution <math>P_Z</math> as measured by the divergence <math>\mathcal{D}_Z(P_Z, Q_Z)</math> and, (2) make sure that the latent space vectors encoded contain enough information so that the reconstruction of the data points are of high quality. The figure below illustrates this:<br />
<br />
[[File:ka2khan_figure_1.png|800px|thumb|center|Figure 1]]<br />
<br />
Figure 1: Both VAE and WAE have objectives which are composed of two terms. The two terms are the reconstruction cost and the regularizer term which penalizes the divergence between <math>P_Z</math> and <math>Q_Z</math>. VAE forces <math>Q(Z|X = x)</math> to match <math>P_Z</math> for the the different training examples drawn from <math>P_X</math>. As shown in the figure above, every red ball representing <math>Q_z</math> is forced to match <math>P_Z</math> depicted as whitish triangles. This causes intersection among red balls and results in reconstruction problems. On the other hand, WAE coerces the mixture <math>Q_Z := \int{Q(Z|X)\ dP_X}</math> to match <math>P_Z</math> as shown in the figure above. This provides a better chance of the encoded latent codes to have more distance between them. As a consequence of this, higher reconstruction quality is achieved.<br />
<br />
==Preliminaries and Notations==<br />
<br />
Authors use calligraphic letters to denote sets (for example, <math>\mathcal{X}</math>), capital letters for random variables (for example, <math>X</math>), and lower case letters for the values (for example, <math>x</math>). Probability distributions are are also denoted with capital letters (for example, <math>P(X)</math>) and the corresponding densities are denoted with lowercase letter (for example, <math>p(x)</math>).<br />
<br />
Several measure of difference between probability distributions are also used by the authors. These include f-divergences given by <math>D_f(p_X||p_G) := \int{f(\frac{p_X(x)}{p_G(x)})p_G(x)}dx\ \text{where}\ f:(0, \infty) &rarr; \mathcal{R}</math> is any convex function satisfying <math>f(1) = 0</math>. Other divergences used include KL divergence (<math>D_{KL}</math>) and Jensen-Shannon (<math>D_{JS}</math>) divergences.<br />
<br />
==Optimal Transport and its Dual Formations==<br />
<br />
A rich class of measure of distances between probability distributions is motivated by the optimal transport problem. One such formulation of the optimal transport problem is the Kantovorich's formulation given by:<br />
<br />
<center><math><br />
W_c(P_X, P_G) := \underset{\Gamma \in \mathcal{P}(X \sim P_X ,Y \sim P_G)}{inf} \mathbb{E}_{(X,Y) \sim \Gamma}[c(X,Y)],<br />
\text{where} \ c(x, y): \mathcal{X} \times \mathcal{X} &rarr; \mathcal{R_{+}}<br />
</math></center><br />
<br />
is any measurable cost function, and <math>\mathcal{P}(X \sim P_X, Y \sim P_G)</math> is a set of all joint distributions of (X, Y) with marginals <math>P_X\ \text{and}\ P_G</math> respectively.<br />
<br />
A particularly interesting case is when <math>(\mathcal{X}, d)</math> is metric space and <math>c(x, y) = d^p(x, y)\ \text{for}\ p &ge; 1</math>. In this case <math>W_p</math>, the <math>p-th</math> root of <math>W_c</math>, is called the p-Wasserstein distance.<br />
<br />
When <math>c(x, y) = d(x, y)</math> the following Kantorovich-Rubinstein duality holds:<br />
<br />
<math>W_1(P_X, P_G) = \underset{f \in \mathcal{F}_L}{sup} \mathbb{E}_{X \sim P_x}[f(X)] = \mathbb{E}_{Y \sim P_G}[f(Y)]</math><br />
where <math>\mathcal{F}_L</math> is the class of all bounded 1-Lipschitz functions on <math>(\mathcal{X}, d)</math>.<br />
<br />
==Application to Generative Models: Wasserstein auto-encoders==<br />
The intuition behind modern generative models like VAEs and GANs is that they try to minimize specific distance measures between the data distribution <math>P_X</math> and the model <math>P_G</math>. Unfortunately, with the current knowledge and tools, it is usually really hard or even impossible to calculate most of the standard discrepancy measures especially when <math>P_X</math> is not known and <math>P_G</math> is parametrized by deep neural networks. Having said that, there are certain tricks available which can be employed to get around that difficulty.<br />
<br />
For KL-divergence <math>D_{KL}(P_X, P_G)</math> minimization, or equivalently the marginal log-likelihood <math>E_{P_X}[log_{P_G}(X)]</math> maximization, one can use the famous variational lower bound which provides a theoretically grounded framework. This has been used quite successfully by the VAEs. In the general case of minimizing f-divergence <math>D_f(P_X, P_G)</math>, using its dual formulation along with f-GANs and adversarial training is viable. Finally, OT cost <math>W_c(P_X, P_G)</math> can be minimized by using the Kantorovich-Rubinstein duality expressed as an adversarial objective. The Wasserstein-GAN implement this idea.<br />
<br />
In this paper, the authors focus on the latent variable models <math>P_G</math> given by a two step procedure. First, a code <math>Z</math> is sampled from a fixed distribution <math>P_Z</math> on a latent space <math>\mathcal{Z}</math>. Second step is to map <math>Z</math> to the image <math>X \in \mathcal{X} = \mathcal{R}^d</math> with a (possibly random) transformation. This gives us a density of the form,<br />
<br />
<center><math><br />
p_G(x) := \int\limits_{\mathcal{Z}}{p_G(x|z)p_z(z)}dz,\ \forall x \in \mathcal{X}, <br />
</math></center><br />
<br />
provided all the probablities involved are properly defined. In order to keep things simple, the authors focus on non-random decoders, i.e., the generative models <math>P_G(X|Z)</math> deterministically map <math>Z</math> to <math>X = G(Z)</math> using a fixed map <math>G: \mathcal{Z} &rarr; \mathcal{X}</math>. Similar results hold for the random decoders as shown by the authors in the appendix B.1.<br />
<br />
Working under the model defined in the preceding paragraph, the authors find that OT cost takes a much simpler form as the transportation plan factors through the map <math>G:</math> instead of finding a coupling <math>\Gamma</math> between two random variables in the <math>\mathcal{X}</math> space, one given by the distribution <math>P_X</math> and the other by the the distribution <math>P_G</math>, it is enough to find a conditional distribution <math>Q(Z|X)</math> such that its <math>Z</math> marginal, <math>Q_Z)Z) := \mathbb{E}_{X \sim P_X}[Q(Z|X)]</math> is the same as the prior distribution <math>P_Z</math>. This is formalized by the theorem given below. The theorem given below was proven in [4] by the authors.<br />
<br />
'''Theorem 1.''' For <math>P_G</math> defined as above with deterministic <math>P_G(X|Z)</math> and any function <math>G:\mathcal{Z} &rarr; \mathcal{X}</math><br />
<br />
<math><br />
\underset{\Gamma \in \mathcal{P}(X \sim P_X ,Y \sim P_G)}{inf} \mathbb{E}_{(X,Y) \sim \Gamma}[c(X,Y)] = \underset{Q: Q_Z = P_Z}{inf} \mathbb{E}_{P_X} \mathbb{E}_{Q(Z|X)}[c(X, G(Z))]<br />
</math><br />
<br />
where <math>Q_Z</math> is the marginal distribution of <math>Z</math> when <math>X \sim P_X</math> and <math>Z \sim Q(Z|X)</math>.<br />
<br />
According to the authors, the result above allows optimization over random encoders <math>Q(Z|X)</math> instead of optimizing overall couplings of <math>X</math> and <math>Y</math>. Both problems are still constrained. To find a numerical solution, the authors relax the constraints on <math>Q_Z</math> by adding a regularizer term to the objective. This gives them the WAE objective:<br />
<br />
<math><br />
D_{WAE}(P_X, P_G) := \underset{Q(Z|X) \in \mathcal{Q}}{inf} \mathbb{E}_{P_X} \mathbb{E}_{Q(Z|X)}[c(X, G(Z))] + \lambda \cdot \mathcal{D}_Z(Q_Z, P_Z)<br />
</math><br />
<br />
where <math>\mathcal{Q}</math> is any nonparametric set of probabilistic encoders, <math>\mathcal{D}_Z</math> is an arbitrary measure of distance between <math>Q_Z</math> and <math>P_Z</math>, and <math>\lambda &gt; 0</math> is a hyperparameter. As is the case with the VAEs, the authors propose using deep neural networks to parameterize both encoders <math>Q</math> and decoders <math>G</math>. Note that, unlike VAEs, WAE allows for non-random encoders deterministically mapping their inputs to their latent codes.<br />
<br />
The authors propose two different regularizers <math>\mathcal{D}_Z(Q_Z, P_Z)</math><br />
<br />
===GAN-based <math>\mathcal{D}_z</math>===<br />
One of the option is to use <math>\mathcal{D}_Z(Q_Z, P_Z) = \mathcal{D}_{JS}(Q_Z, P_Z)</math> along with adversarial training for estimation. In particular, the discriminator (adversary) is used in the latent space <math>\mathcal{Z}</math> to classify "true" points sampled for <math>P_X</math> and "fake" ones samples from <math>Q_Z</math>. This leads to the WAE-GAN as described in Algorithm 1 listed below. Even though WAE-GAN still uses max-min optimization, one positive feature is that it moves the adversary from the input (pixel) space <math>\mathcal{X}</math> to the latent space <math>\mathcal{Z}</math>. Additionally, the true latent space distribution <math>P_Z</math> might have a nice shape with a single mode (for a Gaussian prior), making the task of matching much easier as opposed to matching an unknown, complex, and possibly multi-modal distributions which is usually the case in GANs. This leads to the second penalty.<br />
<br />
===MMD-based <math>\mathcal{D}_z</math>===<br />
For a positive-definite reproducing kernel <math>k: \mathcal{Z} \times \mathcal{Z} &rarr; \mathcal{R}</math>, the maximum mean discrepancy (MMD) is defined as:<br />
<br />
<center><math><br />
MMD_k(P_Z, Q_Z) = \left \Vert \int \limits_{\mathcal{Z}} {k(z, \cdot)dP_Z(z)} - \int \limits_{\mathcal{Z}} {k(z, \cdot)dQ_Z(z)} \right \|_{\mathcal{H}_k}<br />
</math>,</center><br />
<br />
where <math>\mathcal{H}_k</math> is the RKHS (reproducing kernel Hilbert space) of real-valued functions mappings <math>\mathcal{Z}</math> to <math>\mathcal{R}</math>. If <math>k</math> is characteristi then <math>MMD_k</math> defines a metric and can be used as a distance measure. The authors propose to use <math>\mathcal{D}_Z(P_Z, Q_Z) = MMD_k(P_Z, Q_Z)</math>. MMD also have an unbiased U-statistic estimator which can be used alongwith stochastic gradient descent (SGD) methods. This gives us WAE-MMD as described in the Algorithm 2 listed below. Note that MMD is known to perform well when matching high dimensional standard normal distributions, so it is expected that this penalty will work well when the prior <math>P_Z</math> is Gaussian.<br />
<br />
[[File:ka2khan_figure_2.png|800px|thumb|center|Algorithms- WAE-GAN on left and WAE-MMD on right]]<br />
<br />
=Related Work=<br />
==Literature on auto-encoders==<br />
Classical unregularized auto-encoders have an objective function which only tries to minimize the reconstruction cost. This results in distinct data points being encoded into distinct zones distributed chaotically across the latent space <math>\mathcal{Z}</math>. The latent space <math>\mathcal{Z}</math> in this scenario contains huge "holes" for which the decoder <math>P_G(X|Z)</math> has never been trained. In general, the encoder trained this way do not provide terribly useful representations and sampling from the latent space <math>\mathcal{Z}</math> becomes a difficult task [12].<br />
<br />
VAEs [1] minimize the KL-divergence <math>D_{KL}(P_X, P_G)</math> which consists of the reconstruction cost and the regularizer <math>\mathbb{E}_{P_X}[D_{KL}(Q(|X), P_Z)]</math>. The regularizer penalizes the difference in the encoded training images and the prior <math>P_Z</math>. But this penalty still does not guarantee that the overall encoded distribution matches the prior distribution as WAE does. In addition, VAEs require a non-degenerate (i.e. non-deterministic) Gaussian encoders along with random decoders. Another paper [11] later, proposed a method which allows the use of non-Gaussian encoders with VAEs. In the meanwhile, WAE minimizes <math>W_{c}(P_X, P_G)</math> and allows probabilistic and deterministic encoder and decoder pairs.<br />
<br />
When parameters are appropriately defined, WAE is able to generalize AAE in two ways: it can use any cost function in the input space and use any discrepancy measure <math>D_Z</math> in latent space <math>Z</math> other than the adversarial one.<br />
<br />
There has been work done on regularized auto-encoders called InfoVAE [14], which has objective similar to [4] but using different motivations and arguments.<br />
<br />
WAEs explicitly define the cost function <math>c(x,y)</math>, whereas VAEs rely on an implicitly through a negative log likelihood term. It theoretically can induce any arbitrary cost function, but in practice can require an estimation of the normalizing constant that can be different for values of <math>z</math>.<br />
<br />
==Literature on Optimal Transport (OT)==<br />
[15] provides methods for computing OT cost for large-scale data using SGD and sampling. The WGAN [5] proposes a generative model which minimizes 1-Wasserstein distance <math>W_1(P_X, P_G)</math>. The WGAN algorithm does not provide an encoder and cannot be easily applied to any arbitrary cost <math>W_C</math>. The model proposed in [5] uses the dual form, in contrast, the model proposed in this paper uses the primal form. The primal form allows the use of any arbitrary cost function <math>c</math> and naturally, comes with an encoder. <br />
<br />
In order to compute <math>W_c(P_X, P_G)</math> or <math>W_1(P_X, P_G)</math>, the model needs to handle various non-trivial constraints, various methods has be proposed in the literature ([5], [2], [8], [16], [15], [17], [18]) to avoid this difficulty .<br />
<br />
==Literature on GANs==<br />
A lot of the GAN variations which have been proposed in the literature come without an encoder. Examples include WGAN and f-GAN. These models are deficient in cases where a reconstruction of latent space is needed to use the learned manifold.<br />
<br />
There have been numerous models proposed in the literature which try to combine the adversarial training of GANs with auto-encoder architectures. Some examples are [19], [20], [21], and [22]. There has also been work done in which reproducing kernels have been used in the context of GANS ([23], [24]).<br />
<br />
=Experiments=<br />
Experiments were used to empirically evaluate the proposed WAE model. <br />
<br />
'''Experimental setup'''<br />
<br />
For experimental setup, authors used <math> \small P_Z</math> and squared cost function <math> \small c(x,y)</math> for data points.<br />
Deterministic encoder-decoder pairs were used.The authors conducted experiments using the following two real-world datasets: (1) MNIST [27] made up of 70k images, and (2) CelebA [28] consisting of approximately 203k images. For test reconstruction and interpolations a pair of of held out images, <math>(x,y)</math> from the test set are Auto-encoded (separately), to produce <math>(z_x, z_y)</math> in the latent space<br />
<br />
'''Training Details - MNIST'''<br />
<br />
Authos use mini-batches of size 100 and trained the models for 100 epochs. They used λ = 10 and variance of 1. For the encoder-decoder pair they set α = 0.01 for Adam in the beginning and for the adversary in WAE-GAN to α = 0.005. After 30 epochs they decreased both by factor of 2, and after first 50 epochs further by factor of 5. Both encoder and decoder used fully convolutional architectures with 4x4 convolutional filters.<br />
<br />
'''Training Details - CelebA'''<br />
<br />
Authors took the CelebA images and conducted 140x140 center crops and then resized to the 4x64 resolution. They again used mini-batches of size 100 and trained the models for upto 250 epochs. All reported WAE models were trained for 55 epochs and VAE for 68 epochs. For WAE-MMD we used λ = 100 and for WAE-GAN λ = 1. Both used variance of 2.<br />
<br />
For WAE-MMD the learning rate of Adam was initially set to α = 0.01 . For WAE-GAN the learning rate of Adam for the encoder-decoder pair was initially set to α = 0.003 and for the adversary to 0.01. All learning rates were decreased by factor of 2 after 30 epochs, further by factor of 5 after 50 first epochs, and finally additional factor of 10 after 100 first epochs.<br />
<br />
The main evaluation criteria were to see if the WAE model can simultaneously achieve: <br />
<br />
<ol><br />
<li>accurate reconstruction of the data points</li><br />
<li>resonable geometry of the latent manifold</li><br />
<li>generation of high quality random samples</li><br />
</ol><br />
<br />
For the model to generalize well (1) and (2) should be met on both the training and test data set.<br />
<br />
The proposed model achieve reasonably good results as highlighted in the figures given below:<br />
<br />
[[File:ka2khan_figure_3.png|800px|thumb|center|Using CelebA dataset]]<br />
<br />
[[File:ka2khan_figure_4.png|800px|thumb|center|Using CelebA dataset, FID (Fréchet Inception Distance<br />
[32]): smaller is better, sharpness: larger is better]]<br />
<br />
=Conclusion=<br />
The authors proposed a new class of algorithms for building a generative model called Wasserstein Autoencoders based on optimal transport cost. They related the newly proposed model to the existing probabilistic modeling techniques. They empirically evaluated the proposed models using two real-world datasets. They compared the results obtained using their proposed model with the results obtained using VAEs on the same dataset to show that the proposed models generate sample images of higher quality in addition to being easier to train and having good reconstruction quality of the data points.<br />
<br />
The authors claim that in future work, they will further explore the criteria for matching the encoding distribution <math>Q_Z</math> to the prior distribution <math>P_Z</math>, evaluate whether it is feasible to adversarially train the cost function <math>c</math>in the input space <math>\mathcal{X}</math>, and a theoretical analysis of the dual-formations for WAE-GAN and WAE-MMD.<br />
<br />
=Future Work=<br />
Following the work of this paper, another generative model was introduced by [34] that is based on the concept of optimal transport. Optimal transport is basically the distance between probability distributions by transporting one of the distributions to the other (and hence the name of optimal transport). Then, a new simple model called "Sliced-Wasserstein Autoencoders" (SWAE) is presented, which is easily implemented, and provides the capabilities of Wasserstein Autoencoders.<br />
<br />
([https://openreview.net/forum?id=HkL7n1-0b]) The results from MNIST and CelebA datasets look convincing, though could include additional evaluation to compare the adversarial loss with the straightforward MMD metric and potentially discuss their pros and cons. In some sense, given the challenges in evaluating and comparing closely related auto-encoder solutions, the authors could design demonstrative experiments for cases where Wassersterin distance helps and maybe its potential limitations.<br />
<br />
=Critique=<br />
<br />
Although this paper presented some empirical tests to explain its method in an appropriate way, it would be better to provide some clearer notations including the details of the architectures in their experiments. Furthermore, they could benefit from performing some comparisons between the results of their work and other similar works. As pointed out by a reviewer, the closest work to this paper is the adversarial variational bayes framework by Mescheder et.al. which also attempts at unifying VAEs and GANs. Although the authors describe the conceptual differences and advantages over that approach, it will be beneficial to actually include some comparisons in the results section.<br />
Moreover, the performance of the algorithm is not a significant improvement compared to previous VAE algorithm. The performance can be described and tested if the author performed empirical tests on various data sets. However, the methodology is flexible and unified to other types of the algorithm which is a huge benefit without compromising the stability of the training.<br />
<br />
=References=<br />
[1] D. P. Kingma and M. Welling. Auto-encoding variational Bayes. In ICLR, 2014.<br />
<br />
[2] A. Makhzani, J. Shlens, N. Jaitly, and I. Goodfellow. Adversarial autoencoders. In ICLR, 2016.<br />
<br />
[3] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In NIPS, pages 2672–2680, 2014.<br />
<br />
[4] O. Bousquet, S. Gelly, I. Tolstikhin, C. J. Simon-Gabriel, and B. Schölkopf. From optimal transport to generative modeling: the VEGAN cookbook, 2017.<br />
<br />
[5] M. Arjovsky, S. Chintala, and L. Bottou. Wasserstein GAN, 2017.<br />
<br />
[6] C. Villani. Topics in Optimal Transportation. AMS Graduate Studies in Mathematics, 2003.<br />
<br />
[7] Sebastian Nowozin, Botond Cseke, and Ryota Tomioka. f-GAN: Training generative neural samplers using variational divergence minimization. In NIPS, 2016.<br />
<br />
[8] I. Gulrajani, F. Ahmed, M. Arjovsky, V. Domoulin, and A. Courville. Improved training of wasserstein GANs, 2017.<br />
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[9] A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. J. Smola. A kernel two-sample test. Journal of Machine Learning Research, 13:723–773, 2012.<br />
<br />
[10] F. Liese and K.-J. Miescke. Statistical Decision Theory. Springer, 2008.<br />
<br />
[11] L. Mescheder, S. Nowozin, and A. Geiger. Adversarial variational bayes: Unifying variational autoencoders and generative adversarial networks, 2017.<br />
<br />
[12] Y. Bengio, A. Courville, and P. Vincent. Representation learning: A review and new perspectives. Pattern Analysis and Machine Intelligence, 35, 2013.<br />
<br />
[13] M. D. Hoffman and M. Johnson. Elbo surgery: yet another way to carve up the variational evidence lower bound. In NIPS Workshop on Advances in Approximate Bayesian Inference, 2016.<br />
<br />
[14] S. Zhao, J. Song, and S. Ermon. InfoVAE: Information maximizing variational autoencoders, 2017.<br />
<br />
[15] A. Genevay, M. Cuturi, G. Peyré, and F. R. Bach. Stochastic optimization for large-scale optimal transport. In Advances in Neural Information Processing Systems, pages 3432–3440, 2016. <br />
<br />
[16] M. Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems, pages 2292–2300, 2013.<br />
<br />
[17] Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard. Unbalanced optimal transport: geometry and kantorovich formulation. arXiv preprint arXiv:1508.05216, 2015.<br />
<br />
[18] Matthias Liero, Alexander Mielke, and Giuseppe Savaré. Optimal entropy-transport problems and a new hellinger-kantorovich distance between positive measures. arXiv preprint arXiv:1508.07941, 2015.<br />
<br />
[19] J. Zhao, M. Mathieu, and Y. LeCun. Energy-based generative adversarial network. In ICLR, 2017.<br />
<br />
[20] V. Dumoulin, I. Belghazi, B. Poole, A. Lamb, M. Arjovsky, O. Mastropietro, and A. Courville. Adversarially learned inference. In ICLR, 2017.<br />
<br />
[21] D. Ulyanov, A. Vedaldi, and V. Lempitsky. It takes (only) two: Adversarial generator-encoder networks, 2017.<br />
<br />
[22] D. Berthelot, T. Schumm, and L. Metz. Began: Boundary equilibrium generative adversarial networks, 2017.<br />
<br />
[23] Y. Li, K. Swersky, and R. Zemel. Generative moment matching networks. In ICML, 2015. <br />
<br />
[24] G. K. Dziugaite, D. M. Roy, and Z. Ghahramani. Training generative neural networks via maximum mean discrepancy optimization. In UAI, 2015.<br />
<br />
[25] R. Reddi, A. Ramdas, A. Singh, B. Poczos, and L. Wasserman. On the high-dimensional power of a linear-time two sample test under mean-shift alternatives. In AISTATS, 2015.<br />
<br />
[26] C. L. Li, W. C. Chang, Y. Cheng, Y. Yang, and B. Poczos. Mmd gan: Towards deeper understanding of moment matching network, 2017.<br />
<br />
[27] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. In Proceedings of the IEEE, volume 86(11), pages 2278–2324, 1998.<br />
<br />
[28] Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), 2015.<br />
<br />
[29] D. P. Kingma and J. Lei. Adam: A method for stochastic optimization, 2014.<br />
<br />
[30] A. Radford, L. Metz, and S. Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. In ICLR, 2016.<br />
<br />
[31] S. Ioffe and C. Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift, 2015.<br />
<br />
[32] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, Günter Klambauer, and Sepp Hochreiter. GANs trained by a two time-scale update rule converge to a nash equilibrium. arXiv preprint arXiv:1706.08500, 2017.<br />
<br />
[33] B. Poole, A. Alemi, J. Sohl-Dickstein, and A. Angelova. Improved generator objectives for GANs, 2016.<br />
<br />
[34] S. Kolouri, C. E. Martin, and G. K. Rohde. Sliced-wasserstein autoencoder: An embarrassingly simple generative model. arXiv preprint arXiv:1804.01947, 2018.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fix_your_classifier:_the_marginal_value_of_training_the_last_weight_layer&diff=42259Fix your classifier: the marginal value of training the last weight layer2018-12-04T20:57:12Z<p>Npbhatt: /* Possible Caveats */ Techinical Contribution: Added possible caveat</p>
<hr />
<div><br />
The code for the proposed model is available at https://github.com/eladhoffer/fix_your_classifier.<br />
<br />
=Introduction=<br />
<br />
Deep neural networks have become widely used for machine learning, achieving state-of-the-art results on many tasks. One of the most common tasks they are used for is classification. For example, convolutional neural networks (CNNs) are used to classify images to a semantic category. Typically, a learned affine transformation is placed at the end of such models, yielding a per-class value used for classification. This classifier can have a vast number of parameters, which grows linearly with the number of possible classes, thus requiring increasingly more computational resources.<br />
<br />
=Brief Overview=<br />
<br />
In order to alleviate the aforementioned problem, the authors propose that the final layer of the classifier be fixed (up to a global scale constant). They argue that with little or no loss of accuracy for most classification tasks, the method provides significant memory and computational benefits. In addition, they show that by initializing the classifier with a Hadamard matrix the inference could be made faster as well.<br />
<br />
=Previous Work=<br />
<br />
Training NN models and using them for inference requires large amounts of memory and computational resources; thus, extensive amount of research has been done lately to reduce the size of networks which are as follows:<br />
<br />
* Weight sharing and specification (Han et al., 2015)<br />
<br />
* Mixed precision to reduce the size of the neural networks by half (Micikevicius et al., 2017)<br />
<br />
* Low-rank approximations to speed up CNN (Tai et al., 2015)<br />
<br />
* Quantization of weights, activations, and gradients to further reduce computation during training (Hubara et al., 2016b; Li et al., 2016 and Zhou et al., 2016). Although aggressive quantization benefits from smaller model size, the extreme compression rate comes with a loss of accuracy.<br />
<br />
Some of the past works have also put forward the fact that predefined (Park & Sandberg, 1991) and random (Huang et al., 2006) projections can be used together with a learned affine transformation to achieve competitive results on many of the classification tasks. However, the authors' proposal in the current paper suggests the reverse proposal - common Neural Network models used can learn useful representations even without modifying the final output layer, which often holds a large number of parameters that grows linearly with number of classes.<br />
<br />
=Background=<br />
<br />
A Convolutional Neural Network (CNN) is comprised of one or more convolutional layers (often with a subsampling step) and then followed by one or more fully connected layers as in a standard multilayer neural network. The architecture of a CNN is designed to take advantage of the 2D structure of an input image (or other 2D input such as a speech signal). This is achieved with local connections and tied weights followed by some form of pooling which results in translation invariant features. Another benefit of CNNs is that they are easier to train and have many fewer parameters than fully connected networks with the same number of hidden units. <br />
<br />
A CNN consists of a number of convolutional and subsampling layers optionally followed by fully connected layers. The input to a convolutional layer is a <math>m \times m \times r</math> image where m is the height and width of the image and <math>r</math> is the number of channels, e.g. an RGB image has <math>r=3</math>. The convolutional layer will have <math>k</math> filters (or kernels) of size <math>n \times n \times q</math> where <math>n</math> is smaller than the dimension of the image and <math>q</math> can either be the same as the number of channels <math>r</math> or smaller and may vary for each kernel. The size of the filters gives rise to the locally connected structure which are each convolved with the image to produce <math>k</math> feature maps of size <math>m−n+1</math>. Each map is then subsampled typically with mean or max pooling over <math>p \times p</math> contiguous regions where <math>p</math> ranges between 2 for small images (e.g. MNIST) and is usually not more than 5 for larger inputs. Either before or after the subsampling layer an additive bias and sigmoidal nonlinearity is applied to each feature map. <br />
<br />
CNNs are commonly used to solve a variety of spatial and temporal tasks. Earlier architectures of CNNs (LeCun et al., 1998; Krizhevsky et al., 2012) used a set of fully-connected layers at later stages of the network, presumably to allow classification based on global features of an image.<br />
<br />
<br />
<br />
== Shortcomings of the Final Classification Layer and its Solution ==<br />
<br />
Zeiler & Fergus, 2014 showed that despite the enormous number of trainable parameters these layers add to the model, they are known to have a rather marginal impact on the final performance of the network.<br />
<br />
It has been shown previously that these layers could be easily compressed and reduced after a model was trained by simple means such as matrix decomposition and sparsification (Han et al., 2015). Modern architecture choices are characterized with the removal of most of the fully connected layers (Lin et al., 2013; Szegedy et al., 2015; He et al., 2016), that lead to better generalization and overall accuracy, together with a huge decrease in the number of trainable parameters. Additionally, numerous works showed that CNNs can be trained in a metric learning regime (Bromley et al., 1994; Schroff et al., 2015; Hoffer & Ailon, 2015), where no explicit classification layer was introduced and the objective regarded only distance measures between intermediate representations. Hardt & Ma (2017) suggested an all-convolutional network variant, where they kept the original initialization of the classification layer fixed with no negative impact on performance on the CIFAR-10 dataset.<br />
<br />
=Proposed Method=<br />
<br />
The aforementioned works provide evidence that fully-connected layers are in fact redundant and play a small role in learning and generalization. In this work, the authors have suggested that the parameters used for the final classification transform are completely redundant, and can be replaced with a predetermined linear transform. This holds for even in large-scale models and classification tasks, such as recent architectures trained on the ImageNet benchmark (Deng et al., 2009).<br />
<br />
==Using a Fixed Classifier==<br />
<br />
Suppose the final representation obtained by the network (the last hidden layer) is represented as <math>x = F(z;\theta)</math> where <math>F</math> is assumed to be a deep neural network with input z and parameters θ, e.g., a convolutional network, trained by backpropagation.<br />
<br />
In common NN models, this representation is followed by an additional affine transformation, <math>y = W^T x + b</math> ,where <math>W</math> and <math>b</math> are also trained by back-propagation.<br />
<br />
For input <math>x</math> of <math>N</math> length, and <math>C</math> different possible outputs, <math>W</math> is required to be a matrix of <math>N ×<br />
C</math>. Training is done using cross-entropy loss, by feeding the network outputs through a softmax activation<br />
<br />
<math><br />
v_i = \frac{e^{y_i}}{\sum_{j}^{C}{e^{y_j}}}, i &isin; </math> { <math> {1, . . . , C} </math> }<br />
<br />
and reducing the expected negative log likelihood with respect to ground-truth target <math> t &isin; </math> { <math> {1, . . . , C} </math> },<br />
by minimizing the loss function:<br />
<br />
<math><br />
L(x, t) = −\text{log}\ {v_t} = −{w_t}·{x} − b_t + \text{log} ({\sum_{j}^{C}e^{w_j . x + b_j}})<br />
</math><br />
<br />
where <math>w_i</math> is the <math>i</math>-th column of <math>W</math>.<br />
<br />
==Choosing the Projection Matrix==<br />
<br />
To evaluate the conjecture regarding the importance of the final classification transformation, the trainable parameter matrix <math>W</math> is replaced with a fixed orthonormal projection <math> Q &isin; R^{N×C} </math>, such that <math> &forall; i &ne; j : q_i · q_j = 0 </math> and <math> || q_i ||_{2} = 1 </math>, where <math>q_i</math> is the <math>i</math>th column of <math>Q</math>. This is ensured by a simple random sampling and singular-value decomposition<br />
<br />
As the rows of classifier weight matrix are fixed with an equally valued <math>L_{2}</math> norm, we find it beneficial<br />
to also restrict the representation of <math>x</math> by normalizing it to reside on the <math>n</math>-dimensional sphere:<br />
<br />
<center><math><br />
\hat{x} = \frac{x}{||x||_{2}}<br />
</math></center><br />
<br />
This allows faster training and convergence, as the network does not need to account for changes in the scale of its weights. However, it has now an issue that <math>q_i · \hat{x} </math> is bounded between −1 and 1. This causes convergence issues, as the softmax function is scale sensitive, and the network is affected by the inability to re-scale its input. This issue is amended with a fixed scale <math>T</math> applied to softmax inputs <math>f(y) = softmax(\frac{1}{T}y)</math>, also known as the ''softmax temperature''. However, this introduces an additional hyper-parameter which may differ between networks and datasets. So, the authors propose to introduce a single scalar parameter <math>\alpha</math> to learn the softmax scale, effectively functioning as an inverse of the softmax temperature <math>\frac{1}{T}</math>. The normalized weights and an additional scale coefficient are also used, specially using a single scale for all entries in the weight matrix. The additional vector of bias parameters <math>b &isin; \mathbb{R}^{C}</math> is kept the same and the model is trained using the traditional negative-log-likelihood criterion. Explicitly, the classifier output is now:<br />
<br />
<center><br />
<math><br />
v_i=\frac{e^{\alpha q_i &middot; \hat{x} + b_i}}{\sum_{j}^{C} e^{\alpha q_j &middot; \hat{x} + b_j}}, i &isin; </math> { <math> {1,...,C} </math>}<br />
</center><br />
<br />
and the loss to be minimized is:<br />
<br />
<center><math><br />
L(x, t) = -\alpha q_t &middot; \frac{x}{||x||_{2}} + b_t + \text{log} (\sum_{i=1}^{C} \text{exp}((\alpha q_i &middot; \frac{x}{||x||_{2}} + b_i)))<br />
</math></center><br />
<br />
where <math>x</math> is the final representation obtained by the network for a specific sample, and <math> t &isin; </math> { <math> {1, . . . , C} </math> } is the ground-truth label for that sample. The behaviour of the parameter <math> \alpha </math> over time, which is logarithmic in nature and has the same behavior exhibited by the norm of a learned classifier, is shown in<br />
[[Media: figure1_log_behave.png| Figure 1]].<br />
<br />
<center>[[File:figure1_log_behave.png]]</center><br />
<br />
When <math> -1 \le q_i · \hat{x} \le 1 </math>, a possible cosine angle loss is <br />
<br />
<center>[[File:caloss.png]]</center><br />
<br />
But its final validation accuracy has a slight decrease, compared to original models.<br />
<br />
==Using a Hadamard Matrix==<br />
<br />
To recall, Hadamard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are either +1 or −1. <br />
Example:<br />
<br />
<math>\displaystyle H_{4}={\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\end{bmatrix}}</math><br />
<br />
Furthermore, <math> H </math> is orthogonal, such that <math> HH^{T} = nI_n </math> where <math>I_n</math> is the identity matrix. Instead of using the entire Hadamard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all <math>C</math> rows are orthogonal as the final classification layer is such that:<br />
<br />
<center><math><br />
y = \hat{H} \hat{x} + b<br />
</math></center><br />
<br />
This usage allows two main benefits:<br />
* A deterministic, low-memory and easily generated matrix that can be used for classification.<br />
* Removal of the need to perform a full matrix-matrix multiplication - as multiplying by a Hadamard matrix can be done by simple sign manipulation and addition.<br />
<br />
Here, <math>n</math> must be a multiple of 4, but it can be easily truncated to fit normally defined networks. Also, as the classifier weights are fixed to need only 1-bit precision, it is now possible to focus our attention on the features preceding it.<br />
<br />
=Experimental Results=<br />
<br />
The authors have evaluated their proposed model on the following datasets:<br />
<br />
==CIFAR-10/100==<br />
<br />
===About the Dataset===<br />
<br />
CIFAR-10 is an image classification benchmark dataset containing 50,000 training images and 10,000 test images. The images are in color and contain 32×32 pixels. There are 10 possible classes of various animals and vehicles. CIFAR-100 holds the same number of images of the same size, but contains 100 different classes.<br />
<br />
===Training Details===<br />
<br />
The authors trained a residual network ( He et al., 2016) on the CIFAR-10 dataset. The network depth was 56 and the same hyper-parameters as in the original work were used. A comparison of the two variants, i.e., the learned classifier and the proposed classifier with a fixed transformation is shown in [[Media: figure1_resnet_cifar10.png | Figure 2]].<br />
<br />
<center>[[File: figure1_resnet_cifar10.png]]</center><br />
<br />
These results demonstrate that although the training error is considerably lower for the network with learned classifier, both models achieve the same classification accuracy on the validation set. The authors' conjecture is that with the new fixed parameterization, the network can no longer increase the norm of a given sample’s representation - thus learning its label requires more effort. As this may happen for specific seen samples - it affects only training error.<br />
<br />
The authors also compared using a fixed scale variable <math>\alpha </math> at different values vs. the learned parameter. Results for <math> \alpha = </math> {0.1, 1, 10} are depicted in [[Media: figure3_alpha_resnet_cifar.png| Figure 3]] for both training and validation error and as can be seen, similar validation accuracy can be obtained using a fixed scale value (in this case <math>\alpha </math>= 1 or 10 will suffice) at the expense of another hyper-parameter to seek. In all the further experiments the scaling parameter <math> \alpha </math> was regularized with the same weight decay coefficient used on original classifier. Although learning the scale is not necessary, but it will help convergence during training.<br />
<br />
<center>[[File: figure3_alpha_resnet_cifar.png]]</center><br />
<br />
The authors then train the model on CIFAR-100 dataset. They used the DenseNet-BC model from Huang et al. (2017) with a depth of 100 layers and k = 12. The higher number of classes caused the number of parameters to grow and encompassed about 4% of the whole model. However, validation accuracy for the fixed-classifier model remained equally good as the original model, and the same training curve was observed as earlier.<br />
<br />
==IMAGENET==<br />
<br />
===About the Dataset===<br />
<br />
The Imagenet dataset introduced by Deng et al. (2009) spans over 1000 visual classes, and over 1.2 million samples. This is supposedly a more challenging dataset to work on as compared to CIFAR-10/100.<br />
<br />
===Experiment Details===<br />
<br />
The authors evaluated their fixed classifier method on Imagenet using Resnet50 by He et al. (2016) and Densenet169 model (Huang et al., 2017) as described in the original work. Using a fixed classifier removed approximately 2-million parameters were from the model, accounting for about 8% and 12 % of the model parameters respectively. The experiments revealed similar trends as observed on CIFAR-10.<br />
<br />
For a more stricter evaluation, the authors also trained a Shufflenet architecture (Zhang et al., 2017b), which was designed to be used in low memory and limited computing platforms and has parameters making up the majority of the model. They were able to reduce the parameters to 0.86 million as compared to 0.96 million parameters in the final layer of the original model. Again, the proposed modification in the original model gave similar convergence results on validation accuracy. Interestingly, this method allowed Imagenet training in an under-specified regime, where there are<br />
more training samples than the number of parameters. This is an unconventional regime for modern deep networks, which are usually over-specified to have many more parameters than training samples (Zhang et al., 2017a).<br />
<br />
The overall results of the fixed-classifier are summarized in [[Media: table1_fixed_results.png | Table 1]].<br />
<br />
<center>[[File: table1_fixed_results.png]]</center><br />
<br />
==Language Modelling==<br />
<br />
Recent works have empirically found that using the same weights for both word embedding and classifier can yield equal or better results than using a separate pair of weights. So the authors experimented with fix-classifiers on language modeling as it also requires classification of all possible tokens available in the task vocabulary. They trained a recurrent model with 2-layers of LSTM (Hochreiter & Schmidhuber, 1997) and embedding + hidden size of 512 on the WikiText2 dataset (Merity et al., 2016), using same settings as in Merity et al. (2017). WikiText2 dataset contains about 33K different words, so the number of parameters expected in the embedding and classifier layer was about 34-million. This number is about 89% of the total number of parameters used for the whole model which is 38-million. However, using a random orthogonal transform yielded poor results compared to learned embedding. This was suspected to be due to semantic relationships captured in the embedding layer of language models, which is not the case in image classification task. The intuition was further confirmed by the much better results when pre-trained embeddings using word2vec algorithm by Mikolov et al. (2013) or PMI factorization as suggested by Levy & Goldberg (2014), were used. The final result used 89% fewer parameters than a fully learned model, with only marginally worse perplexity. The authors posit that this implies a required structure in word embedding that originates from the semantic relatedness between words, and unbalanced classes. They further suggest that with more efficient ways to train word embeddings, it may be possible to mitigate the issues arising from this structure and class imbalance. <br />
<br />
<center>[[File: language.png]]</center><br />
<br />
=Discussion=<br />
<br />
==Implications and Use Cases==<br />
<br />
With the increasing number of classes in the benchmark datasets, computational demands for the final classifier will increase as well. In order to understand the problem better, the authors observe the work by Sun et al. (2017), which introduced JFT-300M - an internal Google dataset with over 18K different classes. Using a Resnet50 (He et al., 2016), with a 2048 sized representation led to a model with over 36M parameters meaning that over 60% of the model parameters resided in the final classification layer. Sun et al. (2017) also describe the difficulty in distributing so many parameters over the training servers involving a non-trivial overhead during synchronization of the model for update. The authors claim that the fixed-classifier would help considerably in this kind of scenario - where using a fixed classifier removes the need to do any gradient synchronization for the final layer. Furthermore, introduction of Hadamard matrix removes the need to save the transformation altogether, thereby, making it more efficient and allowing considerable memory and computational savings.<br />
<br />
==Possible Caveats==<br />
<br />
The good performance of fixed-classifiers relies on the ability of the preceding layers to learn separable representations. This could be affected when the ratio between learned features and number of classes is small – that is, when <math> C > N</math>. However, they tested their method in such cases and their model performed well and provided good results. <br />
<br />
Some experiments were conducted by the authors with such cases, for example Imagenet classification (C = 1000) using mobilenet-0.5 with N = 512 or using ResNet with N = 256. In both scenarios, this method converged similarly to a fully learned classifier reaching the same final validation accuracy. Although, there is no presentation of this information within the paper itself, if true, it may strengthen the finding that even in cases in which C > N, fixed classifier can provide equally good results.<br />
<br />
Another factor that can affect the performance of their model using a fixed classifier is when the classes are highly correlated. In that case, the fixed classifier actually cannot support correlated classes and thus, the network could have some difficulty to learn. For a language model, word classes tend to have highly correlated instances, which also lead to difficult learning process.<br />
<br />
Also, this proposed approach will only eliminate the computation of the classifier weights, so when the classes are fewer, the computation saving effect will not be readily apparent.<br />
<br />
==Future Work==<br />
<br />
<br />
The use of fixed classifiers might be further simplified in Binarized Neural Networks (Hubara et al., 2016a), where the activations and weights are restricted to ±1 during propagations. In that case, the norm of the last hidden layer would be constant for all samples (equal to the square root of the hidden layer width). The constant could then be absorbed into the scale constant <math>\alpha</math>, and there is no need in a per-sample normalization.<br />
<br />
Additionally, more efficient ways to learn a word embedding should also be explored where similar redundancy in classifier weights may suggest simpler forms of token representations - such as low-rank or sparse versions.<br />
<br />
A related paper was published that claims that fixing most of the parameters of the neural network achieves comparable results with learning all of them [A. Rosenfeld and J. K. Tsotsos]<br />
<br />
=Conclusion=<br />
<br />
In this work, the authors argue that the final classification layer in deep neural networks is redundant and suggest removing the parameters from the classification layer. The empirical results from experiments on the CIFAR and IMAGENET datasets suggest that such a change lead to little or almost no decline in the performance of the architecture. Furthermore, using a Hadmard matrix as classifier might lead to some computational benefits when properly implemented, and save memory otherwise spent on large amount of transformation coefficients.<br />
<br />
Another possible scope of research that could be pointed out for future could be to find new efficient methods to create pre-defined word embeddings, which require huge amount of parameters that can possibly be avoided when learning a new task. Therefore, more emphasis should be given to the representations learned by the non-linear parts of the neural networks - up to the final classifier, as it seems highly redundant.<br />
<br />
=Critique=<br />
<br />
The paper proposes an interesting idea that has a potential use case when designing memory-efficient neural networks. The experiments shown in the paper are quite rigorous and provide support to the authors' claim. However, it would have been more helpful if the authors had described a bit more about efficient implementation of the Hadamard matrix and how to scale this method for larger datasets (cases with <math> C >N</math>).<br />
<br />
Moreover, one of the main intuitions of the paper has introduced to be computational cost but it has left out to compare a fixed and learned classifier based on the computational cost and then investigate whether it worth the drop in performance or not considering the fact that not always the output can be degraded because of need for speed! At least a discussion on this issue is expected.<br />
<br />
On the other hand, the computational cost and performance change after fixation of classifier could be related to dataset and the nature and complexity of it. Mostly, having 1000 classes makes the classification more crucial than 2 classes. An evaluation of this topic is also needed.<br />
<br />
Another interesting experiment to do would be to look this technique interacts with distillation when used in the teacher or student network or both. For instance, Does fixing the features make it more difficult to place dog than on boat when classifying a cat? Do networks with fixed classifier weights make worse teachers for distillation?<br />
<br />
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A. Rosenfeld and J. K. Tsotsos, “Intriguing properties of randomly weighted networks: Generalizing while learning next to nothing,” arXiv preprint arXiv:1802.00844, 2018.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=DETECTING_STATISTICAL_INTERACTIONS_FROM_NEURAL_NETWORK_WEIGHTS&diff=42248DETECTING STATISTICAL INTERACTIONS FROM NEURAL NETWORK WEIGHTS2018-12-04T00:17:47Z<p>Npbhatt: /* Limitations */ Technical contribution: added some limitations</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. Two-way ANOVA has been a standard method of performing pairwise interaction detection that involves conducting hypothesis tests for each interaction candidate by checking each hypothesis with F-statistics (Wonnacott & Wonnacott, 1972). Additive Groves is another method that conducts individual tests for interactions and hence must face the same computational difficulties; however, it is special because the interactions it detects are not constrained to any functional form.<br />
* Define all interaction forms of interest, then later finds the important ones.<br />
<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, providing a tool for visualizing live activations on each layer of a trained CNN, and another for visualizing "Regularized Optimization".) <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 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 of <math>g_i</math> and <math>g_i'</math> are Feed-Forward neural networks. <math>g_i(\cdot)</math> captures the main effects, while <math>g_i'(\cdot)</math> captures the interaction. 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 />
In the case of detecting pairwise interactions, the interlinked pairwise interactions are often confused by the algorithm for complex interactions. This means that the higher-order interaction algorithm fails to separate interlinked pairwise interactions encoded in the neural network. Another issue is that it sometimes detects abrupt interactions or misses interactions as a result of correlations between features<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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=CapsuleNets&diff=41897CapsuleNets2018-11-29T17:56:04Z<p>Npbhatt: /* Critique */ Technical contribution: added a critique on lack of explanation about the intuition behind capsule networks preserving spatial relations.</p>
<hr />
<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 defences 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 kxk 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 />
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 realize the mis-match 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 require.<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 />
[[File:Routing Algo.png|900px]]<br />
<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. 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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=ShakeDrop_Regularization&diff=41895ShakeDrop Regularization2018-11-29T17:50:25Z<p>Npbhatt: /* Critique */ Technical contribution: added downside about long training time in the critique section (not mentioned in the written summary).</p>
<hr />
<div>=Introduction=<br />
Current state of the art techniques for object classification are deep neural networks based on the residual block, first published by (He et al., 2016). This technique has been the foundation of several improved networks, including Wide ResNet (Zagoruyko & Komodakis, 2016), PyramdNet (Han et al., 2017) and ResNeXt (Xie et al., 2017). They have been further improved by regularization, such as Stochastic Depth (ResDrop) (Huang et al., 2016) and Shake-Shake (Gastaldi, 2017), which can avoid some problem like vanishing gradients. Shake-Shake applied to ResNeXt has achieved one of the lowest error rates on the CIFAR-10 and CIFAR-100 datasets. However, it is only applicable to multi-branch architectures and is not memory efficient since it requires two branches of residual blocks to apply. To address this problem, ShakeDrop regularization that can realize a similar disturbance to Shake-Shake on a single residual block is proposed. Moreover, they use ResDrop to stabilize the learning process. This paper seeks to formulate a general expansion of Shake-Shake that can be applied to any residual block based network.<br />
<br />
=Existing Methods=<br />
<br />
'''Deep Approaches'''<br />
<br />
'''ResNet''', was the first use of residual blocks, a foundational feature in many modern state of the art convolution neural networks. They can be formulated as <math>G(x) = x + F(x)</math> where <math>x</math> and <math>G(x)</math> are the input and output of the residual block, and <math>F(x)</math> is the output of the residual branch on the residual block. A residual block typically performs a convolution operation and then passes the result plus its input onto the next block.<br />
<br />
Intuition behind Residual blocks:<br />
If the identity mapping is optimal, We can easily push the residuals to zero (F(x) = 0) than to fit an identity mapping (x, input=output) by a stack of non-linear layers. In simple language it is very easy to come up with a solution like F(x) =0 rather than F(x)=x using stack of non-linear cnn layers as function (Think about it). So, this function F(x) is what the authors called Residual function ([https://medium.com/@14prakash/understanding-and-implementing-architectures-of-resnet-and-resnext-for-state-of-the-art-image-cf51669e1624 Reference]).<br />
<br />
<br />
[[File:ResidualBlock.png|580px|centre|thumb|An example of a simple residual block from Deep Residual Learning for Image Recognition by He et al., 2016]]<br />
<br />
ResNet is constructed out of a large number of these residual blocks sequentially stacked. It is interesting to note that having too many layers can cause overfitting, as pointed out by He et al. (2016) with the high error rates for the 1,202-layer ResNet on CIFAR datasets. Another paper (Veit et al., 2016) empirically showed that the cause of the high error rates can be mostly attributed to specific residual blocks whose channels increase greatly.<br />
<br />
'''PyramidNet''' is an important iteration that built on ResNet and WideResNet by gradually increasing channels on each residual block. The residual block is similar to those used in ResNet. It has been used to generate some of the first successful convolution neural networks with very large depth, at 272 layers. Amongst unmodified residual network architectures, it performs the best on the CIFAR datasets.<br />
<br />
[[File:ResidualBlockComparison.png|980px|centre|thumb|A simple illustration of different residual blocks from Deep Pyramidal Residual Networks by Han et al., 2017. The width of a block reflects the number of channels used in that layer.]]<br />
<br />
<br />
'''Non-Deep Approaches'''<br />
<br />
'''Wide ResNet''' modified ResNet by increasing channels in each layer, having a wider and shallower structure. Similarly to PyramidNet, this architecture avoids some of the pitfalls in the original formulation of ResNet.<br />
<br />
'''ResNeXt''' achieved performance beyond that of Wide ResNet with only a small increase in the number of parameters. It can be formulated as <math>G(x) = x + F_1(x)+F_2(x)</math>. In this case, <math>F_1(x)</math> and <math>F_2(x)</math> are the outputs of two paired convolution operations in a single residual block. The number of branches is not limited to 2, and will control the result of this network.<br />
<br />
<br />
[[File:SimplifiedResNeXt.png|600px|centre|thumb|Simplified ResNeXt Convolution Block. Yamada et al., 2018]]<br />
<br />
<br />
'''Regularization Methods'''<br />
<br />
'''Stochastic Depth''' helped address the issue of vanishing gradients in ResNet. It works by randomly dropping residual blocks. On the <math>l^{th}</math> residual block the Stochastic Depth process is given as <math>G(x)=x+b_lF(x)</math> where <math>b_l \in \{0,1\}</math> is a Bernoulli random variable with probability <math>p_l</math>. Using a constant value for <math>p_l</math> didn't work well, so instead a linear decay rule <math>p_l = 1 - \frac{l}{L}(1-p_L)</math> was used. In this equation, <math>L</math> is the number of layers, and <math>p_L</math> is the initial parameter. <br />
<br />
'''Shake-Shake''' is a regularization method that specifically improves the ResNeXt architecture. It can be given as <math>G(x)=x+\alpha F_1(x)+(1-\alpha)F_2(x)</math>, where <math>\alpha \in [0,1]</math> is a random coefficient. <math>\alpha</math> is used during the forward pass, and another identically distributed random parameter <math>\beta</math> is used in the backward pass. This caused one of the two paired convolution operations to be dropped, and further improved ResNeXt.<br />
<br />
[[File:Paper 32.jpg|600px|centre|thumb| Shake-Shake (ResNeXt + Shake-Shake) (Gastaldi, 2017), in which some processing layers omitted for conciseness.]]<br />
<br />
=Proposed Method=<br />
We give an intuitive interpretation of the forward pass of Shake-Shake regularization. To the best of our knowledge, it has not been given yet, while the phenomenon in the backward pass is experimentally investigated by Gastaldi (2017). In the forward pass, Shake-Shake interpolates the outputs of two residual branches with a random variable α that controls the degree of interpolation. As DeVries & Taylor (2017a) demonstrated that interpolation of two data in the feature space can synthesize reasonable augmented data, the interpolation of two residual blocks of Shake-Shake in the forward pass can be interpreted as synthesizing data. Use of a random variable α generates many different augmented data. On the other hand, in the backward pass, a different random variable β is used to disturb learning to make the network learnable long time. Gastaldi (2017) demonstrated how the difference between <math>\alpha</math> and <math>\beta</math> affects.<br />
<br />
The regularization mechanism of Shake-Shake relies on two or more residual branches, so that it can be applied only to 2-branch networks architectures. In addition, 2-branch network architectures consume more memory than 1-branch network architectures. One may think the number of learnable parameters of ResNeXt can be kept in 1-branch and 2-branch network architectures by controlling its cardinality and the number of channels (filters). For example, a 1-branch network (e.g., ResNeXt 1-64d) and its corresponding 2-branch network (e.g., ResNeXt 2-40d) have almost same number of learnable parameters. However, even so, it increases memory consumption due to the overhead to keep the inputs of residual blocks and so on. By comparing ResNeXt 1-64d and 2-40d, the latter requires more memory than the former by 8% in theory (for one layer) and by 11% in measured values (for 152 layers).<br />
<br />
This paper seeks to generalize the method proposed in Shake-Shake to be applied to any residual structure network. Shake-Shake. The initial formulation of 1-branch shake is <math>G(x) = x + \alpha F(x)</math>. In this case, <math>\alpha</math> is a coefficient that disturbs the forward pass, but is not necessarily constrained to be [0,1]. Another corresponding coefficient <math>\beta</math> is used in the backwards pass. Applying this simple adaptation of Shake-Shake on a 110-layer version of PyramidNet with <math>\alpha \in [0,1]</math> and <math>\beta \in [0,1]</math> performs abysmally, with an error rate of 77.99%.<br />
<br />
This failure is a result of the setup causing too much perturbation. A trick is needed to promote learning with large perturbations, to preserve the regularization effect. The idea of the authors is to borrow from ResDrop and combine that with Shake-Shake. This works by randomly deciding whether to apply 1-branch shake. This creates in effect two networks, the original network without a regularization component, and a regularized network. When mixing up two networks, we expected the following effects: When the non regularized network is selected, learning is promoted; when the perturbed network is selected, learning is disturbed. Achieving good performance requires a balance between the two. <br />
<br />
'''ShakeDrop''' is given as <br />
<br />
<div align="center"><br />
<math>G(x) = x + (b_l + \alpha - b_l \alpha)F(x)</math>,<br />
</div><br />
<br />
where <math>b_l</math> is a Bernoulli random variable following the linear decay rule used in Stochastic Depth. An alternative presentation is <br />
<br />
<div align="center"><br />
<math><br />
G(x) = \begin{cases}<br />
x + F(x) ~~ \text{if } b_l = 1 \\<br />
x + \alpha F(x) ~~ \text{otherwise}<br />
\end{cases}<br />
</math><br />
</div><br />
<br />
If <math>b_l = 1</math> then ShakeDrop is equivalent to the original network, otherwise it is the network + 1-branch Shake. The authors also found that the linear decay rule of ResDrop works well, compared with the uniform rule. Regardless of the value of <math>\beta</math> on the backwards pass, network weights will be updated.<br />
<br />
=Experiments=<br />
<br />
'''Parameter Search'''<br />
<br />
The authors experiments began with a hyperparameter search utilizing ShakeDrop on pyramidal networks. The PyramidNet used was made up of a total of 110 layers which included a convolutional layer and a final fully connected layer. It had 54 additive pyramidal residual blocks and the final residual block had 286 channels. The results of this search are presented below. <br />
<br />
[[File:ShakeDropHyperParameterSearch.png|600px|centre|thumb|Average Top-1 errors (%) of “PyramidNet + ShakeDrop” with several ranges of parameters of 4 runs at the final (300th) epoch on CIFAR-100 dataset in the “Batch” level. In some settings, it is equivalent to PyramidNet and PyramidDrop. Borrowed from ShakeDrop Regularization by Yamada et al., 2018.]]<br />
<br />
The setting that are used throughout the rest of the experiments are then <math>\alpha \in [-1,1]</math> and <math>\beta \in [0,1]</math>. Cases H and F outperform PyramidNet, suggesting that the strong perturbations imposed by ShakeDrop are functioning as intended. However, fully applying the perturbations in the backwards pass appears to destabilize the network, resulting in performance that is worse than standard PyramidNet.<br />
<br />
[[File:ParameterUpdateShakeDrop.png|400px|centre]]<br />
<br />
Following this initial parameter decision, the authors tested 4 different strategies for parameter update among "Batch" (same coefficients for all images in minibatch for each residual block), "Image" (same scaling coefficients for each image for each residual block), "Channel" (same scaling coefficients for each element for each residual block), and "Pixel" (same scaling coefficients for each element for each residual block). While Pixel was the best in terms of error rate, it is not very memory efficient, so Image was selected as it had the second best performance without the memory drawback.<br />
<br />
'''Comparison with Regularization Methods'''<br />
<br />
For these experiments, there are a few modifications that were made to assist with training. For ResNeXt, the EraseRelu formulation has each residual block ends in batch normalization. The Wide ResNet also is compared between vanilla with batch normalization and without. Batch normalization keeps the outputs of residual blocks in a certain range, as otherwise <math>\alpha</math> and <math>\beta</math> could cause perturbations that are too large, causing divergent learning. There is also a comparison of ResDrop/ShakeDrop Type A (where the regularization unit is inserted before the add unit for a residual branch) and after (where the regularization unit is inserted after the add unit for a residual branch). <br />
<br />
These experiments are performed on the CIFAR-100 dataset.<br />
<br />
[[File:ShakeDropArchitectureComparison1.png|800px|centre|thumb|]]<br />
<br />
[[File:ShakeDropArchitectureComparison2.png|800px|centre|thumb|]]<br />
<br />
[[File:ShakeDropArchitectureComparison3.png|800px|centre|thumb|]]<br />
<br />
For a final round of testing, the training setup was modified to incorporate other techniques used in state of the art methods. For most of the tests, the learning rate for the 300 epoch version started at 0.1 and decayed by a factor of 0.1 1/2 & 3/4 of the way through training. The alternative was cosine annealing, based on the presentation by Loshchilov and Hutter in their paper SGDR: Stochastic Gradient Descent with Warm Restarts. This is indicated in the Cos column, with a check indicating cosine annealing. <br />
<br />
[[File:CosineAnnealing.png|400px|centre|thumb|]]<br />
<br />
The Reg column indicates the regularization method used, either none, ResDrop (RD), Shake-Shake (SS), or ShakeDrop (SD). Fianlly, the Fil Column determines the type of data augmentation used, either none, cutout (CO) (DeVries & Taylor, 2017b), or Random Erasing (RE) (Zhong et al., 2017). <br />
<br />
[[File:ShakeDropComparison.png|800px|centre|thumb|Top-1 Errors (%) at final epoch on CIFAR-10/100 datasets]]<br />
<br />
'''State-of-the-Art Comparisons'''<br />
<br />
A direct comparison with state of the art methods is favorable for this new method. <br />
<br />
# Fair comparison of ResNeXt + Shake-Shake with PyramidNet + ShakeDrop gives an improvement of 0.19% on CIFAR-10 and 1.86% on CIFAR-100. Under these conditions, the final error rate is then 2.67% for CIFAR-10 and 13.99% for CIFAR-100.<br />
# Fair comparison of ResNeXt + Shake-Shake + Cutout with PyramidNet + ShakeDrop + Random Erasing gives an improvement of 0.25% on CIFAR-10 and 3.01% on CIFAR 100. Under these conditions, the final error rate is then 2.31% for CIFAR-10 and 12.19% for CIFAR-100.<br />
# Comparison with the state-of-the-arts, PyramidNet + ShakeDrop gives an improvement of 0.25% on CIFAR-10 than ResNeXt + Shake-Shake + Cutout, PyramidNet + ShakeDrop gives an improvement of 2.85% on CIFAR-100 than Coupled Ensemble.<br />
<br />
=Implementation details=<br />
<br />
'''CIFAR-10/100 datasets'''<br />
<br />
All the images in these datasets were color normalized and then horizontally flipped with a probability of 50%. All of then then were zero padded to have a dimentionality of 40 by 40 pixels.<br />
<br />
<br />
=Conclusion=<br />
The paper proposes a new form of regularization that is an extension of "Shake-Shake" regularization [Gastaldi, 2017]. The original "shake-shake" proposes using two residual paths adding to the same output, and during training, considering different randomly selected convex combinations of the two paths (while using an equally weighted combination at test time). This paper contends that this requires additional memory, and attempts to achieve similar regularization with a single path. To do so, they train a network with a single residual path, where the residual is included without attenuation in some cases with some fixed probability, and attenuated randomly (or even inverted) in others. The paper contends that this achieves superior performance than choosing simply a random attenuation for every sample (although, this can be seen as choosing an attenuation under a distribution with some fixed probability mass.<br />
<br />
Their stochastic regularization method, ShakeDrop, which outperforms previous state of the art methods while maintaining similar memory efficiency. It demonstrates that heavily perturbing a network can help to overcome issues with overfitting. It is also an effective way to regularize residual networks for image classification. The method was tested by CIFAR-10/100 and Tiny ImageNet datasets and showed great performance.<br />
<br />
=Critique=<br />
<br />
The novelty of this paper is low as pointed out by the reviewers. Also, there is a confusion whether or not the results could be replicated as <math>\alpha</math> and <math>\beta</math> are choosen randomly. The proposed ShakeDrop regularization is essentially a combination of the PyramidDrop and Shake-Shake regularization. The most surprising part is that the forward weight can be negative thus inverting the output of a convolution. The mathematical justification for ShakeDrop regularization is limited, relying on intuition and empirical evidence instead.<br />
<br />
One downside of this methods (as was identified in the presentation as well) is that the training for cosine annealing variation of the model takes 1800 epochs which is time intensive compared to other methods that were compared as baselines. This can limit practical implementation of this algorithm.<br />
<br />
As pointed out from the above, the method basically relies heavily on the intuition. This means that the performance of the algorithm can not been extended beyond the CIFAR dataset and can vary a lot depending on the characteristics of data sets that users are performing, with some exaggeration. However, the performance is still impressive since it performs better than known algorithms. It is not clear as to how the proposed technique would work with a non-residual architecture.<br />
It lacks conclusive proof that "shake-drop" is a generically useful regularization technique. For one, the method is evaluated only on small toy-datasets: CIFAR-10 and CIFAR-100. Evaluation on Imagenet perhaps would have been valuable.<br />
<br />
=References=<br />
[Yamada et al., 2018] Yamada Y, Iwamura M, Kise K. ShakeDrop regularization. arXiv preprint arXiv:1802.02375. 2018 Feb 7.<br />
<br />
[He et al., 2016] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proc. CVPR, 2016.<br />
<br />
[Zagoruyko & Komodakis, 2016] Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. In Proc. BMVC, 2016.<br />
<br />
[Han et al., 2017] Dongyoon Han, Jiwhan Kim, and Junmo Kim. Deep pyramidal residual networks. In Proc. CVPR, 2017a.<br />
<br />
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<br />
[Gastaldi, 2017] Xavier Gastaldi. Shake-shake regularization. arXiv preprint arXiv:1705.07485v2, 2017.<br />
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[Loshilov & Hutter, 2016] Ilya Loshchilov and Frank Hutter. Sgdr: Stochastic gradient descent with warm restarts. arXiv preprint arXiv:1608.03983, 2016.<br />
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[DeVries & Taylor, 2017b] Terrance DeVries and Graham W. Taylor. Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552, 2017b.<br />
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[Zhong et al., 2017] Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. arXiv preprint arXiv:1708.04896, 2017.<br />
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[Dutt et al., 2017] Anuvabh Dutt, Denis Pellerin, and Georges Qunot. Coupled ensembles of neural networks. arXiv preprint 1709.06053v1, 2017.<br />
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[Veit et al., 2016] Andreas Veit, Michael J Wilber, and Serge Belongie. Residual networks behave like ensembles of relatively shallow networks. Advances in Neural Information Processing Systems 29, 2016.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=policy_optimization_with_demonstrations&diff=41626policy optimization with demonstrations2018-11-27T18:03:12Z<p>Npbhatt: /* Baselines */ Technical Contribution: added some baseline background</p>
<hr />
<div>= Introduction =<br />
<br />
The reinforcement learning (RL) method has made significant progress in a variety of applications, but the exploration problems regarding how to gain more experience from novel policies to improve long-term performance are still challenges, especially in environments where reward signals are sparse and rare. There are currently two ways to solve such exploration problems in RL: <br />
<br />
1) Guide the agent to explore states that have never been seen. <br />
<br />
2) Guide the agent to imitate a demonstration trajectory sampled from an expert policy to learn. <br />
<br />
When guiding the agent to imitate the expert behavior for learning, there are also two methods: putting the demonstration directly into the replay memory [1] [2] [3] or using the demonstration trajectory to pre-train the policy in a supervised manner [4]. However, neither of these methods takes full advantage of the demonstration data. They instead treat the demonstration data identically to self-generated data, requiring a tremendous number of difficult to collect examples to learn effectively. To address this problem, a novel policy optimization method from demonstration (POfD) is proposed, which takes full advantage of the demonstration and there is no need to ensure that the expert policy is the optimal policy. To summarize, the authors bring forth this idea through the following techniques:<br />
<br />
1) A demonstration guided exploration term measuring the divergence between current and the expert policy is added to the policy optimization objective, increasing the similarity to expert-like exploration.<br />
<br />
2) They say that for better learning from demonstrations and getting an optimization friendly lower bound, the proposed objective could be defined on an occupancy measure as in [14].<br />
<br />
3) Finally, they show that the optimization can move towards optimizing the derived lower bound and the generative adversarial training.<br />
<br />
The authors also evaluate the performance of POfD on Mujoco [5] in sparse-reward environments. The experiments results show that the performance of POfD is greatly improved compared with some strong baselines and even to the policy gradient method in dense-reward environments.<br />
<br />
==Intuition==<br />
The agent should imitate the demonstrated behavior when rewards are sparse and then explore new states on its own after acquiring sufficient skills, which is a dynamic intrinsic reward mechanism that can be reshaped in terms of the native rewards in RL. At present the state of the art exploration in Reinforcement learning is simply epsilon greedy which just makes random moves for a small percentage of times to explore unexplored moves. This is very naive and is one of the main reasons for the high sample complexity in RL. On the other hand, if there is an expert demonstrator who can guide exploration, the agent can make more guided and accurate exploratory moves.<br />
<br />
=Related Work =<br />
There are some related works in overcoming exploration difficulties by learning from demonstration [6] and imitation learning in RL.<br />
<br />
For learning from demonstration (LfD),<br />
# Most LfD methods adopt value-based RL algorithms, such as DQfD (Deep Q-learning from Demonstrations) [2] which are applied into the discrete action spaces and DDPGfD (Deep Deterministic Policy Gradient from Demonstrations) [3] which extends this idea to the continuous spaces. But both of them under-utilize the demonstration data.<br />
# There are some methods based on policy iteration [7] [8], which shapes the value function by using demonstration data. But they get the bad performance when demonstration data is imperfect.<br />
# A hybrid framework [9] that learns the policy in which the probability of taking demonstrated actions is maximized is proposed, which considers less demonstration data.<br />
# A reward reshaping mechanism [10] that encourages taking actions close to the demonstrated ones is proposed. It is similar to the method in this paper, but there exists some differences as it is defined as a potential function based on multi-variate Gaussian to model the distribution of state-actions.<br />
All of the above methods require a lot of perfect demonstrations to get satisfactory performance, which is different from POfD in this paper.<br />
<br />
For imitation learning, <br />
# Inverse Reinforce Learning [11] problems are solved by alternating between fitting the reward function and selecting the policy [12] [13]. But it cannot be extended to big-scale problems.<br />
# Generative Adversarial Imitation Learning (GAIL) [14] uses a discriminator to distinguish whether a state-action pair is from the expert or the learned policy and it can be applied into the high-dimensional continuous control problems.<br />
<br />
Both of the above methods are effective for imitation learning, but cannot leverage the valuable feedback given by the environments and usually suffer from bad performance when the expert data is imperfect. That is different from POfD in this paper.<br />
<br />
There is also another idea in which an agent learns using hybrid imitation learning and reinforcement learning reward[23, 24]. However, unlike this paper, they did not provide some theoretical support for their method and only explained some intuitive explanations.<br />
<br />
=Background=<br />
<br />
==Preliminaries==<br />
Markov Decision Process (MDP) [15] is defined by a tuple <math>⟨\mathcal{S}, \mathcal{A}, \mathcal{P}, r, \gamma⟩ </math>, where <math>\mathcal{S}</math> is the state space, <math>\mathcal{A} </math> is the action space, <math>\mathcal{P}(s'|s,a)</math> is the transition distribution of taking action <math> a </math> at state <math>s </math>, <math> r(s,a) </math>is the reward function, and <math> \gamma </math> is the discount factor between 0 and 1. Policy <math> \pi(a|s) </math> is a mapping from state to action probabilities, the performance of <math> \pi </math> is usually evaluated by its expected discounted reward <math> \eta(\pi) </math>: <br />
\[\eta(\pi)=\mathbb{E}_{\pi}[r(s,a)]=\mathbb{E}_{(s_0,a_0,s_1,...)}[\sum_{t=0}^\infty\gamma^{t}r(s_t,a_t)] \]<br />
The value function is <math> V_{\pi}(s) =\mathbb{E}_{\pi}[r(·,·)|s_0=s] </math>, the action value function is <math> Q_{\pi}(s,a) =\mathbb{E}_{\pi}[r(·,·)|s_0=s,a_0=a] </math>, and the advantage function that reflects the expected additional reward after taking action a at state s is <math> A_{\pi}(s,a)=Q_{\pi}(s,a)-V_{\pi}(s)</math>.<br />
Then the authors define Occupancy measure, which is used to estimate the probability that state <math>s</math> and state action pairs <math>(s,a)</math> when executing a certain policy.<br />
[[File:def1.png|500px|center]]<br />
Then the performance of <math> \pi </math> can be rewritten to: <br />
[[File:equ2.png|500px|center]]<br />
At the same time, the authors propose a lemma: <br />
[[File:lemma1.png|500px|center]]<br />
<br />
==Problem Definition==<br />
Generally, RL tasks and environments do not provide a comprehensive reward and instead rely on sparse feedback indicating whether the goal is reached.<br />
<br />
In this paper, the authors aim to develop a method that can boost exploration by leveraging effectively the demonstrations <math>D^E </math>from the expert policy <math> \pi_E </math> and maximize <math> \eta(\pi) </math> in the sparse-reward environment. The authors define the demonstrations <math>D^E=\{\tau_1,\tau_2,...,\tau_N\} </math>, where the i-th trajectory <math>\tau_i=\{(s_0^i,a_0^i),(s_1^i,a_1^i),...,(s_T^i,a_T^i)\} </math> is generated from the unknown expert policy <math>\pi_E </math>. In addition, there is an assumption on the quality of the expert policy:<br />
[[File:asp1.png|500px|center]]<br />
<br />
<br />
Throughout the paper, they use <math>\pi_E </math> to denote the expert policy that gives the relatively good <math>\eta_\pi </math>, and use <math>\hat{\mathbb{E}}_D </math>to denote empirical expectation estimated from the demonstrated trajectories <math>D^E </math>. We have the following reasonable and necessary assumption on the quality of the expert policy <math>\pi_E </math>.<br />
<br />
<br />
Moreover, it is not necessary to ensure that the expert policy is advantageous over all the policies. This is because that POfD will learn a better policy than expert policy by exploring on its own in later learning stages.<br />
<br />
=Method=<br />
<br />
==Policy Optimization with Demonstration (POfD)==<br />
<br />
[[File:ff1.png|thumb|500px|center |Figure 1: Demonstrations (the blue curve) enables POfD to explore in the high-reward regions (red arrows). On the other hand random explorations (olive green dashed curves) occur in sparse-reward environments.]]<br />
<br />
This method optimizes the policy by forcing the policy to explore in the nearby region of the expert policy that is specified by several demonstrated trajectories <math>D^E </math> (as shown in Fig.1) in order to avoid causing slow convergence or failure when the environment feedback is sparse. In addition, the authors encourage the policy π to explore by "following" the demonstrations <math>D^E </math>. Thus, a new learning objective is given:<br />
\[ \mathcal{L}(\pi_{\theta})=-\eta(\pi_{\theta})+\lambda_{1}D_{JS}(\pi_{\theta},\pi_{E})\]<br />
where <math>D_{JS}(\pi_{\theta},\pi_{E})</math> is Jensen-Shannon divergence between current policy <math>\pi_{\theta}</math> and the expert policy <math>\pi_{E}</math> , <math>\lambda_1</math> is a trading-off parameter, and <math>\theta</math> is policy parameter. According to Lemma 1, the authors use <math>D_{JS}(\rho_{\theta},\rho_{E})</math> to instead of <math>D_{JS}(\pi_{\theta},\pi_{E})</math>, because it is easier to optimize through adversarial training on demonstrations. The learning objective is: <br />
\[ \mathcal{L}(\pi_{\theta})=-\eta(\pi_{\theta})+\lambda_{1}D_{JS}(\rho_{\theta},\rho_{E})\]<br />
<br />
==Benefits of Exploration with Demonstrations==<br />
The authors introduce the benefits of POfD. Firstly, we consider the expression of expected return in policy gradient methods [16].<br />
\[ \eta(\pi)=\eta(\pi_{old})+\mathbb{E}_{\tau\sim\pi}[\sum_{t=0}^\infty\gamma^{t}A_{\pi_{old}}(s,a)]\]<br />
<math>\eta(\pi)</math>is the advantage over the policy <math>\pi_{old}</math> in the previous iteration, so the expression can be rewritten by<br />
\[ \eta(\pi)=\eta(\pi_{old})+\sum_{s}\rho_{\pi}(s)\sum_{a}\pi(a|s)A_{\pi_{old}}(s,a)\]<br />
The local approximation to <math>\eta(\pi)</math> up to first order is usually as the surrogate learning objective to be optimized by policy gradient methods due to the difficulties brought by complex dependency of <math>\rho_{\pi}(s)</math> over <math> \pi </math>:<br />
\[ J_{\pi_{old}}(\pi)=\eta(\pi_{old})+\sum_{s}\rho_{\pi_{old}}(s)\sum_{a}\pi(a|s)A_{\pi_{old}}(s,a)\]<br />
The policy gradient methods improve <math>\eta(\pi)</math> monotonically by optimizing the above <math>J_{\pi_{old}}(\pi)</math> with a sufficiently small update step from <math>\pi_{old}</math> to <math>\pi</math> such that <math>D_{KL}^{max}(\pi, \pi_{old})</math> is bounded [16] [17] [18]. POfD imposes an additional regularization <math>D_{JS}(\pi_{\theta}, \pi_{E})</math> between <math>\pi_\theta</math> and <math>\pi_{E}</math> in order to encourage explorations around regions demonstrated by the expert policy. Theorem 1 shows such benefits,<br />
[[File:them1.png|500px|center]]<br />
<br />
In fact, POfD brings another factor, <math>D_{J S}^{max}(\pi_{i}, \pi_{E})</math>, that would fully use the advantage <math>{\hat \delta}</math>and add improvements with a margin over pure policy gradient methods.<br />
<br />
==Optimization==<br />
<br />
For POfD, the authors choose to optimize the lower bound of the Jensen-Shannon divergence instead of directly optimizing the difficult Jensen-Shannon divergence. This optimization method is compatible with any policy gradient methods. Theorem 2 gives the lower bound of <math>D_{JS}(\rho_{\theta}, \rho_{E})</math>：<br />
[[File:them2.png|450px|center]]<br />
Thus, the occupancy measure matching objective can be written as:<br />
[[File:eqnlm.png|450px|center]]<br />
where <math> D(s,a)=\frac{1}{1+e^{-U(s,a)}}: \mathcal{S}\times \mathcal{A} \rightarrow (0,1)</math> is an arbitrary mapping function followed by a sigmoid activation function used for scaling, and its supremum ranging is like a discriminator for distinguishing whether the state-action pair is a current policy or an expert policy.<br />
To avoid overfitting, the authors add causal entropy <math>−H (\pi_{\theta}) </math> as the regularization term. Thus, the learning objective is: <br />
\[\min_{\theta}\mathcal{L}=-\eta(\pi_{\theta})-\lambda_{2}H(\pi_{\theta})+\lambda_{1} \sup_{{D\in(0,1)}^{S\times A}} \mathbb{E}_{\pi_{\theta}}[\log(D(s,a))]+\mathbb{E}_{\pi_{E}}[\log(1-D(s,a))]\]<br />
At this point, the problem closely resembles the minimax problem related to the Generative Adversarial Networks (GANs) [19]. The difference is that the discriminative model D of GANs is well-trained but the expert policy of POfD is not optimal. Then suppose D is parameterized by w. If it is from an expert policy, <math>D_w</math>is toward 1, otherwise it is toward 0. Thus, the minimax learning objective is:<br />
\[\min_{\theta}\max_{w}\mathcal{L}=-\eta(\pi_{\theta})-\lambda_{2}H (\pi_{\theta})+\lambda_{1}( \mathbb{E}_{\pi_{\theta}}[\log(D_{w}(s,a))]+\mathbb{E}_{\pi_{E}}[\log(1-D_{w}(s,a))])\]<br />
The minimax learning objective can be rewritten by substituting the expression of <math> \eta(\pi) </math>:<br />
\[\min_{\theta}\max_{w}-\mathbb{E}_{\pi_{\theta}}[r'(s,a)]-\lambda_{2}H (\pi_{\theta})+\lambda_{1}\mathbb{E}_{\pi_{E}}[\log(1-D_{w}(s,a))]\]<br />
where <math> r'(s,a)=r(a,b)-\lambda_{1}\log(D_{w}(s,a))</math> is the reshaped reward function.<br />
The above objective can be optimized efficiently by alternately updating policy parameters θ and discriminator parameters w, then the gradient is given by:<br />
\[\mathbb{E}_{\pi}[\nabla_{w}\log(D_{w}(s,a))]+\mathbb{E}_{\pi_{E}}[\nabla_{w}\log(1-D_{w}(s,a))]\]<br />
Then, fixing the discriminator <math>D_w</math>, the reshaped policy gradient is:<br />
\[\nabla_{\theta}\mathbb{E}_{\pi_{\theta}}[r'(s,a)]=\mathbb{E}_{\pi_{\theta}}[\nabla_{\theta}\log\pi_{\theta}(a|s)Q'(s,a)]\]<br />
where <math>Q'(\bar{s},\bar{a})=\mathbb{E}_{\pi_{\theta}}[r'(s,a)|s_0=\bar{s},a_0=\bar{a}]</math>.<br />
<br />
At the end, Algorithm 1 gives the detailed process.<br />
[[File:pofd.png|450px|center]]<br />
<br />
=Discussion on Existing LfD Methods=<br />
<br />
To connect with the proposed POfD method, interpretation of the existing methods DQfD and DDPGfD through occupancy measure matching is provided. Both of the existing methods leverage demonstrations to aid exploration in RL.<br />
<br />
==DQFD==<br />
DQFD [2] puts the demonstrations into a replay memory D and keeps them throughout the Q-learning process. The objective for DQFD is:<br />
\[J_{DQfD}={\hat{\mathbb{E}}}_{D}[(R_t(n)-Q_w(s_t,a_t))^2]+\alpha{\hat{\mathbb{E}}}_{D^E}[(R_t(n)-Q_w(s_t,a_t))^2]\]<br />
The second term can be rewritten as <math> {\hat{\mathbb{E}}}_{D^E}[(R_t(n)-Q_w(s_t,a_t))^2]={\hat{\mathbb{E}}}_{D^E}[(\hat{\rho}_E(s,a)-\rho_{\pi}(s,a))^{2}r^2(s,a)]</math>, which can be regarded as a regularization forcing current policy's occupancy measure to match the expert's empirical occupancy measure, weighted by the potential reward.<br />
<br />
==DDPGfD==<br />
DDPGfD [3] also puts the demonstrations into a replay memory D, but it is based on an actor-critic framework [21]. The objective for DDPGfD is the same as DQFD. Its policy gradient is:<br />
\[\nabla_{\theta}J_{DDPGfD}\approx \mathbb{E}_{s,a}[\nabla_{a}Q_w(s,a)\nabla_{\theta}\pi_{\theta}(s)], a=\pi_{\theta}(s) \]<br />
From this equation, policy is updated relying on learned Q-network <math>Q_w </math>rather than the demonstrations <math>D^{E} </math>. DDPGfD shares the same objective function for <math>Q_w </math> as DQfD, thus they have the same way of leveraging demonstrations, that is the demonstrations in DQfD and DDPGfD induce an occupancy measure matching regularization.<br />
<br />
=Experiments=<br />
<br />
==Goal==<br />
The authors aim at investigating 1) whether POfD can aid exploration by leveraging a few demonstrations, even though the demonstrations are imperfect. 2) whether POfD can succeed and achieve high empirical return, especially in environments where reward signals are sparse and rare. <br />
<br />
==Settings==<br />
The authors conduct the experiments on 8 physical control tasks, ranging from low-dimensional spaces to high-dimensional spaces and naturally sparse environments based on OpenAI Gym [20] and Mujoco (Multi-Joint dynamics with Contact) [5] (Gym is a toolkit for developing and comparing reinforcement learning algorithms. It supports teaching agents everything from walking to playing games like Pong or Pinball. MuJoCo is a physics engine aiming to facilitate research and development in robotics, biomechanics, graphics and animation, and other areas where fast and accurate simulation is needed. In order to get familiar with OpenAI Gym and Mujoco environment, you can watch these videos, respectively: [http://www.mujoco.org/image/home/mujocodemo.mp4 Mujoco], [https://gym.openai.com/v2018-02-21/videos/SpaceInvaders-v0-4184afb3-1223-4ac6-b52b-8e863cbe24a5/original.mp4 OpenAI Gym]). Due to the uniqueness of the environments, the authors introduce 4 ways to sparsify their built-in dense rewards. TYPE1: a reward of +1 is given when the agent reaches the terminal state, and otherwisel 0. TYPE2: a reward of +1 is given when the agent survives for a while. TYPE3: a reward of +1 is given for every time the agent moves forward over a specific number of units in Mujoco environments. TYPE4: specially designed for InvertedDoublePendulum, a reward +1 is given when the second pole stays above a specific height of 0.89. The details are shown in Table 1. Moreover, only one single imperfect trajectory is used as the demonstrations in this paper. The authors collect the demonstrations by training an agent insufficiently by running TRPO (Trust Region Policy Optimization) in the corresponding dense environment. <br />
[[File:pofdt1.png|900px|center]]<br />
<br />
==Baselines==<br />
The authors compare POfD against 5 strong baselines:<br />
* training the policy with TRPO [17] in dense environments, which is called expert <br />
* training the policy with TRPO [17] in sparse environments<br />
* applying GAIL [14] to learn the policy from demonstrations<br />
* DQfD [2]<br />
* DDPGfD [3]<br />
<br />
<br />
1. Trust Region Policy Optimization (TRPO) is an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, a practical algorithm such as this can be developed. This algorithm is similar to natural policy gradient methods and is effective for optimizing neural networks.<br />
<br />
2. Generative Adversarial Imitation Learning (GAIL) is a method to directly extract a policy from data, as if it were obtained by reinforcement learning and by following inverse reinforcement learning.<br />
<br />
3. Deep Q-learning from Demonstrations (DQfD), is a method that leverages small sets of demonstration data to speed up the learning process from relatively small amounts of demonstration data and is able to automatically assess the necessary ratio of demonstration data while learning thanks to a prioritized replay mechanism.<br />
<br />
4. DDPGfD (Deep Deterministic Policy Gradients From Demonstrations) uses prioritized replay to enable efficient propagation of the reward information, which is essential in problems with sparse rewards.<br />
<br />
==Results==<br />
Firstly, the authors test the performance of POfD in sparse control environments with discrete actions. From Table 1, POfD achieves performance comparable with the policy learned under dense environments. From Figure 2, only POfD successes to explore sufficiently and achieves great performance in both sparse environments. TRPO [17] and DQFD [2] fail to explore and GAIL [14] converges to the imperfect demonstration in MountainCar [22].<br />
<br />
[[File:pofdf2.png|500px|center]]<br />
<br />
Then, the authors test the performance of POfD under spares environments with continuous actions space. From Figure 3, POfD achieves expert-level performance in terms of accumulated rewards and surpasses other strong baselines training the policy with TRPO. By watching the learning process of different methods, we can see that TRPO consistently fails to explore the environments when the feedback is sparse, except for HalfCheetah. This may be because there is no terminal state in HalfCheetah, thus a random agent can perform reasonably well as long as the time horizon is sufficiently long. This is shown in Figure3 where the improvement of TRPO begins to show after 400 iterations. DDPGfD and GAIL have common drawback: during training process, they both converge to the imperfect demonstration data. For HalfCheetah, GAIL fails to converge and DDPGfD converges to an even worse point. This situation is expected because the policy and value networks tend to over-fit when having few data, so the training process of GAIL and DDPGfD is severely biased by the imperfect data. Finally, our proposed method can effectively explore the environment with the help of demonstration-based intrinsic reward reshaping, and succeeds consistently across different tasks both in terms of learning stability and convergence speed.<br />
[[File:pofdf3.png|900px|center]]<br />
<br />
The authors also implement a locomotion task <math>Humanoid</math>, which teaches a human-like robot to walk. The state space of dimension is 376, which is very hard to render. As a result, POfD still outperformed all three baselike methods, as they failed to learn policies in such a sparse reward environment.<br />
<br />
The reacher environment is a task that the target is to control a robot arm to touch an object. the location of the object is random for each instantiation. The environment reward is sparse: every time the arm reaches the ball and holds for a while (e.g., 5 time steps), it receives a reward of +1; otherwise it gets zero reward. The authors select 15 random trajectories as demonstration data, and the performance of POfD is much better than the expert, while all other baseline methods failed.<br />
<br />
=Conclusion=<br />
In this paper, a method, POfD, is proposed that can acquire knowledge from a limited amount of imperfect demonstration data to aid exploration in environments with sparse feedback. It is compatible with any policy gradient method. POfD induces implicit dynamic reward shaping and brings provable benefits for policy improvement. Moreover, the experiments results have shown the validity and effectivness of POfD in encouraging the agent to explore around the nearby region of the expert policy and learn better policies. The key contribution is that POfD helps the agent work with few and imperfect demonstrations in an environment with sparse rewards.<br />
<br />
=Critique=<br />
# A novel demonstration-based policy optimization method is proposed. In the process of policy optimization, POfD reshapes the reward function. This new reward function can guide the agent to imitate the expert behaviour when the reward is sparse and explore on its own when the reward value can be obtained, which can take full advantage of the demonstration data and there is no need to ensure that the expert policy is the optimal policy.<br />
# POfD can be combined with any policy gradient methods. Its performance surpasses five strong baselines and can be comparable to the agents trained in the dense-reward environment.<br />
# The paper is structured and the flow of ideas is easy to follow. For related work, the authors clearly explain similarities and differences among these related works.<br />
# This paper's scalability is demonstrated. The experiments environments are ranging from low-dimensional spaces to high-dimensional spaces and from discrete action spaces to continuous actions spaces. For future work, can it be realized in the real world?<br />
# There is a doubt that whether it is a correct method to use the trajectory that was insufficiently learned in dense-reward environment as the imperfect demonstration.<br />
# In this paper, the performance only is judged by the cumulative reward, can other evaluation terms be considered? For example, the convergence rate.<br />
# The performance of this algorithm hinges on the assumption that expert demonstrations are near optimal in the action space. As seen in figure 3, there appears to be an upper bound to performance near (or just above) the expert accuracy -- this may be an indication of a performance ceiling. In games where near-optimal policies can differ greatly (e.g.; offensive or defensive strategies in chess), the success of the model will depend on the selection of expert demonstrations that are closest to a truly optimal policy (i.e.; just because a policy is the current expert, it does not mean it resembles the true optimal policy).<br />
<br />
=References=<br />
[1] Nair, A., McGrew, B., Andrychowicz, M., Zaremba, W., and Abbeel, P. Overcoming exploration in reinforcement learning with demonstrations. arXiv preprint arXiv:1709.10089, 2017.<br />
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[13] Syed, U., Bowling, M., and Schapire, R. E. Apprenticeship learning using linear programming. In Proceedings of the 25th international conference on Machine learning, pp. 1032–1039. ACM, 2008.<br />
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[14] Ho, J. and Ermon, S. Generative adversarial imitation learn- ing. In Advances in Neural Information Processing Sys- tems, pp. 4565–4573, 2016.<br />
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[15] Sutton, R. S. and Barto, A. G. Reinforcement learning: An introduction, volume 1. MIT press Cambridge, 1998.<br />
<br />
[16] Kakade, S. M. A natural policy gradient. In Advances in neural information processing systems, pp. 1531–1538, 2002.<br />
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[17] Schulman, J., Levine, S., Abbeel, P., Jordan, M., and Moritz, P. Trust region policy optimization. In Proceedings of the 32nd International Conference on Machine Learning (ICML-15), pp. 1889–1897, 2015.<br />
<br />
[18] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.<br />
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[19] Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. Generative adversarial nets. In Advances in neural information processing systems, pp. 2672–2680, 2014.<br />
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[20] Brockman, G., Cheung, V., Pettersson, L., Schneider, J., Schulman, J., Tang, J., and Zaremba, W. Openai gym, 2016.<br />
<br />
[21] Lillicrap, T. P., Hunt, J. J., Pritzel, A., Heess, N., Erez, T., Tassa, Y., Silver, D., and Wierstra, D. Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971, 2015.<br />
<br />
[22] Moore, A. W. Efficient memory-based learning for robot control. 1990.<br />
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[23] Zhu, Y., Wang, Z., Merel, J., Rusu, A., Erez, T., Cabi, S., Tunyasuvunakool, S., Kramar, J., Hadsell, R., de Freitas, N., et al. Reinforcement and imitation learning for diverse visuomotor skills. arXiv preprint arXiv:1802.09564, 2018.<br />
<br />
[24] Li, Y., Song, J., and Ermon, S. Infogail: Interpretable imitation learning from visual demonstrations. In Advances in Neural Information Processing Systems, pp. 3815–3825, 2017.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Visual_Reinforcement_Learning_with_Imagined_Goals&diff=41623Visual Reinforcement Learning with Imagined Goals2018-11-27T17:44:15Z<p>Npbhatt: /* Algorithm */ Technical Contribution: Added the base equation from which the rewards are computed.</p>
<hr />
<div>Video and details of this work are available [https://sites.google.com/site/visualrlwithimaginedgoals/ here]<br />
<br />
=Introduction and Motivation=<br />
<br />
Humans are able to accomplish many tasks without any explicit or supervised training, simply by exploring their environment. We are able to set our own goals and learn from our experiences, and thus able to accomplish specific tasks without ever having been trained explicitly for them. It would be ideal if an autonomous agent can also set its own goals and learn from its environment.<br />
<br />
In the paper “Visual Reinforcement Learning with Imagined Goals”, the authors are able to devise such an unsupervised reinforcement learning system. They introduce a system that sets abstract (self-generated) goals and autonomously learns to achieve those goals. They then show that the system can use these autonomously learned skills to perform a variety of user-specified goals, such as pushing objects, grasping objects, and opening doors, without any additional learning. Lastly, they demonstrate that their method is efficient enough to work in the real world on a Sawyer robot. The robot learns to set and achieve goals with only images as the input to the system.<br />
<br />
The algorithm proposed by the authors is summarized below. A Variational Auto Encoder (VAE) on the (left) learns a latent representation of images gathered during training time (center). These latent variables are used to train a policy on imagined goals (center), which can then be used for accomplishing user-specified goals (right).<br />
<br />
[[File: WF_Sec_11Nov25_01.png |center| 800px]]<br />
<br />
=Related Work =<br />
<br />
Many previous works on vision-based deep reinforcement learning for robotics studied a variety of behaviours such as grasping [1], pushing [2], navigation [3], and other manipulation tasks [4]. However, their assumptions on the models limit their suitability for training general-purpose robots. Some previous works such as Levine et al. [11] proposed time-varying models which require episodic setups. There are also other works such as Pinto et al. [12] that proposed an approach using goal images, but it requires instrumented training simulations. Lillicrap et al. [13] uses fully model-free training (Model-based RL uses experience to construct an internal model of the transitions and<br />
immediate outcomes in the environment. Appropriate actions are then chosen by searching or planning in this world model. Model-free RL, on the other hand, uses experience to learn directly one or both of two simpler quantities (state/action values or policies) which can achieve the same optimal behavior but without estimation or use of a world model. Given a policy, a state has a value, defined in terms of the future utility that is expected to accrue starting from that state [https://www.princeton.edu/~yael/Publications/DayanNiv2008.pdf Reinforcement learning: The Good, The Bad and The Ugly].), but does not learn goal-conditioned skills. There are currently no examples that use model-free reinforcement learning for learning policies to train on real-world robotic systems without having ground-truth information.<br />
<br />
In this paper, the authors utilize a goal-conditioned value function to tackle more general tasks through goal relabelling, which improves sample efficiency. Goal relabelling is to retroactively relabel samples in the replay buffer with goals sampled from the latent representation. The paper uses sample random goals from learned latent space to use as replay goals for off-policy Q-learning rather than restricting to states seen along the sampled trajectory as was done in the earlier works. Specifically, they use a model-free Q-learning method that operates on raw state observations and actions. This approach allows for a single transition tuple to be converted into potentially infinite valid training examples. <br />
<br />
Unsupervised learning has been used in a number of prior works to acquire better representations of reinforcement learning. In these methods, the learned representation is used as a substitute for the state for the policy. However, these methods require additional information, such as access to the ground truth reward function based on the true state during training time [5], expert trajectories [6], human demonstrations [7], or pre-trained object-detection features [8]. In contrast, the authors learn to generate goals and use the learned representation to get a reward function for those goals without any of these extra sources of supervision.<br />
<br />
=Goal-Conditioned Reinforcement Learning=<br />
<br />
The ultimate goal in reinforcement learning is to learn a policy <math>\pi</math>, that when given a state <math>s_t</math> and goal <math>g</math> (desired state), can dictate the optimal action <math>a_t</math>. The optimal action <math>a_t</math> is defined as an action which maximizes the expected return denoted by <math>R_t</math> and defined as <math>R_t = \mathbb{E}[\sum_{i = t}^T\gamma^{(i-t)}r_i]</math>, where <math>r_i = r(s_i, a_i, s_{i+1})</math> is the reward for performing action <math>a_i</math> when the current state is <math>s_i</math> and the goal state is <math>s_{i+1}</math> and <math>\gamma</math> is a discount factor which determines the relative importance given to rewards at different times. <br />
<br />
In this paper, goals are not explicitly defined during training. If a goal is not explicitly defined, the agent must be able to generate a set of synthetic goals automatically. Suppose we let an autonomous agent explore an environment with a random policy. After executing each action, start and stop state observations are collected and stored. All state observations are images. For training, the agent can randomly select starting states and goals images from the set of state observations.<br />
<br />
Now given a set of all possible states, a goal, and an initial state, a reinforcement learning framework can be used to find the optimal policy such that a chosen value function is maximized. However, to implement such a framework, a reward function needs to be defined. One choice for the reward is the negative distance between the current state and the goal state, so that maximizing the reward corresponds to minimizing the distance to the goal state.<br />
<br />
[[File:human-giving-goal.png|center|thumb|400px|The task: Make the world look like this image. [9]]]<br />
<br />
In reinforcement learning, a goal-conditioned Q-function can be used to find a single policy to maximize rewards and therefore reach goal states. A goal-conditioned Q-function <math>Q(s,a,g)</math> tells us how good an action <math>a</math> is, given the current state <math>s</math> and goal <math>g</math>. For example, a Q-function tells us, “How good is it to move my hand up (action <math>a</math>), if I’m holding a plate (state <math>s</math>) and want to put the plate on the table (goal <math>g</math>)?” Once this Q-function is trained, a goal-conditioned policy can be obtained by performing the following optimization<br />
<br />
<div align="center"><br />
<math>\pi(s,g) = max_a Q(s,a,g)</math><br />
</div><br />
<br />
which effectively says, “choose the best action according to this Q-function.” By using this procedure, one can obtain a policy that maximizes the sum of rewards, i.e. reaches various goals.<br />
<br />
The reason why Q-learning is popular is that it can be trained in an off-policy manner. Therefore, the only things a Q-function needs are samples of state, action, next state, goal, and reward <math>(s,a,s′,g,r)</math>. This data can be collected by any policy and can be reused across multiples tasks. So a preliminary goal-conditioned Q-learning algorithm looks like this:<br />
<br />
[[File:ql.png|center|600px]]<br />
<br />
From the tuple <math>(s,a,s',g,r)</math>, an approximate Q-function paramaterized by <math>w</math> can be trained by minimizing the Bellman error:<br />
<br />
<div align="center"><br />
<math>\mathcal{E}(w) = \frac{1}{2} || Q_w(s,a,g) -(r + \gamma \max_{a'} Q_{\overline{w}}(s',a',g)) ||^2 </math><br />
</div><br />
<br />
where <math>\overline{w}</math> is treated as some constant.<br />
<br />
The main drawback in this training procedure is collecting data. In theory, one could learn to solve various tasks without even interacting with the world if more data are available. Unfortunately, it is difficult to learn an accurate model of the world, so sampling is usually performed to get state-action-next-state data, (s,a,s′). However, if the reward function <math>r(s,g)</math> can be accessed, one can retroactively relabel goals and recompute rewards. This way, more data can be artificially generated given a single <math>(s,a,s′)</math> tuple. As a result, the training procedure can be modified like so:<br />
<br />
[[File:qlr.png|center|600px]]<br />
<br />
This goal resampling makes it possible to simultaneously learn how to reach multiple goals at once without needing more data from the environment. Thus, this simple modification can result in substantially faster learning. However, the method described above makes two major assumptions: (1) you have access to a reward function and (2) you have access to a goal sampling distribution <math>p(g)</math>. When moving to vision-based tasks where goals are images, both of these assumptions introduce practical concerns.<br />
<br />
For one, a fundamental problem with this reward function is that it assumes that the distance between raw images will yield semantically useful information. But images are noisy and a large amount of information in an image may not be related to the object we analyze. Thus, the distance between two images may not correlate with their semantic distance.<br />
<br />
Second, because the goals are images, a goal image distribution <math>p(g)</math> is needed so that one can sample goal images. Manually designing a distribution over goal images is a non-trivial task and image generation is still an active field of research. It would be ideal if the agent can autonomously imagine its own goals and learn how to reach them.<br />
<br />
=Variational Autoencoder=<br />
An autoencoder is a type of machine learning model that can learn to extract a robust, space-efficient feature vector from an image. This generative model converts high-dimensional observations <math>x</math>, like images, into low-dimensional latent variables <math>z</math>, and vice versa. The model is trained so that the latent variables capture the underlying factors of variation in an image. A current image <math>x</math> and goal image <math>x_g</math> can be converted into latent variables <math>z</math> and <math>z_g</math>, respectively. These latent variables can then be used to represent the state and goal for the reinforcement learning algorithm. Learning Q functions and policies on top of this low-dimensional latent space rather than directly on images results in faster learning.<br />
<br />
[[File:robot-interpreting-scene.png|center|thumb|600px|The agent encodes the current image (<math>x</math>) and goal image (<math>x_g</math>) into a latent space and use distances in that latent space for reward. [9]]]<br />
<br />
Using the latent variable representations for the images and goals also solves the problem of computing rewards. Instead of using pixel-wise error as our reward, the distance in the latent space is used as the reward to train the agent to reach a goal. The paper shows that this corresponds to rewarding reaching states that maximize the probability of the latent goal <math>z_g</math>.<br />
<br />
This generative model is also important because it allows an agent to easily generate goals in the latent space. In particular, the authors design the generative model so that latent variables are sampled from the VAE prior. This sampling mechanism is used for two reasons: First, it provides a mechanism for an agent to set its own goals. The agent simply samples a value for the latent variable from the generative model, and tries to reach that latent goal. Second, this resampling mechanism is also used to relabel goals as mentioned above. Since the VAE prior is trained by real images, meaningful latent goals can be sampled from the latent variable prior. This will help the agent set its own goals and practice towards them if no goal is provided at test time.<br />
<br />
[[File:robot-imagining-goals.png|center|thumb|600px|Even without a human providing a goal, our agent can still generate its own goals, both for exploration and for goal relabeling. [9]]]<br />
<br />
The authors summarize the purpose of the latent variable representation of images as follows: (1) captures the underlying factors of a scene, (2) provides meaningful distances to optimize, and (3) provides an efficient goal sampling mechanism which can be used by the agent to generate its own goals. The overall method is called reinforcement learning with imagined goals (RIG) by the authors.<br />
The process involves starts with collecting data through a simple exploration policy. Possible alternative explorations could be employed here including off-the-shelf exploration bonuses or unsupervised reinforcement learning methods. Then, a VAE latent variable model is trained on state observations and fine-tuned during training. The latent variable model is used for multiple purposes: sampling a latent goal <math>z_g</math> from the model and conditioning the policy on this goal. All states and goals are embedded using the model’s encoder and then used to train the goal-conditioned value function. The authors then resample goals from the prior and compute rewards in the latent space.<br />
<br />
=Algorithm=<br />
[[File:algorithm1.png|center|thumb|600px|]]<br />
<br />
Algorithm 1 is called reinforcement learning with imagined goals (RIG). The data is first collected via a simple exploration policy. The proposed model allows for alternate exploration policies to be used which include off-the-shelf exploration bonuses or unsupervised reinforcement learning methods. Then, the authors train a VAE latent variable model on state observations and finetune it over the course of training. VAE latent space modeling is used to allow the conditioning of policy on the goal which is sampled from the latent model. The VAE model is also used to encode all the goals and the states. When the goal-conditioned value function is trained, the authors resample prior goals and compute rewards in the latent space using the equation <math display="inline"> r(s, g) = - || z - z_g ||_A \propto \sqrt{log(e_{\Phi}(z_g | s))} </math>.<br />
<br />
This equation is derived from the equation below. This is based on the choice to use the negative Mahalanobis distance in the latent space for the reward:<br />
<br />
<math display="inline"> r(s, g) = - || e(s) - e(g) ||_A = - || z - z_g ||_A </math><br />
<br />
=Experiments=<br />
<br />
The authors evaluated their method against some prior algorithms and ablated versions of their approach on a suite of simulated and real-world tasks: Visual Reacher, Visual Pusher, and Visual Multi-Object Pusher. They compared their model with the following prior works: L&R, DSAE, HER, and Oracle. It is concluded that their approach substantially outperforms the previous methods and is close to the state-based "oracle" method in terms of efficiency and performance.<br />
<br />
The figure below shows the performance of different algorithms on this task. This involved a simulated environment with a Sawyer arm. The authors' algorithm was given only visual input, and the available controls were end-effector velocity. The plots show the distance to the goal state as a function of simulation steps. The oracle, as a baseline, was given true object location information, as opposed to visual pixel information.<br />
<br />
[[File:WF_Sec_11Nov_25_02.png|1000px]]<br />
<br />
<br />
They then investigated the effectiveness of distances in the VAE latent space for the Visual Pusher task. They observed that latent distance significantly outperforms the log probability and pixel mean-squared error. The resampling strategies are also varied while fixing other components of the algorithm to study the effect of relabeling strategy. In this experiment, the RIG, which is an equal mixture of the VAE and Future sampling strategies, performs best. Subsequently, learning with variable numbers of objects was studied by evaluating on a task where the environment, based on the Visual Multi-Object Pusher, randomly contains zero, one, or two objects during testing. The results show that their model can tackle this task successfully.<br />
<br />
Finally, the authors tested the RIG in a real-world robot for its ability to reach user-specified positions and push objects to desired locations, as indicated by a goal image. The robot is trained with access only to 84x84 RGB images and without access to joint angles or object positions. The robot first learns by settings its own goals in the latent space and autonomously practices reaching different positions without human involvement. After a reasonable amount of time of training, the robot is given a goal image. Because the robot has practiced reaching so many goals, it is able to reach this goal without additional training:<br />
<br />
[[File:reaching.JPG|center|thumb|600px|(Left) The robot setup is pictured. (Right) Test rollouts of the learned policy.]]<br />
<br />
The method for reaching only needs 10,000 samples and an hour of real-world interactions.<br />
<br />
They also used RIG to train a policy to push objects to target locations:<br />
<br />
[[File:pushing.JPG|center|thumb|600px|The robot pushing setup is<br />
pictured, with frames from test rollouts of the learned policy.]]<br />
<br />
The pushing task is more complicated and the method requires about 25,000 samples. Since the authors do not have the true position during training, so they used test episode returns as the VAE latent distance reward. As learning proceeds, RIG makes steady progress at optimizing the latent distance.<br />
<br />
=Conclusion & Future Work=<br />
<br />
In this paper, a new RL algorithm is proposed to efficiently solve goal-conditioned, vision-based tasks without any ground truth state information or reward functions. The author suggests that one could instead use other representations, such as language and demonstrations, to specify goals. Also, while the paper provides a mechanism to sample goals for autonomous exploration, one can combine the proposed method with existing work by choosing these goals in a more principled way, i.e. a procedure that is not only goal-oriented, but also information seeking or uncertainty aware, to perform even better exploration. Furthermore, combining the idea of this paper with methods from multitask learning and meta-learning is a promising path to create general-purpose agents that can continuously and efficiently acquire skill. Lastly, there are a variety of robot tasks whose state representation would be difficult to capture with sensors, such as manipulating deformable objects or handling scenes with variable number of objects. It is interesting to see whether the RIG can be scaled up to solve these tasks. A new paper [10] was published last week that built on the framework of goal conditioned Reinforcement Learning to extract state representations based on the actions required to reach them, which is abbreviated ARC for actionable representation for control.<br />
<br />
=Critique=<br />
1. This paper is novel because it uses visual data and trains in an unsupervised fashion. The algorithm has no access to a ground truth state or to a pre-defined reward function. It can perform well in a real-world environment with no explicit programming.<br />
<br />
2. From the videos, one major concern is that the output of robotic arm's position is not stable during training and test time. It is likely that the encoder reduces the image features too much so that the images in the latent space are too blury to be used goal images. It would be better if this can be investigated in future. It would be better, if a method is investigated with multiple data sources, and the agent is trained to choose the source which has more complete information. <br />
<br />
3. The algorithm seems to perform better when there is only one object in the images. For example, in Visual Multi-Object Pusher experiment, the relative positions of two pucks do not correspond well with the relative positions of two pucks in goal images. The same situation is also observed in Variable-object experiment. We may guess that the more information contained in an image, the less likely the robot will perform well. This limits the applicability of the current algorithm to solving real-world problems.<br />
<br />
4. The instability mentioned in #2 is even more apparent in the multi-object scenario, and appears to result from the model attempting to optimize on the position of both objects at the same time. Reducing the problem to a sequence of single-object targets may reduce the amount of time the robots spends moving between the multiple objects in the scene (which it currently does quite frequently).<br />
<br />
=References=<br />
1. Lerrel Pinto, Marcin Andrychowicz, Peter Welinder, Wojciech Zaremba, and Pieter Abbeel. Asymmetric<br />
Actor Critic for Image-Based Robot Learning. arXiv preprint arXiv:1710.06542, 2017.<br />
<br />
2. Pulkit Agrawal, Ashvin Nair, Pieter Abbeel, Jitendra Malik, and Sergey Levine. Learning to Poke by<br />
Poking: Experiential Learning of Intuitive Physics. In Advances in Neural Information Processing Systems<br />
(NIPS), 2016.<br />
<br />
3. Deepak Pathak, Parsa Mahmoudieh, Guanghao Luo, Pulkit Agrawal, Dian Chen, Yide Shentu, Evan<br />
Shelhamer, Jitendra Malik, Alexei A Efros, and Trevor Darrell. Zero-Shot Visual Imitation. In International<br />
Conference on Learning Representations (ICLR), 2018.<br />
<br />
4. Timothy P Lillicrap, Jonathan J Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David<br />
Silver, and Daan Wierstra. Continuous control with deep reinforcement learning. In International<br />
Conference on Learning Representations (ICLR), 2016.<br />
<br />
5. Irina Higgins, Arka Pal, Andrei A Rusu, Loic Matthey, Christopher P Burgess, Alexander Pritzel, Matthew<br />
Botvinick, Charles Blundell, and Alexander Lerchner. Darla: Improving zero-shot transfer in reinforcement<br />
learning. International Conference on Machine Learning (ICML), 2017.<br />
<br />
6. Aravind Srinivas, Allan Jabri, Pieter Abbeel, Sergey Levine, and Chelsea Finn. Universal Planning<br />
Networks. In International Conference on Machine Learning (ICML), 2018.<br />
<br />
7. Pierre Sermanet, Corey Lynch, Yevgen Chebotar, Jasmine Hsu, Eric Jang, Stefan Schaal, and Sergey<br />
Levine. Time-contrastive networks: Self-supervised learning from video. arXiv preprint arXiv:1704.06888,<br />
2017.<br />
<br />
8. Alex Lee, Sergey Levine, and Pieter Abbeel. Learning Visual Servoing with Deep Features and Fitted<br />
Q-Iteration. In International Conference on Learning Representations (ICLR), 2017.<br />
<br />
9. Online source: https://bair.berkeley.edu/blog/2018/09/06/rig/<br />
<br />
10. https://arxiv.org/pdf/1811.07819.pdf<br />
<br />
11. Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. End-to-End Training of Deep Visuomotor Policies. Journal of Machine Learning Research (JMLR), 17(1):1334–1373, 2016. ISSN 15337928.<br />
<br />
12. Lerrel Pinto, Marcin Andrychowicz, Peter Welinder, Wojciech Zaremba, and Pieter Abbeel. Asymmetric Actor Critic for Image-Based Robot Learning. arXiv preprint arXiv:1710.06542, 2017.<br />
<br />
13. Timothy P Lillicrap, Jonathan J Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, and Daan Wierstra. Continuous control with deep reinforcement learning. In International Conference on Learning Representations (ICLR), 2016.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Unsupervised_Neural_Machine_Translation&diff=41613Unsupervised Neural Machine Translation2018-11-27T17:30:06Z<p>Npbhatt: Techincal Contribution: added section or related work</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.<br />
<br />
Other authors have recently tried to address this problem using semi-supervised approaches (small set of parallel corpora). 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).<br />
<br />
=== 2.3 LOW-RESOURCE NEURAL MACHINE TRANSLATION ===<br />
<br />
A simple yet effective approach is to create a synthetic parallel corpus by backtranslating 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 backtranslation. 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, backtranslation is necessary. The denoising technique alone is below the baseline while big improvements appear when introducing backtranslation.<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 backtranslation, 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. Specially, the authors points 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"</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Mapping_Images_to_Scene_Graphs_with_Permutation-Invariant_Structured_Prediction&diff=41106Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction2018-11-23T04:10:10Z<p>Npbhatt: /* Related Work */</p>
<hr />
<div>The paper ''Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction'' was written by Roei Herzig* from Tel Aviv University, Moshiko Raboh* from Tel Aviv University, Gal Chechik from Google Brain, Bar-Ilan University, Jonathan Berant from Tel Aviv University, and Amir Globerson from Tel Aviv University. This paper is part of the NIPS 2018 conference to be hosted in December 2018 at Montréal, Canada. This paper summary is based on version 3 of the pre-print (as of May 2018) obtained from [https://arxiv.org/pdf/1802.05451v3.pdf arXiv] <br />
<br />
(*) Equal contribution<br />
<br />
=Motivation=<br />
In the field of artificial intelligence, a major goal is to enable machines to understand complex images, such as the underlying relationships between objects that exist in each scene. Although there are models today that capture both complex labels and interactions between labels, there is a disconnect for what guidelines should be used when leveraging deep learning. This paper introduces a design principle for such models that stem from the concept of permutation invariance and proves state of the art performance on models that follow this principle.<br />
<br />
The primary contributions that this paper makes include:<br />
# Deriving sufficient and necessary conditions for respecting graph-permutation invariance in deep structured prediction architectures<br />
# Empirically proving the benefit of graph-permutation invariance<br />
# Developing a state-of-the-art model for scene graph predictions over a large set of complex visual scenes<br />
<br />
=Introduction=<br />
In order to make a machine to interpret complex visual scenes, it must recognize and understand both objects and relationships between the objects in the scene. A '''scene graph''' is a representation of the set of objects and relations that exist in the scene, where objects are represented as nodes, relations are represented as edges connecting the different nodes. Hence, the prediction of the scene graph is analogous to inferring the joint set of objects and relations of a visual scene.<br />
<br />
[[File:scene_graph_example.png|600px|center]]<br />
<br />
Given that objects in scenes are interdependent on each other, joint prediction of the objects and relations is necessary. The field of structured prediction, which involves the general problem of inferring multiple inter-dependent labels, is of interest for this problem.<br />
<br />
In structured prediction models, a score function <math>s(x, y)</math> is defined to evaluate the compatibility between label <math>y</math> and input <math>x</math>. For instance, when interpreting the scene of an image, <math>x</math> refers to the image itself, and <math>y</math> refers to a complex label, which contains both the objects and the relations between objects. As with most other inference methods, the goal is to find the label <math>y^*</math> such that <math>s(x,y)</math> is maximized, <math> y^*=argmax_y s(x,y)</math>. However, the major concern is that the space for possible label assignments grows exponentially with respect to input size. For example, although an image may seem very simple, the corpus containing possible labels for objects may be very large, rendering it difficult to optimize the scoring function. <br />
<br />
The paper presents an alternative approach, for which input <math>x</math> is mapped to structured output <math>y</math> using a "black box" neural network, omitting the definition of a score function. The main concern for this approach is the determination of the network architecture.<br />
<br />
The model is evaluated by firstly demonstrating the importance of permutation invariance on a synthetic data set. The approach laid out by the authors is then shown to respect permutation invariance, and results are compared to a competitive benchmark. This method achieves state-of-the-art results.<br />
<br />
=Structured prediction=<br />
This paper further considers structured predictions using score-based methods. For structured predictions that follow a score-based approach, a score function <math>s(x, y)</math> is used to measure how compatible label <math>y</math> is for input <math>x</math> and is also used to infer a label by maximizing <math>s(x, y)</math>. To optimize the score function, previous works have decomposed <math>s(x,y) = \sum_i f_i(x,y)</math> in order to facilitate efficient optimization which is done by optimizing the local score function, <math>\max_y f_i(x,y)</math>, with a small subset of the <math>y</math> variables.<br />
<br />
Recently, modeling the <math>f_i </math> functions as deep networks is a new interest. In such area of structured predictions, the most commonly-used score functions include the singleton score function <math>f_i(y_i, x)</math> and pairwise score function <math>f_{ij} (y_i, y_j, x)</math>. Previous works explored a two-stage architectures (learn local scores independently of the structured prediction goal), end-to-end architectures (to include the inference algorithm within the computation graph), and modelling global factors. <br />
<br />
==Advantages of using score-based methods==<br />
# Allow for intuitive specification of local dependencies between labels, and how they map to global dependencies<br />
# Linear score functions offer natural convex surrogates<br />
# Inference in large label space is sometimes possible via exact algorithms or empirically accurate approximations<br />
<br />
The concern for modelling score functions using deep networks is that learning may no longer be convex. Hence, the paper presents properties for how deep networks can be used for structured predictions by considering architectures that do not require explicit maximization of a score function.<br />
<br />
=Background, Notations, and Definitions=<br />
We denote <math>y</math> as a structured label where <math>y = [y_1, \dots, y_n]</math><br />
<br />
'''Score functions:''' for score-based methods, the score is defined as either the sum of a set of singleton scores <math>f_i = f_i(y_i, x)</math> or the sum of pairwise scores <math>f_{ij} = f_{ij}(y_i, y_j, x)</math>.<br />
<br />
Let <math>s(x,y)</math> be the score of a score-based method. Then:<br />
<br />
<div align="center"><br />
<math>s(x,y) = \begin{cases}<br />
\sum_i f_i ~ \text{if we have a set of singleton scores}\\<br />
\sum_{ij} f_{ij} ~ \text{if we have a set of pairwise scores } \\<br />
\end{cases}</math><br />
</div><br />
<br />
'''Inference algorithm:''' an inference algorithm takes input set of local scores (either <math>f_i</math> or <math>f_{ij}</math>) and outputs an assignment of labels <math>y_1, \dots, y_n</math> that maximizes score function <math>s(x,y)</math><br />
<br />
'''Graph labeling function:''' a graph labeling function <math>\mathcal{F} : (V,E) \rightarrow Y</math> is a function that takes input of: an ordered set of node features <math>V = [z_1, \dots, z_n]</math> and an ordered set of edge features <math>E = [z_{1,2},\dots,z_{i,j},\dots,z_{n,n-1}]</math> to output set of node labels <math>\mathbf{y} = [y_1, \dots, y_n]</math>. For instance, <math>z_i</math> can be set equal to <math>f_i</math> and <math>z_{ij}</math> can be set equal to <math>f_{ij}</math>.<br />
<br />
For convenience, the joint set of nodes and edges will be denoted as <math>\mathbf{z}</math> to be a size <math>n^2</math> vector (<math>n</math> nodes and <math>n(n-1)</math> edges).<br />
<br />
'''Permutation:''' Let <math>z</math> be a set of node and edge features. Given a permutation <math>\sigma</math> of <math>\{1,\dots,n\}</math>, let <math>\sigma(z)</math> be a new set of node and edge features given by [<math>\sigma(z)]_i = z_{\sigma(i)}</math> and <math>[\sigma(z)]_{i,j} = z_{\sigma(i), \sigma(j)}</math><br />
<br />
'''One-hot representation:''' <math>\mathbf{1}[j]</math> be a one-hot vector with 1 in the <math>j^{th}</math> coordinate<br />
<br />
=Permutation-Invariant Structured prediction=<br />
<br />
With permutation-invariant structured prediction, we would expect the algorithm to produce the same result given the same score function. For instance, consider the case where we have label space for 3 variables <math>y_1, y_2, y_3</math> with input <math>\mathbf{z} = (f_1, f_2, f_3, f_{12}, f_{13}, f_{23})</math> that outputs label <math>\mathbf{y} = (y_1^*, y_2^*, y_3^*)</math>. Then if the algorithm is run on a permuted version input <math>z' = (f_2, f_1, f_3, f_{21}, f_{23}, f_{13})</math>, we would expect <math>\mathbf{y} = (y_2^*, y_1^*, y_3^*)</math> given the same score function.<br />
<br />
'''Graph permutation invariance (GPI):''' a graph labeling function <math>\mathcal{F}</math> is graph-permutation invariant, if for all permutations <math>\sigma</math> of <math>\{1, \dots, n\}</math> and for all nodes <math>z</math>, <math>\mathcal{F}(\sigma(\mathbf{z})) = \sigma(\mathcal{F}(\mathbf{z}))</math>. Practically speaking, graph permutation means that the same graph is constructed, no matter the order in which elements are predicted. In scene graph generation approaches, Region Proposal Networks are often used as an initial pre-processing step. The results from these (cropped images representing bounding boxes) are then sequentially fed through a respective vertex (or edge) detection network. The idea behind Permutation Invariance is that, no matter the order these are passed in, the final scene graph is identical. In effect, this means not connecting vertices that should not be connected simply because a more promising vertex has not yet been identified. <br />
<br />
The paper presents a theorem on the necessary and sufficient conditions for a function <math>\mathcal{F}</math> to be graph permutation invariant. Intuitively, because <math>\mathcal{F}</math> is a function that takes an ordered set <math>z</math> as input, the output on <math>\mathbf{z}</math> could very well be different from <math>\sigma(\mathbf{z})</math>, which means <math>\mathcal{F}</math> needs to have some sort of symmetry in order to sustain <math>[\mathcal{F}(\sigma(\mathbf{z}))]]_k = [\mathcal{F}(\mathbf{z})]_{\sigma(k)}</math>.<br />
<br />
[[File:graph_permutation_invariance.jpg|400px|center]]<br />
<br />
==Theorem 1==<br />
Let <math>\mathcal{F}</math> be a graph labeling function. Then <math>\mathcal{F}</math> is graph-permutation invariant if and only if there exist functions <math>\alpha, \rho, \phi</math> such that for all <math>k=1, .., n</math>:<br />
\begin{align}<br />
[\mathcal{F}(\mathbf{z})]_k = \rho(\mathbf{z}_k, \sum_{i=1}^n \alpha(\mathbf{z}_i, \sum_{i\neq j} \phi(\mathbf{z}_i, \mathbf{z}_{i,j}, \mathbf{z}_j)))<br />
\end{align}<br />
where <math>\phi: \mathbb{R}^{2d+e} \rightarrow \mathbb{R}^L, \alpha: \mathbb{R}^{d + L} \rightarrow \mathbb{R}^{W}, p: \mathbb{R}^{W+d} \rightarrow \mathbb{R}</math>.<br />
<br />
Notice that for the dimensions of inputs and outputs, <math>d</math> refers to the number of singleton features in <math>z</math> and <math>e</math> refers to the number of edges. <br />
<br />
[[File:GPI_architecture.jpg|thumb|A schematic representation of the GPI architecture. Singleton features <math>z_i</math> are omitted for simplicity. First, the features <math>z_{i,j}</math> are processed element-wise by <math>\phi</math>. Next, they are summed to create a vector <math>s_i</math>, which is concatenated with <math>z_i</math>. Third, a representation of the entire graph is created by applying <math>\alpha\ n</math> times and summing the created vector. The graph representation is then finally processed by <math>\rho</math> together with <math>z_k</math>.|600px|center]]<br />
<br />
==Proof Sketch for Theorem 1==<br />
The proof of this theorem can be found in the paper. A proof sketch is provided below:<br />
<br />
'''For the forward direction''' (function that follows the form set out in equation (1) is GPI):<br />
# Using definition of permutation <math>\sigma</math>, and rewriting <math>[F(z)]_{\sigma(k)}</math> in the form from equation (1)<br />
# Second argument of <math>\rho</math> is invariant under <math>\sigma</math>, since it takes the sum of all indices <math>i</math> and all other indices <math>j \neq i </math>.<br />
<br />
'''For the backward direction''' (any black-box GPI function can be expressed in the form of equation 1):<br />
# Construct <math>\phi, \alpha</math> such that second argument of <math>\rho</math> contains all information about graph features of <math>z</math>, including edges that the features originate from<br />
# Assume each <math>z_k</math> uniquely identifies the node and <math>\mathcal{F}</math> is a function only of pairwise features <math>z_{i,j}</math><br />
# Construct <math>H</math> be a perfect hash function with <math>L</math> buckets, and <math>\phi</math> which maps '''pairwise features''' to a vector of size <math>L</math><br />
# <math>*</math>Construct <math>\phi(z_i, z_{i,j}, z_j) = \mathbf{1}[H(z_j)] z_{i,j}</math>, which intuitively means that <math>\phi</math> stores <math>z_{i,j}</math> in the unique bucket for node <math>j</math><br />
# Construct function <math>\alpha</math> to output a matrix <math>\mathbb{R}^{L \times L}</math> that maps each pairwise feature into unique positions (<math>\alpha(z_i, s_i) = \mathbf{1}[H(z_i)]s_i^T</math>)<br />
# Construct matrix <math>M = \sum_i \alpha(z_i,s_i)</math> by discarding rows/columns in <math>M</math> that do not correspond to original nodes (which reduces dimension to <math>n\times n</math>; set <math>\rho</math> to have same outcome as <math>\mathcal{F}</math>, and set the output of <math>\mathcal{F}</math> on <math>M</math> to be the labels <math>\mathbf{y} = y_1, \dots, y_n</math><br />
<br />
<math>*</math>The paper presents the proof for the edge features <math>z_{ij}</math> being scalar (<math>e = 1</math>) for simplicity, which can be extended easily to vectors with additional indexing.<br />
<br />
Although the results discussed previously apply to complete graphs (edges apply to all feature pairs), it can be easily extended to incomplete graphs. For incomplete graphs, the input to F only contains the features corresponding to valid edges of the graph. The authors are only interested in invariances that preserve the graph structure. Thus, in place of permutation-invariance, it is now an automorphism-invariance.<br />
<br />
==Implications and Applications of Theorem 1==<br />
===Key Implications of Theorem 1===<br />
# Architecture "collects" information from the different edges of the graph, and does so in an invariant fashion using <math>\alpha</math> and <math>\phi</math><br />
# Architecture is parallelizable, since all <math>\phi</math> functions can be applied simultaneously. In contrast, recurrent models (Zellers et al. 2017) are harder to parallelize and are thus practically slower.<br />
<br />
===Some applications of Theorem 1===<br />
# '''Attention:''' the concept of attention can be implemented in the GPI characterization, with slight alterations to the functions <math>\alpha</math> and <math>\phi</math>. In attention each node aggregates features of neighbours through a function of neighbour's relevance. Which means the lable of an entity could depend strongly on its close entity. The complete details can be found in the supplementary materials of the paper.<br />
<br />
# '''RNN:''' recurrent architectures can maintain GPI property, since all GPI function <math>\mathcal{F}</math> are closed under composition. The output of one step after running <math>\mathcal{F}</math> will act as input for the next step, but maintain the GPI property throughout.<br />
<br />
=Related Work=<br />
# '''Architectural invariance:''' suggested recently in a 2017 paper called Deep Sets by Zaheer et al., which considers the case of invariance that is more restrictive.<br />
# '''Deep structured prediction:''' previous work applied deep learning to structured prediction, for instance, semantic segmentation. Some algorithms include message passing algorithms, gradient descent for maximizing score functions, greedy decoding (inference of labels based on time of previous labels). For example, Xu et al. 2017 proposes a novel end-to-end model that generates structured scene representation, and their model solves the scene graph inference problem using standard RNNs and learns to iteratively improves its predictions via message passing. Apart from those algorithms, deep learning has been applied to other graph-based problems such as the Travelling Salesman Problem (Bello et al., 2016; Gilmer et al., 2017; Khalil et al., 2017). However, none of the previous work specifically address the notion of invariance in the general architecture, but rather focus on message passing architectures that can be generalized by this paper.<br />
# '''Scene graph prediction:''' scene graph extraction allows for reasoning, question answering, and image retrieval (Johnson et al., 2015; Lu et al., 2016; Raposo et al., 2017). Some other works in this area include object detection, action recognition, and even detection of human-object interactions (Liao et al., 2016; Plummer et al., 2017). Additional work has been done with the use of message passing algorithms (Xu et al., 2017), word embeddings (Lu et al., 2016), and end-to-end prediction directly from pixels (Newell & Deng, 2017). A notable mention is NeuralMotif (Zellers et al., 2017), which the authors describe as the current state-of-the-art model for scene graph predictions on Visual Genome dataset. It uses an RNN that supplies global context by reading the independent predictions sequentially for each entity and relation and then conducts further refinement on the predictions. The NeuralMotif model has a fixed order in which the RNN reads its inputs and thereby maintains GPI. However, this fixed order is not guaranteed to be optimal.<br />
# '''Burst Image Deblurring Using Permutation Invariant Convolutional Neural Networks:''' similar ideas were applied, where Permutation Invariant CNN, are used to restore sharp and noise-free images from bursts of photographs affected by hand tremor and noise. This presented good quality images with lots of details for challenging datasets.<br />
<br />
=Experimental Results=<br />
<br />
The authors evaluated the advantage of GPI architectures empirically. They first utilized synthetic graph labeling and then used scene-graph classification for mapping images.<br />
<br />
==Synthetic Graph Labeling==<br />
The authors created a synthetic problem to study GPI. This involved using an input graph <math>G = (V,E)</math> where each node <math>i</math> belongs to the set <math>\Gamma(i) \in \{1, \dots, K\}</math> where <math>K</math> is the number of samples. The task is to compute for each node, the number of neighbours that belong to the same set (i.e. finding the label of the node <math>i</math> if <math>y_i = \sum_{j \in N(i)} \mathbf{1}[\Gamma(i) = \Gamma(j)]</math>) . Then, random graphs (each with 10 nodes) were generated by sampling edges, and the set <math>\Gamma(i) \in \{1, \dots, K\}</math>for each node independently and uniformly.<br />
The node features of the graph <math>z_i \in \{0,1\}^K</math> are one-hot vectors of <math>\Gamma(i)</math>, and each pairwise edge feature <math>z_{ij} \in \{0, 1\}</math> denote whether the edge <math>ij</math> is in the edge set <math>E</math>. <br />
3 architectures were studied in this paper:<br />
# '''GPI-architecture for graph prediction''' (without attention and RNN)<br />
# '''LSTM''': replacing <math>\sum \phi(\cdot)</math> and <math>\sum \alpha(\cdot)</math> in the form of Theorem 1 using two LSTMs with state size 200, reading their input in random order<br />
# '''Fully connected feed-forward network''': with 2 hidden layers, each layer containing 1,000 nodes; the input is a concatenation of all nodes and pairwise features, and the output is all node predictions<br />
<br />
The results show that the GPI architecture requires far fewer samples to converge to the correct solution.<br />
[[File:GPI_synthetic_example.jpg|450px|center]]<br />
<br />
This experimental result is meant to demonstrate sample complexity. For fairness, all three models were constructed with a similar number of trainable parameters. The results tie back in with the author's comment that a black-box model which violates permutation invariant structure wastes capacity on learning it at training time. This illustrates the advantage of an architecture with a proper inductive bias.<br />
<br />
==Scene-Graph Classification==<br />
Applying the concept of GPI to Scene-Graph Prediction (SGP) is the main task of this paper. The input to this problem is an image, along with a set of annotated bounding boxes for the entities in the image. The goal is to correctly label each entity within the bounding boxes and the relationship between every pair of entities, resulting in a coherent scene graph.<br />
<br />
The authors describe two different types of variables to predict. The first type is entity variables <math>[y_1, \dots, y_n]</math> for all bounding boxes, where each <math>y_i</math> can take one of L values and refers to objects such as "dog" or "man". The second type is relation variables <math>[y_{n+1}, \cdots, y_{n^2}]</math>, where each <math>y_i</math> represents the relation (e.g. "on", "below") between a pair of bounding boxes (entities).<br />
<br />
The scene graph and contain two types of edges:<br />
# '''Entity-entity edge''': connecting two entities <math>y_i</math> and <math>y_j</math> for <math>1 \leq i \neq j \leq n</math><br />
# '''Entity-relation edges''': connecting every relation variable <math>y_k</math> for <math>k > n</math> to two entities<br />
<br />
The feature set <math>\mathbf{z}</math> is based on the baseline model from Zellers et al. (2017). For entity variables <math>y_i</math>, the vector <math>\mathbf{z}_i \in \mathbb{R}^L</math> models the probability of the entity appearing in <math>y_i</math>. <math>\mathbf{z}_i</math> is augmented by the coordinates of the bounding box. Similarly for relation variables <math>y_j</math>, the vector <math>\mathbf{z}_j \in \mathbb{R}^R</math>, models the probability of the relations between the two entities in <math>j</math>. For entity-entity pairwise features <math>\mathbf{z}_{i,j}</math>, there is a similar representation of the probabilities for the pair. The SGP outputs probability distributions over all entities and relations, which will then be used as input recurrently to maintain GPI. Finally, word embeddings are used and concatenated for the most probable entity-relation labels.<br />
<br />
'''Components of the GPI architecture''' (ent for entity, rel for relation)<br />
# <math>\phi_{ent}</math>: network that integrates two entity variables <math>y_i</math> and <math>y_j</math>, with input <math>z_i, z_j, z_{i,j}</math> and output vector of <math>\mathbb{R}^{n_1}</math> <br />
# <math>\alpha_{ent}</math>: network with inputs from <math>\phi_{ent}</math> for all neighbours of an entity, and uses attention mechanism to output vector <math>\mathbb{R}^{n_2}</math> <br />
# <math>\rho_{ent}</math>: network with inputs from the various <math>\mathbb{R}^{n_2}</math> vectors, and outputs <math>L</math> logits to predict entity value<br />
# <math>\rho_{rel}</math>: network with inputs <math>\alpha_{ent}</math> of two entities and <math>z_{i,j}</math>, and output into <math>R</math> logits<br />
<br />
==Set-up and Results==<br />
'''Dataset''': based on Visual Genome (VG) by (Krishna et al., 2017), which contains a total of 108,077 images annotated with bounding boxes, entities, and relations. An average of 12 entities and 7 relations exist per image. For a fair comparison with previous works, data from (Xu et al., 2017) for train and test splits were used. The authors used the same 150 entities and 50 relations as in (Xu et al., 2017; Newell & Deng, 2017; Zellers et al., 2017). Hyperparameters were tuned using a 70K/5K/32K split for training, validation, and testing respectively.<br />
<br />
'''Training''': all networks were trained using the Adam optimizer, with a batch size of 20. The loss function was the sum of cross-entropy losses over all of entities and relations. Penalties for misclassified entities were 4 times stronger than that of relations. Penalties for misclassified negative relations were 10 times weaker than that of positive relations.<br />
<br />
'''Evaluation''': there are three major tasks when inferring from the scene graph. The authors focus on the following:<br />
# '''SGCIs''': given ground-truth entity bounding boxes, predict all entity and relations categories<br />
# '''PredCIs''': given annotated bounding boxes with entity labels, predict all relations<br />
<br />
The evaluation metric Recall@K (shortened to R@K) is drawn from (Lu et al., 2016). This metric is the fraction of correct ground-truth triplets that appear within the <math>K</math> most confident triplets predicted by the model. Graph-constrained protocol requires the top-<math>K</math> triplets to assign one consistent class per entity and relation. The unconstrained protocol does not enforce such constraint.<br />
<br />
'''Models and baselines''': The authors compared variants of the GPI approach against four baselines, state-of-the-art models on completing scene graph sub-tasks. To maintain consistency, all models used the same training/testing data split, in addition to the preprocessing as per (Xu et al., 2017).<br />
<br />
'''Baselines from existing state-of-the-art models'''<br />
# (Lu et al., 2016): use of word embeddings to fine-tune the likelihood of predicted relations<br />
# (Xu et al., 2017): message passing algorithm between entities and relations to iteratively improve feature map for prediction<br />
# (Newell & Deng, 2017): Pixel2Graph, uses associative embeddings to produce a full graph from image<br />
# (Zellers et al., 2017): NeuralMotif method, encodes global context to capture higher-order motif in scene graphs; Baseline outputs entities and relations distributions without using global context<br />
<br />
'''GPI models'''<br />
# '''GPI with no attention mechanism''': simply following Theorem 1's functional form, with summation over features<br />
# '''GPI NeighborAttention''': same GPI model, but considers attention over neighbours features<br />
# '''GPI Linguistic''': similar to NeighborAttention model, but concatenates word embedding vectors<br />
<br />
'''Key Results''': The GPI Linguistic approach outperforms all baseline for SGCIs, and has similar performance to the state of the art NeuralMotifs method. The authors argue that PredCI is an easier task with less structure, yielding high performance for the existing state of the art models.<br />
<br />
[[File:GPI_table_results.png|700px|center]]<br />
<br />
=Conclusion=<br />
<br />
A deep learning approach was presented in this paper to structured prediction, which constrains the architecture to be invariant to structurally identical inputs. This approach relies on pairwise features which are capable of describing inter-label correlations and inherits the intuitive aspect of score-based approaches. The output produced is invariant to equivalent representation of the pairwise terms. <br />
<br />
As future work, the axiomatic approach can be extended; for example in image labeling, geometric variances such as shifts or rotations may be desired (or in other cases invariance to feature permutations may be desired). Additionally, exploring algorithms that discover symmetries for deep structured prediction when invariant structure is unknown and should be discovered from data is also an interesting extension of this work.<br />
<br />
=Critique=<br />
The paper's contribution comes from the novelty of the permutation invariance as a design guideline for structured prediction. Although not explicitly considered in many of the previous works, the idea of invariance in architecture has already been considered in Deep Sets by (Zaheer et al., 2017). This paper characterizes relaxes the condition on the invariance as compared to that of previous works. In the evaluation of the benefit of GPI models, the paper used a synthetic problem to illustrate the fact that far fewer samples are required for the GPI model to converge to 100% accuracy. However, when comparing the true task of scene graph prediction against the state-of-the-art baselines, the GPI variants had only marginal higher Recall@K scores. The true benefit of this paper's discovery is the avoidance of maximizing a score function (leading computationally difficult problem), and instead directly producing output invariant to how we represent the pairwise terms.<br />
<br />
=References=<br />
<br />
[Lu et al., 2016] Lu, Cewu, Krishna, Ranjay, Bernstein, Michael S., and Li, Fei-Fei. Visual relationship detection with<br />
language priors. In European Conf. Comput. Vision, pp. 852–869, 2016.<br />
<br />
Roei Herzig, Moshiko Raboh, Gal Chechik, Jonathan Berant, Amir Globerson, Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction, 2018.<br />
<br />
Additional resources from Moshiko Raboh's [https://github.com/shikorab/SceneGraph GitHub]</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Mapping_Images_to_Scene_Graphs_with_Permutation-Invariant_Structured_Prediction&diff=41105Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction2018-11-23T04:09:34Z<p>Npbhatt: Technical Contribution: elaborated the neuralmotifs model definition and disadvantage.</p>
<hr />
<div>The paper ''Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction'' was written by Roei Herzig* from Tel Aviv University, Moshiko Raboh* from Tel Aviv University, Gal Chechik from Google Brain, Bar-Ilan University, Jonathan Berant from Tel Aviv University, and Amir Globerson from Tel Aviv University. This paper is part of the NIPS 2018 conference to be hosted in December 2018 at Montréal, Canada. This paper summary is based on version 3 of the pre-print (as of May 2018) obtained from [https://arxiv.org/pdf/1802.05451v3.pdf arXiv] <br />
<br />
(*) Equal contribution<br />
<br />
=Motivation=<br />
In the field of artificial intelligence, a major goal is to enable machines to understand complex images, such as the underlying relationships between objects that exist in each scene. Although there are models today that capture both complex labels and interactions between labels, there is a disconnect for what guidelines should be used when leveraging deep learning. This paper introduces a design principle for such models that stem from the concept of permutation invariance and proves state of the art performance on models that follow this principle.<br />
<br />
The primary contributions that this paper makes include:<br />
# Deriving sufficient and necessary conditions for respecting graph-permutation invariance in deep structured prediction architectures<br />
# Empirically proving the benefit of graph-permutation invariance<br />
# Developing a state-of-the-art model for scene graph predictions over a large set of complex visual scenes<br />
<br />
=Introduction=<br />
In order to make a machine to interpret complex visual scenes, it must recognize and understand both objects and relationships between the objects in the scene. A '''scene graph''' is a representation of the set of objects and relations that exist in the scene, where objects are represented as nodes, relations are represented as edges connecting the different nodes. Hence, the prediction of the scene graph is analogous to inferring the joint set of objects and relations of a visual scene.<br />
<br />
[[File:scene_graph_example.png|600px|center]]<br />
<br />
Given that objects in scenes are interdependent on each other, joint prediction of the objects and relations is necessary. The field of structured prediction, which involves the general problem of inferring multiple inter-dependent labels, is of interest for this problem.<br />
<br />
In structured prediction models, a score function <math>s(x, y)</math> is defined to evaluate the compatibility between label <math>y</math> and input <math>x</math>. For instance, when interpreting the scene of an image, <math>x</math> refers to the image itself, and <math>y</math> refers to a complex label, which contains both the objects and the relations between objects. As with most other inference methods, the goal is to find the label <math>y^*</math> such that <math>s(x,y)</math> is maximized, <math> y^*=argmax_y s(x,y)</math>. However, the major concern is that the space for possible label assignments grows exponentially with respect to input size. For example, although an image may seem very simple, the corpus containing possible labels for objects may be very large, rendering it difficult to optimize the scoring function. <br />
<br />
The paper presents an alternative approach, for which input <math>x</math> is mapped to structured output <math>y</math> using a "black box" neural network, omitting the definition of a score function. The main concern for this approach is the determination of the network architecture.<br />
<br />
The model is evaluated by firstly demonstrating the importance of permutation invariance on a synthetic data set. The approach laid out by the authors is then shown to respect permutation invariance, and results are compared to a competitive benchmark. This method achieves state-of-the-art results.<br />
<br />
=Structured prediction=<br />
This paper further considers structured predictions using score-based methods. For structured predictions that follow a score-based approach, a score function <math>s(x, y)</math> is used to measure how compatible label <math>y</math> is for input <math>x</math> and is also used to infer a label by maximizing <math>s(x, y)</math>. To optimize the score function, previous works have decomposed <math>s(x,y) = \sum_i f_i(x,y)</math> in order to facilitate efficient optimization which is done by optimizing the local score function, <math>\max_y f_i(x,y)</math>, with a small subset of the <math>y</math> variables.<br />
<br />
Recently, modeling the <math>f_i </math> functions as deep networks is a new interest. In such area of structured predictions, the most commonly-used score functions include the singleton score function <math>f_i(y_i, x)</math> and pairwise score function <math>f_{ij} (y_i, y_j, x)</math>. Previous works explored a two-stage architectures (learn local scores independently of the structured prediction goal), end-to-end architectures (to include the inference algorithm within the computation graph), and modelling global factors. <br />
<br />
==Advantages of using score-based methods==<br />
# Allow for intuitive specification of local dependencies between labels, and how they map to global dependencies<br />
# Linear score functions offer natural convex surrogates<br />
# Inference in large label space is sometimes possible via exact algorithms or empirically accurate approximations<br />
<br />
The concern for modelling score functions using deep networks is that learning may no longer be convex. Hence, the paper presents properties for how deep networks can be used for structured predictions by considering architectures that do not require explicit maximization of a score function.<br />
<br />
=Background, Notations, and Definitions=<br />
We denote <math>y</math> as a structured label where <math>y = [y_1, \dots, y_n]</math><br />
<br />
'''Score functions:''' for score-based methods, the score is defined as either the sum of a set of singleton scores <math>f_i = f_i(y_i, x)</math> or the sum of pairwise scores <math>f_{ij} = f_{ij}(y_i, y_j, x)</math>.<br />
<br />
Let <math>s(x,y)</math> be the score of a score-based method. Then:<br />
<br />
<div align="center"><br />
<math>s(x,y) = \begin{cases}<br />
\sum_i f_i ~ \text{if we have a set of singleton scores}\\<br />
\sum_{ij} f_{ij} ~ \text{if we have a set of pairwise scores } \\<br />
\end{cases}</math><br />
</div><br />
<br />
'''Inference algorithm:''' an inference algorithm takes input set of local scores (either <math>f_i</math> or <math>f_{ij}</math>) and outputs an assignment of labels <math>y_1, \dots, y_n</math> that maximizes score function <math>s(x,y)</math><br />
<br />
'''Graph labeling function:''' a graph labeling function <math>\mathcal{F} : (V,E) \rightarrow Y</math> is a function that takes input of: an ordered set of node features <math>V = [z_1, \dots, z_n]</math> and an ordered set of edge features <math>E = [z_{1,2},\dots,z_{i,j},\dots,z_{n,n-1}]</math> to output set of node labels <math>\mathbf{y} = [y_1, \dots, y_n]</math>. For instance, <math>z_i</math> can be set equal to <math>f_i</math> and <math>z_{ij}</math> can be set equal to <math>f_{ij}</math>.<br />
<br />
For convenience, the joint set of nodes and edges will be denoted as <math>\mathbf{z}</math> to be a size <math>n^2</math> vector (<math>n</math> nodes and <math>n(n-1)</math> edges).<br />
<br />
'''Permutation:''' Let <math>z</math> be a set of node and edge features. Given a permutation <math>\sigma</math> of <math>\{1,\dots,n\}</math>, let <math>\sigma(z)</math> be a new set of node and edge features given by [<math>\sigma(z)]_i = z_{\sigma(i)}</math> and <math>[\sigma(z)]_{i,j} = z_{\sigma(i), \sigma(j)}</math><br />
<br />
'''One-hot representation:''' <math>\mathbf{1}[j]</math> be a one-hot vector with 1 in the <math>j^{th}</math> coordinate<br />
<br />
=Permutation-Invariant Structured prediction=<br />
<br />
With permutation-invariant structured prediction, we would expect the algorithm to produce the same result given the same score function. For instance, consider the case where we have label space for 3 variables <math>y_1, y_2, y_3</math> with input <math>\mathbf{z} = (f_1, f_2, f_3, f_{12}, f_{13}, f_{23})</math> that outputs label <math>\mathbf{y} = (y_1^*, y_2^*, y_3^*)</math>. Then if the algorithm is run on a permuted version input <math>z' = (f_2, f_1, f_3, f_{21}, f_{23}, f_{13})</math>, we would expect <math>\mathbf{y} = (y_2^*, y_1^*, y_3^*)</math> given the same score function.<br />
<br />
'''Graph permutation invariance (GPI):''' a graph labeling function <math>\mathcal{F}</math> is graph-permutation invariant, if for all permutations <math>\sigma</math> of <math>\{1, \dots, n\}</math> and for all nodes <math>z</math>, <math>\mathcal{F}(\sigma(\mathbf{z})) = \sigma(\mathcal{F}(\mathbf{z}))</math>. Practically speaking, graph permutation means that the same graph is constructed, no matter the order in which elements are predicted. In scene graph generation approaches, Region Proposal Networks are often used as an initial pre-processing step. The results from these (cropped images representing bounding boxes) are then sequentially fed through a respective vertex (or edge) detection network. The idea behind Permutation Invariance is that, no matter the order these are passed in, the final scene graph is identical. In effect, this means not connecting vertices that should not be connected simply because a more promising vertex has not yet been identified. <br />
<br />
The paper presents a theorem on the necessary and sufficient conditions for a function <math>\mathcal{F}</math> to be graph permutation invariant. Intuitively, because <math>\mathcal{F}</math> is a function that takes an ordered set <math>z</math> as input, the output on <math>\mathbf{z}</math> could very well be different from <math>\sigma(\mathbf{z})</math>, which means <math>\mathcal{F}</math> needs to have some sort of symmetry in order to sustain <math>[\mathcal{F}(\sigma(\mathbf{z}))]]_k = [\mathcal{F}(\mathbf{z})]_{\sigma(k)}</math>.<br />
<br />
[[File:graph_permutation_invariance.jpg|400px|center]]<br />
<br />
==Theorem 1==<br />
Let <math>\mathcal{F}</math> be a graph labeling function. Then <math>\mathcal{F}</math> is graph-permutation invariant if and only if there exist functions <math>\alpha, \rho, \phi</math> such that for all <math>k=1, .., n</math>:<br />
\begin{align}<br />
[\mathcal{F}(\mathbf{z})]_k = \rho(\mathbf{z}_k, \sum_{i=1}^n \alpha(\mathbf{z}_i, \sum_{i\neq j} \phi(\mathbf{z}_i, \mathbf{z}_{i,j}, \mathbf{z}_j)))<br />
\end{align}<br />
where <math>\phi: \mathbb{R}^{2d+e} \rightarrow \mathbb{R}^L, \alpha: \mathbb{R}^{d + L} \rightarrow \mathbb{R}^{W}, p: \mathbb{R}^{W+d} \rightarrow \mathbb{R}</math>.<br />
<br />
Notice that for the dimensions of inputs and outputs, <math>d</math> refers to the number of singleton features in <math>z</math> and <math>e</math> refers to the number of edges. <br />
<br />
[[File:GPI_architecture.jpg|thumb|A schematic representation of the GPI architecture. Singleton features <math>z_i</math> are omitted for simplicity. First, the features <math>z_{i,j}</math> are processed element-wise by <math>\phi</math>. Next, they are summed to create a vector <math>s_i</math>, which is concatenated with <math>z_i</math>. Third, a representation of the entire graph is created by applying <math>\alpha\ n</math> times and summing the created vector. The graph representation is then finally processed by <math>\rho</math> together with <math>z_k</math>.|600px|center]]<br />
<br />
==Proof Sketch for Theorem 1==<br />
The proof of this theorem can be found in the paper. A proof sketch is provided below:<br />
<br />
'''For the forward direction''' (function that follows the form set out in equation (1) is GPI):<br />
# Using definition of permutation <math>\sigma</math>, and rewriting <math>[F(z)]_{\sigma(k)}</math> in the form from equation (1)<br />
# Second argument of <math>\rho</math> is invariant under <math>\sigma</math>, since it takes the sum of all indices <math>i</math> and all other indices <math>j \neq i </math>.<br />
<br />
'''For the backward direction''' (any black-box GPI function can be expressed in the form of equation 1):<br />
# Construct <math>\phi, \alpha</math> such that second argument of <math>\rho</math> contains all information about graph features of <math>z</math>, including edges that the features originate from<br />
# Assume each <math>z_k</math> uniquely identifies the node and <math>\mathcal{F}</math> is a function only of pairwise features <math>z_{i,j}</math><br />
# Construct <math>H</math> be a perfect hash function with <math>L</math> buckets, and <math>\phi</math> which maps '''pairwise features''' to a vector of size <math>L</math><br />
# <math>*</math>Construct <math>\phi(z_i, z_{i,j}, z_j) = \mathbf{1}[H(z_j)] z_{i,j}</math>, which intuitively means that <math>\phi</math> stores <math>z_{i,j}</math> in the unique bucket for node <math>j</math><br />
# Construct function <math>\alpha</math> to output a matrix <math>\mathbb{R}^{L \times L}</math> that maps each pairwise feature into unique positions (<math>\alpha(z_i, s_i) = \mathbf{1}[H(z_i)]s_i^T</math>)<br />
# Construct matrix <math>M = \sum_i \alpha(z_i,s_i)</math> by discarding rows/columns in <math>M</math> that do not correspond to original nodes (which reduces dimension to <math>n\times n</math>; set <math>\rho</math> to have same outcome as <math>\mathcal{F}</math>, and set the output of <math>\mathcal{F}</math> on <math>M</math> to be the labels <math>\mathbf{y} = y_1, \dots, y_n</math><br />
<br />
<math>*</math>The paper presents the proof for the edge features <math>z_{ij}</math> being scalar (<math>e = 1</math>) for simplicity, which can be extended easily to vectors with additional indexing.<br />
<br />
Although the results discussed previously apply to complete graphs (edges apply to all feature pairs), it can be easily extended to incomplete graphs. For incomplete graphs, the input to F only contains the features corresponding to valid edges of the graph. The authors are only interested in invariances that preserve the graph structure. Thus, in place of permutation-invariance, it is now an automorphism-invariance.<br />
<br />
==Implications and Applications of Theorem 1==<br />
===Key Implications of Theorem 1===<br />
# Architecture "collects" information from the different edges of the graph, and does so in an invariant fashion using <math>\alpha</math> and <math>\phi</math><br />
# Architecture is parallelizable, since all <math>\phi</math> functions can be applied simultaneously. In contrast, recurrent models (Zellers et al. 2017) are harder to parallelize and are thus practically slower.<br />
<br />
===Some applications of Theorem 1===<br />
# '''Attention:''' the concept of attention can be implemented in the GPI characterization, with slight alterations to the functions <math>\alpha</math> and <math>\phi</math>. In attention each node aggregates features of neighbours through a function of neighbour's relevance. Which means the lable of an entity could depend strongly on its close entity. The complete details can be found in the supplementary materials of the paper.<br />
<br />
# '''RNN:''' recurrent architectures can maintain GPI property, since all GPI function <math>\mathcal{F}</math> are closed under composition. The output of one step after running <math>\mathcal{F}</math> will act as input for the next step, but maintain the GPI property throughout.<br />
<br />
=Related Work=<br />
# '''Architectural invariance:''' suggested recently in a 2017 paper called Deep Sets by Zaheer et al., which considers the case of invariance that is more restrictive.<br />
# '''Deep structured prediction:''' previous work applied deep learning to structured prediction, for instance, semantic segmentation. Some algorithms include message passing algorithms, gradient descent for maximizing score functions, greedy decoding (inference of labels based on time of previous labels). For example, Xu et al. 2017 proposes a novel end-to-end model that generates structured scene representation, and their model solves the scene graph inference problem using standard RNNs and learns to iteratively improves its predictions via message passing. Apart from those algorithms, deep learning has been applied to other graph-based problems such as the Travelling Salesman Problem (Bello et al., 2016; Gilmer et al., 2017; Khalil et al., 2017). However, none of the previous work specifically address the notion of invariance in the general architecture, but rather focus on message passing architectures that can be generalized by this paper.<br />
# '''Scene graph prediction:''' scene graph extraction allows for reasoning, question answering, and image retrieval (Johnson et al., 2015; Lu et al., 2016; Raposo et al., 2017). Some other works in this area include object detection, action recognition, and even detection of human-object interactions (Liao et al., 2016; Plummer et al., 2017). Additional work has been done with the use of message passing algorithms (Xu et al., 2017), word embeddings (Lu et al., 2016), and end-to-end prediction directly from pixels (Newell & Deng, 2017). A notable mention is NeuralMotif (Zellers et al., 2017), which the authors describe as the current state-of-the-art model for scene graph predictions on Visual Genome dataset. It uses an RNN that supplies global context by reading the independent predictions sequentially for each entity and relation and then conducts further refinement on the predictions. The NeuralMotif has a fixed order in which the RNN reads its inputs and thereby maintains GPI. However, this fixed order is not guaranteed to be optimal.<br />
# '''Burst Image Deblurring Using Permutation Invariant Convolutional Neural Networks:''' similar ideas were applied, where Permutation Invariant CNN, are used to restore sharp and noise-free images from bursts of photographs affected by hand tremor and noise. This presented good quality images with lots of details for challenging datasets.<br />
<br />
=Experimental Results=<br />
<br />
The authors evaluated the advantage of GPI architectures empirically. They first utilized synthetic graph labeling and then used scene-graph classification for mapping images.<br />
<br />
==Synthetic Graph Labeling==<br />
The authors created a synthetic problem to study GPI. This involved using an input graph <math>G = (V,E)</math> where each node <math>i</math> belongs to the set <math>\Gamma(i) \in \{1, \dots, K\}</math> where <math>K</math> is the number of samples. The task is to compute for each node, the number of neighbours that belong to the same set (i.e. finding the label of the node <math>i</math> if <math>y_i = \sum_{j \in N(i)} \mathbf{1}[\Gamma(i) = \Gamma(j)]</math>) . Then, random graphs (each with 10 nodes) were generated by sampling edges, and the set <math>\Gamma(i) \in \{1, \dots, K\}</math>for each node independently and uniformly.<br />
The node features of the graph <math>z_i \in \{0,1\}^K</math> are one-hot vectors of <math>\Gamma(i)</math>, and each pairwise edge feature <math>z_{ij} \in \{0, 1\}</math> denote whether the edge <math>ij</math> is in the edge set <math>E</math>. <br />
3 architectures were studied in this paper:<br />
# '''GPI-architecture for graph prediction''' (without attention and RNN)<br />
# '''LSTM''': replacing <math>\sum \phi(\cdot)</math> and <math>\sum \alpha(\cdot)</math> in the form of Theorem 1 using two LSTMs with state size 200, reading their input in random order<br />
# '''Fully connected feed-forward network''': with 2 hidden layers, each layer containing 1,000 nodes; the input is a concatenation of all nodes and pairwise features, and the output is all node predictions<br />
<br />
The results show that the GPI architecture requires far fewer samples to converge to the correct solution.<br />
[[File:GPI_synthetic_example.jpg|450px|center]]<br />
<br />
This experimental result is meant to demonstrate sample complexity. For fairness, all three models were constructed with a similar number of trainable parameters. The results tie back in with the author's comment that a black-box model which violates permutation invariant structure wastes capacity on learning it at training time. This illustrates the advantage of an architecture with a proper inductive bias.<br />
<br />
==Scene-Graph Classification==<br />
Applying the concept of GPI to Scene-Graph Prediction (SGP) is the main task of this paper. The input to this problem is an image, along with a set of annotated bounding boxes for the entities in the image. The goal is to correctly label each entity within the bounding boxes and the relationship between every pair of entities, resulting in a coherent scene graph.<br />
<br />
The authors describe two different types of variables to predict. The first type is entity variables <math>[y_1, \dots, y_n]</math> for all bounding boxes, where each <math>y_i</math> can take one of L values and refers to objects such as "dog" or "man". The second type is relation variables <math>[y_{n+1}, \cdots, y_{n^2}]</math>, where each <math>y_i</math> represents the relation (e.g. "on", "below") between a pair of bounding boxes (entities).<br />
<br />
The scene graph and contain two types of edges:<br />
# '''Entity-entity edge''': connecting two entities <math>y_i</math> and <math>y_j</math> for <math>1 \leq i \neq j \leq n</math><br />
# '''Entity-relation edges''': connecting every relation variable <math>y_k</math> for <math>k > n</math> to two entities<br />
<br />
The feature set <math>\mathbf{z}</math> is based on the baseline model from Zellers et al. (2017). For entity variables <math>y_i</math>, the vector <math>\mathbf{z}_i \in \mathbb{R}^L</math> models the probability of the entity appearing in <math>y_i</math>. <math>\mathbf{z}_i</math> is augmented by the coordinates of the bounding box. Similarly for relation variables <math>y_j</math>, the vector <math>\mathbf{z}_j \in \mathbb{R}^R</math>, models the probability of the relations between the two entities in <math>j</math>. For entity-entity pairwise features <math>\mathbf{z}_{i,j}</math>, there is a similar representation of the probabilities for the pair. The SGP outputs probability distributions over all entities and relations, which will then be used as input recurrently to maintain GPI. Finally, word embeddings are used and concatenated for the most probable entity-relation labels.<br />
<br />
'''Components of the GPI architecture''' (ent for entity, rel for relation)<br />
# <math>\phi_{ent}</math>: network that integrates two entity variables <math>y_i</math> and <math>y_j</math>, with input <math>z_i, z_j, z_{i,j}</math> and output vector of <math>\mathbb{R}^{n_1}</math> <br />
# <math>\alpha_{ent}</math>: network with inputs from <math>\phi_{ent}</math> for all neighbours of an entity, and uses attention mechanism to output vector <math>\mathbb{R}^{n_2}</math> <br />
# <math>\rho_{ent}</math>: network with inputs from the various <math>\mathbb{R}^{n_2}</math> vectors, and outputs <math>L</math> logits to predict entity value<br />
# <math>\rho_{rel}</math>: network with inputs <math>\alpha_{ent}</math> of two entities and <math>z_{i,j}</math>, and output into <math>R</math> logits<br />
<br />
==Set-up and Results==<br />
'''Dataset''': based on Visual Genome (VG) by (Krishna et al., 2017), which contains a total of 108,077 images annotated with bounding boxes, entities, and relations. An average of 12 entities and 7 relations exist per image. For a fair comparison with previous works, data from (Xu et al., 2017) for train and test splits were used. The authors used the same 150 entities and 50 relations as in (Xu et al., 2017; Newell & Deng, 2017; Zellers et al., 2017). Hyperparameters were tuned using a 70K/5K/32K split for training, validation, and testing respectively.<br />
<br />
'''Training''': all networks were trained using the Adam optimizer, with a batch size of 20. The loss function was the sum of cross-entropy losses over all of entities and relations. Penalties for misclassified entities were 4 times stronger than that of relations. Penalties for misclassified negative relations were 10 times weaker than that of positive relations.<br />
<br />
'''Evaluation''': there are three major tasks when inferring from the scene graph. The authors focus on the following:<br />
# '''SGCIs''': given ground-truth entity bounding boxes, predict all entity and relations categories<br />
# '''PredCIs''': given annotated bounding boxes with entity labels, predict all relations<br />
<br />
The evaluation metric Recall@K (shortened to R@K) is drawn from (Lu et al., 2016). This metric is the fraction of correct ground-truth triplets that appear within the <math>K</math> most confident triplets predicted by the model. Graph-constrained protocol requires the top-<math>K</math> triplets to assign one consistent class per entity and relation. The unconstrained protocol does not enforce such constraint.<br />
<br />
'''Models and baselines''': The authors compared variants of the GPI approach against four baselines, state-of-the-art models on completing scene graph sub-tasks. To maintain consistency, all models used the same training/testing data split, in addition to the preprocessing as per (Xu et al., 2017).<br />
<br />
'''Baselines from existing state-of-the-art models'''<br />
# (Lu et al., 2016): use of word embeddings to fine-tune the likelihood of predicted relations<br />
# (Xu et al., 2017): message passing algorithm between entities and relations to iteratively improve feature map for prediction<br />
# (Newell & Deng, 2017): Pixel2Graph, uses associative embeddings to produce a full graph from image<br />
# (Zellers et al., 2017): NeuralMotif method, encodes global context to capture higher-order motif in scene graphs; Baseline outputs entities and relations distributions without using global context<br />
<br />
'''GPI models'''<br />
# '''GPI with no attention mechanism''': simply following Theorem 1's functional form, with summation over features<br />
# '''GPI NeighborAttention''': same GPI model, but considers attention over neighbours features<br />
# '''GPI Linguistic''': similar to NeighborAttention model, but concatenates word embedding vectors<br />
<br />
'''Key Results''': The GPI Linguistic approach outperforms all baseline for SGCIs, and has similar performance to the state of the art NeuralMotifs method. The authors argue that PredCI is an easier task with less structure, yielding high performance for the existing state of the art models.<br />
<br />
[[File:GPI_table_results.png|700px|center]]<br />
<br />
=Conclusion=<br />
<br />
A deep learning approach was presented in this paper to structured prediction, which constrains the architecture to be invariant to structurally identical inputs. This approach relies on pairwise features which are capable of describing inter-label correlations and inherits the intuitive aspect of score-based approaches. The output produced is invariant to equivalent representation of the pairwise terms. <br />
<br />
As future work, the axiomatic approach can be extended; for example in image labeling, geometric variances such as shifts or rotations may be desired (or in other cases invariance to feature permutations may be desired). Additionally, exploring algorithms that discover symmetries for deep structured prediction when invariant structure is unknown and should be discovered from data is also an interesting extension of this work.<br />
<br />
=Critique=<br />
The paper's contribution comes from the novelty of the permutation invariance as a design guideline for structured prediction. Although not explicitly considered in many of the previous works, the idea of invariance in architecture has already been considered in Deep Sets by (Zaheer et al., 2017). This paper characterizes relaxes the condition on the invariance as compared to that of previous works. In the evaluation of the benefit of GPI models, the paper used a synthetic problem to illustrate the fact that far fewer samples are required for the GPI model to converge to 100% accuracy. However, when comparing the true task of scene graph prediction against the state-of-the-art baselines, the GPI variants had only marginal higher Recall@K scores. The true benefit of this paper's discovery is the avoidance of maximizing a score function (leading computationally difficult problem), and instead directly producing output invariant to how we represent the pairwise terms.<br />
<br />
=References=<br />
<br />
[Lu et al., 2016] Lu, Cewu, Krishna, Ranjay, Bernstein, Michael S., and Li, Fei-Fei. Visual relationship detection with<br />
language priors. In European Conf. Comput. Vision, pp. 852–869, 2016.<br />
<br />
Roei Herzig, Moshiko Raboh, Gal Chechik, Jonathan Berant, Amir Globerson, Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction, 2018.<br />
<br />
Additional resources from Moshiko Raboh's [https://github.com/shikorab/SceneGraph GitHub]</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Learning_to_Navigate_in_Cities_Without_a_Map&diff=41101Learning to Navigate in Cities Without a Map2018-11-23T03:55:14Z<p>Npbhatt: /* Related Work */ Technical Contribution: Added another relevant related work on recent efforts on improving simulation to resemble reality.</p>
<hr />
<div>Paper: <br />
[https://arxiv.org/pdf/1804.00168.pdf Learning to Navigate in Cities Without a Map]<br />
A video of the paper is available [https://sites.google.com/view/streetlearn here].<br />
<br />
== Introduction ==<br />
Navigation is an attractive topic in many research disciplines and technology related domains such as neuroscience and robotics. The majority of algorithms are based on the following steps.<br />
<br />
1. Building an explicit map<br />
<br />
2. Planning and acting using that map. <br />
<br />
In this article, based on this fact that human can learn to navigate through cities without using any special tool such as maps or GPS, authors propose new methods to show that a neural network agent can do the same thing by using visual observations. To do so, an interactive environment using Google StreetView Images and a dual pathway agent architecture is designed. As shown in figure 1, some parts of the environment are built using Google StreetView images of New York City (Times Square, Central Park) and London (St. Paul’s Cathedral). The green cone represents the agent’s location and orientation. Although learning to navigate using visual aids is shown to be successful in some domains such as games and simulated environments using deep reinforcement learning (RL), it suffers from data inefficiency and sensitivity to changes in the environment. Thus, it is unclear whether this method could be used for large-scale navigation. That’s why it became the subject of investigation in this paper.<br />
[[File:figure1-soroush.png|600px|thumb|center|Figure 1. Our environment is built of real-world places from StreetView. The figure shows diverse views and corresponding local maps (neither map nor current position have not been used by the agent) in New York City (Times Square, Central Park) and London (St. Paul’s Cathedral). The green cone represents the agent’s location and orientation.]]<br />
<br />
==Contribution==<br />
This paper has made the following contributions:<br />
<br />
1. Designing a dual pathway agent architecture. This agent can navigate through a real city and is trained with end-to-end reinforcement learning to handle real-world navigations.<br />
<br />
2. Using Goal-dependent learning. This means that the policy and value functions must adapt themselves to a sequence of goals that are provided as input.<br />
<br />
3. Leveraging a recurrent neural architecture. Using that, not only could navigation through a city be possible, but also the model is scalable for navigation in new cities. This architecture supports both locale-specific learnings and general transferable navigations. The authors achieved these by separating a recurrent neural pathway. This pathway receives and interprets the current goal as well as encapsulates and memorizes features of a single region.<br />
<br />
4. Using a new environment which is built on top of Google StreetView images. This provides real-world images for agent’s observation. Using this environment, the agent can navigate from an arbitrary starting point to a goal and then to another goal etc. Also, London, Paris, and New York City are chosen for navigation.<br />
<br />
==Related Work==<br />
<br />
1. Localization from real-world imagery. For example, (Weyand et al., 2016), a CNN was able to achieve excellent results on geolocation task. This paper provides novel work by not including supervised training with ground-truth labels, and by including planning as a goal. Some other works also improve by exploiting spatiotemporal continuity or estimating camera pose or depth estimation from pixels. These methods rely on supervised training with ground truth labels, which is not possible in every environment. <br />
<br />
2. Deep RL methods for navigation. For instance, (Mirowski et al., 2016; Jaderberg et al., 2016) used self-supervised auxiliary tasks to produce visual navigation in several created mazes. Some other researches used text descriptions to incorporate goal instructions. Researchers developed realistic, higher-fidelity environment simulations to make the experiment more realistic, but that still came with lack of diversities. This paper makes use of real-world data, in contrast to many related papers in this area. It's diverse and visually realistic but still, it does not contain dynamic elements, and the street topology cannot be regenerated or altered.<br />
<br />
3. Deep RL for path planning and mapping. For example, (Zhang et al., 2017) created an agent that represented a global map via an RL agent with external memory; some other work uses a hierarchical control strategy to propose a structured memory and Memory Augmented Control Maps. Explicit neural mapper and navigation planner with joint training was also used. Among all these works, the target-driven visual navigation with a goal-conditional policy approach was most related to our method.<br />
<br />
4. To make simulations resemble reality, researchers have developed higher-fidelity simulated environments (Dosovitskiy et al., 2017; Kolve et al., 2017; Shah et al., 2018; Wu et al., 2018). However, in spite of the photo-realism, the inherent problems of simulated environments pertain to the limited diversity of the environments and the idealistic cleanliness of the observations.<br />
<br />
==Environment==<br />
Google StreetView consists of both high-resolution 360-degree imagery and graph connectivity. Also, it provides a public API. These features make it a valuable resource. In this work, large areas of New York, Paris, and London that contain between 7,000 and 65,500 nodes<br />
(and between 7,200 and 128,600 edges, respectively), have a mean node spacing of 10m and cover a range of up to<br />
5km chosen (Figure 2), without simplifying the underlying connections. This means that there are many areas 'congested' with nodes, occlusions, available footpaths, etc. The agent only sees RGB images that are visible in StreetView images (Figure 1) and is not aware of the underlying graph.<br />
<br />
[[File:figure2-soroush.png|700px|thumb|center|Figure 2. Map of the 5 environments in New York City; our experiments focus on the NYU area as well as on transfer learning from the other areas to Wall Street (see Section 5.3). In the zoomed in area, each green dot corresponds to a unique panorama, the goal is marked in blue, and landmark locations are marked with red pins.]]<br />
<br />
==Agent Interface and the Courier Task==<br />
In an RL environment, we need to define observations and actions in addition to tasks. The inputs to the agent are the image <math>x_t</math> and the goal <math>g_t</math>. Also, a first-person view of the 3D environment is simulated by cropping <math>x_t</math> to a 60-degree square RGB image that is scaled to 84*84 pixels. Furthermore, the action space consists of 5 movements: “slow” rotate left or right (±22:5), “fast” rotate left or right (±67.5), or move forward (implemented as a ''noop'' in the case where this is not a viable action). The most central edge is chosen if there are multiple edges in the agents viewing cone.<br />
<br />
There are lots of ways to specify the goal to the agent. In this paper, the current goal is chosen to be represented in terms of its proximity to a set L of fixed landmarks <math> L={(Lat_k, Long_k)}</math> which are specified using Latitude and Longitude coordinate system. For distance to the <math> k_{th}</math> landmark <math>{(d_{(t,k)}^g})_k</math> the goal vector contains <math> g_{(t,i)}=\tfrac{exp(-αd_{(t,i)}^g)}{∑_k exp(-αd_{(t,k)}^g)} </math>for <math>i_{th}</math> landmark with <math>α=0.002</math> (Figure 3).<br />
<br />
[[File:figure3-soroush.PNG|400px|thumb|center|Figure 3. We illustrate the goal description by showing a goal and a set of 5 landmarks that are nearby, plus 4 that are more distant. The code <math>g_i</math> is a vector with a softmax-normalised distance to each landmark.]]<br />
<br />
This form of representation has several advantages: <br />
<br />
1. It could easily be extended to new environments.<br />
<br />
2. It is intuitive. Even humans and animals use landmarks to be able to move from one place to another.<br />
<br />
3. It does not rely on arbitrary map coordinates, and provides an absolute (as opposed to relative) goal.<br />
<br />
In this work, 644 landmarks for New York, Paris, and London are manually defined. The courier task is the problem of navigating to a list of random locations within a city. In each episode, which consists of 1000 steps, the agent starts from a random place with random orientation. when an agent gets within 100 meters of goal, the next goal is randomly chosen. An episode ends after 1000 agent steps. Finally, the reward is proportional to the shortest path between agent and goal when the goal is first assigned (providing more reward for longer journeys). Thus the agent needs to learn the mapping between the images observed at the goal location and the goal vector in order to solve the courier task problem. Furthermore, the agent must learn the association between the images observed at its current location and the policy to reach the goal destination.<br />
<br />
==Methods==<br />
<br />
===Goal-dependent Actor-Critic Reinforcement Learning===<br />
In this paper, the learning problem is based on Markov Decision Process, with state space <math>\mathcal{S}</math>, action space <math>\mathcal{A}</math>, environment <math>\mathcal{E}</math>, and a set of possible goals <math>\mathcal{G}</math>. The reward function depends on the current goal and state: <math>\mathcal{R}: \mathcal{S} \times \mathcal{G} \times \mathcal{A} &rarr; \mathbb{R}</math>. Typically, in reinforcement learning the main goal is to find the policy which maximizes the expected return. Expected return is defined as the sum of<br />
discounted rewards starting from state <math>s_0</math> with discount <math>\gamma</math>. Also, the expected return from a state <math>s_t</math> depends on the goals that are sampled. The policy is defined as a distribution over the actions, given the current state <math>s_t</math> and the goal <math>g_t</math>: <br />
<br />
\begin{align}<br />
\pi(\alpha|s,g)=Pr(\alpha_t=\alpha|s_t=s, g_t=g)<br />
\end{align}<br />
<br />
Value function is defined as the expected return obtained by sampling actions from policy <math>\pi</math> from state <math>s_t</math> with goal <math>g_t</math>:<br />
<br />
\begin{align}<br />
V^{\pi}(s,g)=E[R_t]=E[Σ_{k=0}^{\infty}\gamma^kr_{t+k}|s_t=s, g_t=g]<br />
\end{align}<br />
<br />
Also, an architecture with multiple pathways is designed to support two types of learning that is required for this problem. First, an agent needs an internal representation which is general and gives an understanding of a scene. Second, to better understand a scene the agent needs to remember unique features of the scene which then help the agent to organize and remember the scenes.<br />
<br />
===Architectures===<br />
<br />
[[File:figure4-soroush.png|400px|thumb|center|Figure 4. Comparison of architectures. Left: GoalNav is a convolutional encoder plus policy LSTM with goal description input. Middle: CityNav is a single-city navigation architecture with a separate goal LSTM and optional auxiliary heading (θ). Right: MultiCityNav is a multi-city architecture with individual goal LSTM pathways for each city.]]<br />
<br />
The authors use neural networks to parameterize policy and value functions. These neural networks share weights in all layers except the final linear layer. The agent takes image pixels as input. These pixels are passed through a convolutional network. The output of the Convolution network is fed to a Long Short-Term Memory (LSTM) as well as the past reward <math>r_{t-1}</math> and previous action <math>\alpha_{t-1}</math>.<br />
<br />
Three different architectures are described below.<br />
<br />
The '''GoalNav''' architecture (Fig. 4a) which consists of a convolutional architecture and policy LSTM. Goal description <math>g_t</math>, previous action, and reward are the inputs of this LSTM.<br />
<br />
The '''CityNav''' architecture (Fig. 4b) consists of the previous architecture alongside an additional LSTM, called the goal LSTM. Inputs of this LSTM are visual features and the goal description. The CityNav agent also adds an auxiliary heading (θ) prediction task which is defined as an angle between the north direction and the agent’s pose. This auxiliary task can speed up learning and provides relevant information. <br />
<br />
The '''MultiCityNav''' architecture (Fig. 4c) is an extension of CityNav for learning in different cities. This is done using the parallel connection of goal LSTMs for encapsulating locale-specific features, for each city. Moreover, the convolutional architecture and the policy LSTM become general after training on a number of cities. So, new goal LSTMs are required to be trained in new cities.<br />
<br />
In this paper, the authors use IMPALA [1] to train the agents because IMPALA can get similar performance to A3C [2].<br />
<br />
===Prior on agent training: IMPALA and A3C===<br />
<br />
IMPALA (Importance Weighted Actor-Learner Architecture) is an actor-critic implementation of deep reinforcement learning that decouples actions from learning. IMPALA results in a comparable performance to A3C (Google DeepMind's previous algorithm: Asynchronous Actor-Critic Agents) on a single city task, but it has been shown to handle better multi-task learning than A3C. The authors use 256 actors for CityNav and 512 actors for MultiCityNav, with batch sizes of 256 or 512 respectively, and sequences are unrolled to length 50.<br />
<br />
===Curriculum Learning===<br />
In curriculum learning, the model is trained using simple examples in first steps. As soon as the model learns those examples, more complex and difficult examples would be fed to the model. In this paper, this approach is used to teach agent to navigate to further destinations. This courier task suffers from a common problem of RL tasks which is sparse rewards (similar to Montezuma’s Revenge) . To overcome this problem, a natural curriculum scheme is defined, in which sampling each new goal would be within 500m of the agent’s position. This is called phase 1. In phase 2, the maximum range is gradually increased to cover the full graph (3.5km in the smaller New York areas, or 5km for central London or Downtown Manhattan)<br />
<br />
Curriculum learning was first introduced by Bengio et. al in 2009. It serves as a continuation method for non-convex optimization, and improves training time by injecting noisy data. One example outside this paper for curriculum learning is outlined below:<br />
<br />
1. We aim to classify shapes within the following three classes: triangles, ellipses, and rectangles. We can create a curriculum by first starting with a simplified dataset that consists of only special cases of these three classes: equilateral triangles, circles, and squares. By first training on these special cases, and then introducing the full model, we can allow the algorithm to converge more quickly towards a local minima before providing "harder" examples. Feeding only these specialized examples also serves as a method to make the classes fall on more distinct manifold locations; with less overlap, these networks will perform better when noise is later added as well.<br />
<br />
==Results==<br />
In this section, the performance of the proposed architectures on the courier task is shown.<br />
<br />
[[File:figure5-2.png|600px|thumb|center|Figure 5. Average per-episode goal rewards (y-axis) are plotted vs. learning steps (x-axis) for the courier task in the NYU (New York City) environment (top), and in central London (bottom). We compare the GoalNav agent, the CityNav agent, and the CityNav agent without skip connection on the NYU environment, and the CityNav agent in London. We also compare the Oracle performance and a Heuristic agent, described below. The London agents were trained with a 2-phase curriculum– we indicate the end of phase 1 (500m only) and the end of phase 2 (500m to 5000m). Results on the Rive Gauche part of Paris (trained in the same way<br />
as in London) are comparable and the agent achieved mean goal reward 426.]]<br />
<br />
It is first shown that the CityNav agent, trained with curriculum learning, succeeds in learning the courier task in New York, London and Paris. Figure 5 compares the following agents:<br />
<br />
1. Goal Navigation agent.<br />
<br />
2. City Navigation Agent.<br />
<br />
3. A City Navigation agent without the skip connection from the vision layers to the policy LSTM. This is needed to regularise the interface between the goal LSTM and the policy LSTM in multi-city transfer scenario.<br />
<br />
Also, a lower bound (Heuristic) and an upper bound(Oracle) on the performance is considered. As it is said in the paper: "Heuristic is a random walk on the street graph, where the agent turns in a random direction if it cannot move forward; if at an intersection it will turn with a probability <math>P=0.95</math>. Oracle uses the full graph to compute the optimal path using breadth-first search.". As it is clear in Figure 5, CityNav architecture with the previously mentioned architecture attains a higher performance and is more stable than the simpler GoalNav agent.<br />
<br />
The trajectories of the trained agent over two 1000 step episodes and the value function of the agent during navigation to a destination is shown in Figure 6.<br />
<br />
[[File:figure6-soroush.png|400px|thumb|center|Figure 6. Trained CityNav agent’s performance in two environments: Central London (left panes), and NYU (right panes). Top: examples of the agent’s trajectory during one 1000-step episode, showing successful consecutive goal acquisitions. The arrows show the direction of travel of the agent. Bottom: We visualize the value function of the agent during 100 trajectories with random starting points and the same goal (respectively St Paul’s Cathedral and Washington Square). Thicker and warmer color lines correspond to higher value functions.]]<br />
<br />
Figure 7 shows that navigation policy is learned by agent successfully in St Paul’s Cathedral in London and Washington Square in New York.<br />
[[File:figure7-soroush.png|400px|thumb|center|Figure 7. Number of steps required for the CityNav agent to reach<br />
a goal (Washington Square in New York or St Paul’s Cathedral in<br />
London) from 100 start locations vs. the straight-line distance to<br />
the goal in meters. One agent step corresponds to a forward movement<br />
of about 10m or a left/right turn by 22.5 or 67.5 degrees.]]<br />
<br />
The authors mask 25% of the possible goals and train on the remaining ones in order to investigate the generalisation capability of a trained agent. Figure 8 Showa that the agent is still able to traverse through these areas, it just never samples a goal there. <br />
[[File:fff8.png|600px|center]]<br />
<br />
A critical test for this article is to transfer model to new cities by learning a new set of landmarks, but without re-learning visual representation, behaviors, etc. Therefore, the MultiCityNav agent is trained on a number of cities besides freezing both the policy LSTM and the convolutional encoder. Then a new locale-specific goal LSTM is trained. The performance is compared using three different training regimes, illustrated in Fig. 9: Training on only the target city (single training); training on multiple cities, including the target city, together (joint training); and joint training on all but the target city, followed by training on the target city with the rest of the architecture frozen (pre-train and transfer). Figure 10 shows that transferring to other cities is possible. Also, training the model on more cities would increase its effectiveness. According to the paper: "Remarkably, the agent that is pre-trained on 4 regions and then transferred to Wall Street achieves comparable performance to an agent trained jointly on all the regions, and only slightly worse than single-city training on Wall Street alone". Training the model in a single city using skip connection is useful. However, it is not useful in multi-city transferring.<br />
[[File:figure9-soroush.png|400px|thumb|center|Figure 9. Illustration of training regimes: (a) training on a single city (equivalent to CityNav); (b) joint training over multiple cities with a dedicated per-city pathway and shared convolutional net and policy LSTM; (c) joint pre-training on a number of cities followed by training on a target city with convolutional net and policy LSTM frozen (only the target city pathway is optimized).]]<br />
[[File:figure10-soroush.png|400px|thumb|center|Figure 10. Joint multi-city training and transfer learning performance of variants of the MultiCityNav agent evaluated only on the target city (Wall Street). We compare single-city training on the target environment alone vs. joint training on multiple cities (3, 4, or 5-way joint training including Wall Street), vs. pre-training on multiple cities and then transferring to Wall Street while freezing the entire agent except for the new pathway (see Fig. 10). One variant has skip connections between the convolutional encoder and the policy LSTM, the other does not (no-skip).]]<br />
<br />
Giving early rewards before agent reaches the goal or adding random rewards (coins) to encourage exploration is investigated in this article. Figure 11a suggests that coins by themselves are ineffective as our task does not benefit from wide explorations. Also, as it is clear from Figure 11b, reducing the density of the landmarks does not seem to reduce the performance. Based on the results, authors chose to start sampling the goal within a radius of 500m from the agent’s location, and then progressively extend it to the maximum distance an agent could travel within the environment. In addition, to asses the importance of the goal-conditioned agents, a Goal-less CityNav agent is trained by removing inputs gt. The poor performance of this agent is clear in Figure 11b. Furthermore, reducing the density of the landmarks by the ratio of 50%, 25%, and 12:5% does not reduce the performance that much. Finally, some alternative for goal representation is investigated:<br />
<br />
a) Latitude and longitude scalar coordinates normalized to be between 0 and 1.<br />
<br />
b) Binned representation. <br />
<br />
The latitude and longitude scalar goal representations perform the best. However, since the all landmarks representation performs well while remaining independent of the coordinate system, we use this representation as the canonical one.<br />
<br />
[[File:figure11-soroush.PNG|300px|thumb|center|Figure 11. Top: Learning curves of the CityNav agent on NYU, comparing reward shaping with different radii of early rewards (ER) vs. ER with random coins vs. curriculum learning with ER 200m and no coins (ER 200m, Curr.). Bottom: Learning curves for CityNav agents with different goal representations: landmark-based, as well as latitude and longitude classification-based and regression-based.]]<br />
<br />
==Conclusion==<br />
In this paper, a deep reinforcement learning approach that enables navigation in cities is presented through the use of Google StreetView for its photographic content and worldwide coverage. Furthermore, the authors discussed a new courier task and a multi-city neural network agent architecture that is able to be transferred to new cities. A successful navigation architecture is presented which relies on integration of general policies with locale-specific knowledge.<br />
<br />
==Critique==<br />
1. It is not clear how this model is applicable to the real world. A real-world navigation problem needs to detect objects, people, and cars. However, it is not clear whether they are modeling them or not. From what I understood, they did not care about the collision, which is against their claim that it is a real-world problem.<br />
<br />
2. This paper is only using static Google Street View images as its primary source of data. But the authors must at least complement this with other dynamic data like traffic and road blockage information for a realistic model of navigation in the world. Also, this is quite understandable not to use maps but is not clear why have they not used GPS to know their position and maybe even made up with a map. This can be something useful in an emergency or even for investigating places that are not known or there is no access to them. The resulting map could be easily compared with the real one and could also be used in training to achieve higher performance. The availability should not be a serious problem because if they are simulating a real city and the google images are available, why should not GPS be? What is the intuition? At lease, a complementary description on this could be helpful.<br />
<br />
3. The 'Transfer in Multi-City Experiments' results could be strengthened significantly via cross-validation (only Wall Street, which covers the smallest area of the four regions, is used as the test case). Additionally, the results do not show true 'multi-city' transfer learning, since all regions are within New York City. It is stated in the paper that not having to re-learn visual representations when transferring between cities is one of the outcomes, but the tests do not actually check for this. There are likely significant differences in the features that would be learned in NYC vs. Waterloo, for example, and this type of transfer has not been evaluated.<br />
<br />
==Reference==<br />
[1] Espeholt, Lasse, Soyer, Hubert, Munos, Remi, Simonyan, Karen, Mnih, Volodymir, Ward, Tom, Doron, Yotam, Firoiu, Vlad, Harley, Tim, Dunning, Iain, Legg, Shane, and Kavukcuoglu, Koray. Impala: Scalable distributed deep-rl with importance weighted actor-learner architec- tures. arXiv preprint arXiv:1802.01561, 2018.<br />
<br />
[2] Mnih, Volodymyr, Badia, Adria Puigdomenech, Mirza, Mehdi, Graves, Alex, Lillicrap, Timothy, Harley, Tim, Silver, David, and Kavukcuoglu, Koray. Asynchronous methods for deep reinforcement learning. In Interna- tional Conference on Machine Learning, pp. 1928–1937, 2016.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Learning_to_Navigate_in_Cities_Without_a_Map&diff=40887Learning to Navigate in Cities Without a Map2018-11-22T17:01:20Z<p>Npbhatt: Technical Contribution: Added a section - Prior on agent training: IMPALA and A3C</p>
<hr />
<div>Paper: <br />
[https://arxiv.org/pdf/1804.00168.pdf Learning to Navigate in Cities Without a Map]<br />
A video of the paper is available [https://sites.google.com/view/streetlearn here].<br />
<br />
== Introduction ==<br />
Navigation is an attractive topic in many research disciplines and technology related domains such as neuroscience and robotics. The majority of algorithms are based on the following steps.<br />
<br />
1. Building an explicit map<br />
<br />
2. Planning and acting using that map. <br />
<br />
In this article, based on this fact that human can learn to navigate through cities without using any special tool such as maps or GPS, authors propose new methods to show that a neural network agent can do the same thing by using visual observations. To do so, an interactive environment using Google StreetView Images and a dual pathway agent architecture is designed. As shown in figure 1, some parts of the environment are built using Google StreetView images of New York City (Times Square, Central Park) and London (St. Paul’s Cathedral). The green cone represents the agent’s location and orientation. Although learning to navigate using visual aids is shown to be successful in some domains such as games and simulated environments using deep reinforcement learning (RL), it suffers from data inefficiency and sensitivity to changes in the environment. Thus, it is unclear whether this method could be used for large-scale navigation. That’s why it became the subject of investigation in this paper.<br />
[[File:figure1-soroush.png|600px|thumb|center|Figure 1. Our environment is built of real-world places from StreetView. The figure shows diverse views and corresponding local maps (neither map nor current position have not been used by the agent) in New York City (Times Square, Central Park) and London (St. Paul’s Cathedral). The green cone represents the agent’s location and orientation.]]<br />
<br />
==Contribution==<br />
This paper has made the following contributions:<br />
<br />
1. Designing a dual pathway agent architecture. This agent can navigate through a real city and is trained with end-to-end reinforcement learning to handle real-world navigations.<br />
<br />
2. Using Goal-dependent learning. This means that the policy and value functions must adapt themselves to a sequence of goals that are provided as input.<br />
<br />
3. Leveraging a recurrent neural architecture. Using that, not only could navigation through a city be possible, but also the model is scalable for navigation in new cities. This architecture supports both locale-specific learnings and general transferable navigations. The authors achieved these by separating a recurrent neural pathway. This pathway receives and interprets the current goal as well as encapsulates and memorizes features of a single region.<br />
<br />
4. Using a new environment which is built on top of Google StreetView images. This provides real-world images for agent’s observation. Using this environment, the agent can navigate from an arbitrary starting point to a goal and then to another goal etc. Also, London, Paris, and New York City are chosen for navigation.<br />
<br />
==Related Work==<br />
<br />
1. Localization from real-world imagery. For example, (Weyand et al., 2016), a CNN was able to achieve excellent results on geolocation task. This paper provides novel work by not including supervised training with ground-truth labels, and by including planning as a goal. Some other works also improve by exploiting spatiotemporal continuity or estimating camera pose or depth estimation from pixels. These methods rely on supervised training with ground truth labels, which is not possible in every environment. <br />
<br />
2. Deep RL methods for navigation. For instance, (Mirowski et al., 2016; Jaderberg et al., 2016) used self-supervised auxiliary tasks to produce visual navigation in several created mazes. Some other researches used text descriptions to incorporate goal instructions. Researchers developed realistic, higher-fidelity environment simulations to make the experiment more realistic, but that still came with lack of diversities. This paper makes use of real-world data, in contrast to many related papers in this area. It's diverse and visually realistic but still, it does not contain dynamic elements, and the street topology cannot be regenerated or altered.<br />
<br />
3. Deep RL for path planning and mapping. For example, (Zhang et al., 2017) created an agent that represented a global map via an RL agent with external memory; some other work uses a hierarchical control strategy to propose a structured memory and Memory Augmented Control Maps. Explicit neural mapper and navigation planner with joint training was also used. Among all these works, the target-driven visual navigation with a goal-conditional policy approach was most related to our method.<br />
<br />
==Environment==<br />
Google StreetView consists of both high-resolution 360-degree imagery and graph connectivity. Also, it provides a public API. These features make it a valuable resource. In this work, large areas of New York, Paris, and London that contain between 7,000 and 65,500 nodes<br />
(and between 7,200 and 128,600 edges, respectively), have a mean node spacing of 10m and cover a range of up to<br />
5km chosen (Figure 2), without simplifying the underlying connections. This means that there are many areas 'congested' with nodes, occlusions, available footpaths, etc. The agent only sees RGB images that are visible in StreetView images (Figure 1) and is not aware of the underlying graph.<br />
<br />
[[File:figure2-soroush.png|700px|thumb|center|Figure 2. Map of the 5 environments in New York City; our experiments focus on the NYU area as well as on transfer learning from the other areas to Wall Street (see Section 5.3). In the zoomed in area, each green dot corresponds to a unique panorama, the goal is marked in blue, and landmark locations are marked with red pins.]]<br />
<br />
==Agent Interface and the Courier Task==<br />
In an RL environment, we need to define observations and actions in addition to tasks. The inputs to the agent are the image <math>x_t</math> and the goal <math>g_t</math>. Also, a first-person view of the 3D environment is simulated by cropping <math>x_t</math> to a 60-degree square RGB image that is scaled to 84*84 pixels. Furthermore, the action space consists of 5 movements: “slow” rotate left or right (±22:5), “fast” rotate left or right (±67.5), or move forward (implemented as a ''noop'' in the case where this is not a viable action). The most central edge is chosen if there are multiple edges in the agents viewing cone.<br />
<br />
There are lots of ways to specify the goal to the agent. In this paper, the current goal is chosen to be represented in terms of its proximity to a set L of fixed landmarks <math> L={(Lat_k, Long_k)}</math> which are specified using Latitude and Longitude coordinate system. For distance to the <math> k_{th}</math> landmark <math>{(d_{(t,k)}^g})_k</math> the goal vector contains <math> g_{(t,i)}=\tfrac{exp(-αd_{(t,i)}^g)}{∑_k exp(-αd_{(t,k)}^g)} </math>for <math>i_{th}</math> landmark with <math>α=0.002</math> (Figure 3).<br />
<br />
[[File:figure3-soroush.PNG|400px|thumb|center|Figure 3. We illustrate the goal description by showing a goal and a set of 5 landmarks that are nearby, plus 4 that are more distant. The code <math>g_i</math> is a vector with a softmax-normalised distance to each landmark.]]<br />
<br />
This form of representation has several advantages: <br />
<br />
1. It could easily be extended to new environments.<br />
<br />
2. It is intuitive. Even humans and animals use landmarks to be able to move from one place to another.<br />
<br />
3. It does not rely on arbitrary map coordinates, and provides an absolute (as opposed to relative) goal.<br />
<br />
In this work, 644 landmarks for New York, Paris, and London are manually defined. The courier task is the problem of navigating to a list of random locations within a city. In each episode, which consists of 1000 steps, the agent starts from a random place with random orientation. when an agent gets within 100 meters of goal, the next goal is randomly chosen. An episode ends after 1000 agent steps. Finally, the reward is proportional to the shortest path between agent and goal when the goal is first assigned (providing more reward for longer journeys). Thus the agent needs to learn the mapping between the images observed at the goal location and the goal vector in order to solve the courier task problem. Furthermore, the agent must learn the association between the images observed at its current location and the policy to reach the goal destination.<br />
<br />
==Methods==<br />
<br />
===Goal-dependent Actor-Critic Reinforcement Learning===<br />
In this paper, the learning problem is based on Markov Decision Process, with state space <math>\mathcal{S}</math>, action space <math>\mathcal{A}</math>, environment <math>\mathcal{E}</math>, and a set of possible goals <math>\mathcal{G}</math>. The reward function depends on the current goal and state: <math>\mathcal{R}: \mathcal{S} \times \mathcal{G} \times \mathcal{A} &rarr; \mathbb{R}</math>. Typically, in reinforcement learning the main goal is to find the policy which maximizes the expected return. Expected return is defined as the sum of<br />
discounted rewards starting from state <math>s_0</math> with discount <math>\gamma</math>. Also, the expected return from a state <math>s_t</math> depends on the goals that are sampled. The policy is defined as a distribution over the actions, given the current state <math>s_t</math> and the goal <math>g_t</math>: <br />
<br />
\begin{align}<br />
\pi(\alpha|s,g)=Pr(\alpha_t=\alpha|s_t=s, g_t=g)<br />
\end{align}<br />
<br />
Value function is defined as the expected return obtained by sampling actions from policy <math>\pi</math> from state <math>s_t</math> with goal <math>g_t</math>:<br />
<br />
\begin{align}<br />
V^{\pi}(s,g)=E[R_t]=E[Σ_{k=0}^{\infty}\gamma^kr_{t+k}|s_t=s, g_t=g]<br />
\end{align}<br />
<br />
Also, an architecture with multiple pathways is designed to support two types of learning that is required for this problem. First, an agent needs an internal representation which is general and gives an understanding of a scene. Second, to better understand a scene the agent needs to remember unique features of the scene which then help the agent to organize and remember the scenes.<br />
<br />
===Architectures===<br />
<br />
[[File:figure4-soroush.png|400px|thumb|center|Figure 4. Comparison of architectures. Left: GoalNav is a convolutional encoder plus policy LSTM with goal description input. Middle: CityNav is a single-city navigation architecture with a separate goal LSTM and optional auxiliary heading (θ). Right: MultiCityNav is a multi-city architecture with individual goal LSTM pathways for each city.]]<br />
<br />
The authors use neural networks to parameterize policy and value functions. These neural networks share weights in all layers except the final linear layer. The agent takes image pixels as input. These pixels are passed through a convolutional network. The output of the Convolution network is fed to a Long Short-Term Memory (LSTM) as well as the past reward <math>r_{t-1}</math> and previous action <math>\alpha_{t-1}</math>.<br />
<br />
Three different architectures are described below.<br />
<br />
The '''GoalNav''' architecture (Fig. 4a) which consists of a convolutional architecture and policy LSTM. Goal description <math>g_t</math>, previous action, and reward are the inputs of this LSTM.<br />
<br />
The '''CityNav''' architecture (Fig. 4b) consists of the previous architecture alongside an additional LSTM, called the goal LSTM. Inputs of this LSTM are visual features and the goal description. The CityNav agent also adds an auxiliary heading (θ) prediction task which is defined as an angle between the north direction and the agent’s pose. This auxiliary task can speed up learning and provides relevant information. <br />
<br />
The '''MultiCityNav''' architecture (Fig. 4c) is an extension of CityNav for learning in different cities. This is done using the parallel connection of goal LSTMs for encapsulating locale-specific features, for each city. Moreover, the convolutional architecture and the policy LSTM become general after training on a number of cities. So, new goal LSTMs are required to be trained in new cities.<br />
<br />
In this paper, the authors use IMPALA [1] to train the agents because IMPALA can get similar performance to A3C [2].<br />
<br />
===Prior on agent training: IMPALA and A3C===<br />
<br />
IMPALA (Importance Weighted Actor-Learner Architecture) is an actor-critic implementation of deep reinforcement learning that decouples actions from learning. IMPALA results in a comparable performance to A3C (Google DeepMind's previous algorithm: Asynchronous Actor-Critic Agents) on a single city task, but it has been shown to handle better multi-task learning than A3C. The authors use 256 actors for CityNav and 512 actors for MultiCityNav, with batch sizes of 256 or 512 respectively, and sequences are unrolled to length 50.<br />
<br />
===Curriculum Learning===<br />
In curriculum learning, the model is trained using simple examples in first steps. As soon as the model learns those examples, more complex and difficult examples would be fed to the model. In this paper, this approach is used to teach agent to navigate to further destinations. This courier task suffers from a common problem of RL tasks which is sparse rewards (similar to Montezuma’s Revenge) . To overcome this problem, a natural curriculum scheme is defined, in which sampling each new goal would be within 500m of the agent’s position. This is called phase 1. In phase 2, the maximum range is gradually increased to cover the full graph (3.5km in the smaller New York areas, or 5km for central London or Downtown Manhattan)<br />
<br />
==Results==<br />
In this section, the performance of the proposed architectures on the courier task is shown.<br />
<br />
[[File:figure5-2.png|600px|thumb|center|Figure 5. Average per-episode goal rewards (y-axis) are plotted vs. learning steps (x-axis) for the courier task in the NYU (New York City) environment (top), and in central London (bottom). We compare the GoalNav agent, the CityNav agent, and the CityNav agent without skip connection on the NYU environment, and the CityNav agent in London. We also compare the Oracle performance and a Heuristic agent, described below. The London agents were trained with a 2-phase curriculum– we indicate the end of phase 1 (500m only) and the end of phase 2 (500m to 5000m). Results on the Rive Gauche part of Paris (trained in the same way<br />
as in London) are comparable and the agent achieved mean goal reward 426.]]<br />
<br />
It is first shown that the CityNav agent, trained with curriculum learning, succeeds in learning the courier task in New York, London and Paris. Figure 5 compares the following agents:<br />
<br />
1. Goal Navigation agent.<br />
<br />
2. City Navigation Agent.<br />
<br />
3. A City Navigation agent without the skip connection from the vision layers to the policy LSTM. This is needed to regularise the interface between the goal LSTM and the policy LSTM in multi-city transfer scenario.<br />
<br />
Also, a lower bound (Heuristic) and an upper bound(Oracle) on the performance is considered. As it is said in the paper: "Heuristic is a random walk on the street graph, where the agent turns in a random direction if it cannot move forward; if at an intersection it will turn with a probability <math>P=0.95</math>. Oracle uses the full graph to compute the optimal path using breadth-first search.". As it is clear in Figure 5, CityNav architecture with the previously mentioned architecture attains a higher performance and is more stable than the simpler GoalNav agent.<br />
<br />
The trajectories of the trained agent over two 1000 step episodes and the value function of the agent during navigation to a destination is shown in Figure 6.<br />
<br />
[[File:figure6-soroush.png|400px|thumb|center|Figure 6. Trained CityNav agent’s performance in two environments: Central London (left panes), and NYU (right panes). Top: examples of the agent’s trajectory during one 1000-step episode, showing successful consecutive goal acquisitions. The arrows show the direction of travel of the agent. Bottom: We visualize the value function of the agent during 100 trajectories with random starting points and the same goal (respectively St Paul’s Cathedral and Washington Square). Thicker and warmer color lines correspond to higher value functions.]]<br />
<br />
Figure 7 shows that navigation policy is learned by agent successfully in St Paul’s Cathedral in London and Washington Square in New York.<br />
[[File:figure7-soroush.png|400px|thumb|center|Figure 7. Number of steps required for the CityNav agent to reach<br />
a goal (Washington Square in New York or St Paul’s Cathedral in<br />
London) from 100 start locations vs. the straight-line distance to<br />
the goal in meters. One agent step corresponds to a forward movement<br />
of about 10m or a left/right turn by 22.5 or 67.5 degrees.]]<br />
<br />
The authors mask 25% of the possible goals and train on the remaining ones in order to investigate the generalisation capability of a trained agent. Figure 8 Showa that the agent is still able to traverse through these areas, it just never samples a goal there. <br />
[[File:fff8.png|600px|center]]<br />
<br />
A critical test for this article is to transfer model to new cities by learning a new set of landmarks, but without re-learning visual representation, behaviors, etc. Therefore, the MultiCityNav agent is trained on a number of cities besides freezing both the policy LSTM and the convolutional encoder. Then a new locale-specific goal LSTM is trained. The performance is compared using three different training regimes, illustrated in Fig. 9: Training on only the target city (single training); training on multiple cities, including the target city, together (joint training); and joint training on all but the target city, followed by training on the target city with the rest of the architecture frozen (pre-train and transfer). Figure 10 shows that transferring to other cities is possible. Also, training the model on more cities would increase its effectiveness. According to the paper: "Remarkably, the agent that is pre-trained on 4 regions and then transferred to Wall Street achieves comparable performance to an agent trained jointly on all the regions, and only slightly worse than single-city training on Wall Street alone". Training the model in a single city using skip connection is useful. However, it is not useful in multi-city transferring.<br />
[[File:figure9-soroush.png|400px|thumb|center|Figure 9. Illustration of training regimes: (a) training on a single city (equivalent to CityNav); (b) joint training over multiple cities with a dedicated per-city pathway and shared convolutional net and policy LSTM; (c) joint pre-training on a number of cities followed by training on a target city with convolutional net and policy LSTM frozen (only the target city pathway is optimized).]]<br />
[[File:figure10-soroush.png|400px|thumb|center|Figure 10. Joint multi-city training and transfer learning performance of variants of the MultiCityNav agent evaluated only on the target city (Wall Street). We compare single-city training on the target environment alone vs. joint training on multiple cities (3, 4, or 5-way joint training including Wall Street), vs. pre-training on multiple cities and then transferring to Wall Street while freezing the entire agent except for the new pathway (see Fig. 10). One variant has skip connections between the convolutional encoder and the policy LSTM, the other does not (no-skip).]]<br />
<br />
Giving early rewards before agent reaches the goal or adding random rewards (coins) to encourage exploration is investigated in this article. Figure 11a suggests that coins by themselves are ineffective as our task does not benefit from wide explorations. Also, as it is clear from Figure 11b, reducing the density of the landmarks does not seem to reduce the performance. Based on the results, authors chose to start sampling the goal within a radius of 500m from the agent’s location, and then progressively extend it to the maximum distance an agent could travel within the environment. In addition, to asses the importance of the goal-conditioned agents, a Goal-less CityNav agent is trained by removing inputs gt. The poor performance of this agent is clear in Figure 11b. Furthermore, reducing the density of the landmarks by the ratio of 50%, 25%, and 12:5% does not reduce the performance that much. Finally, some alternative for goal representation is investigated:<br />
<br />
a) Latitude and longitude scalar coordinates normalized to be between 0 and 1.<br />
<br />
b) Binned representation. <br />
<br />
The latitude and longitude scalar goal representations perform the best. However, since the all landmarks representation performs well while remaining independent of the coordinate system, we use this representation as the canonical one.<br />
<br />
[[File:figure11-soroush.PNG|300px|thumb|center|Figure 11. Top: Learning curves of the CityNav agent on NYU, comparing reward shaping with different radii of early rewards (ER) vs. ER with random coins vs. curriculum learning with ER 200m and no coins (ER 200m, Curr.). Bottom: Learning curves for CityNav agents with different goal representations: landmark-based, as well as latitude and longitude classification-based and regression-based.]]<br />
<br />
==Conclusion==<br />
In this paper, a deep reinforcement learning approach that enables navigation in cities is presented through the use of Google StreetView for its photographic content and worldwide coverage. Furthermore, the authors discussed a new courier task and a multi-city neural network agent architecture that is able to be transferred to new cities. A successful navigation architecture is presented which relies on integration of general policies with locale-specific knowledge.<br />
<br />
==Critique==<br />
1. It is not clear how this model is applicable in the real world. A real-world navigation problem needs to detect objects, people, and cars. However, it is not clear whether they are modelling them or not. From what I understood, they did not care about the collision, which is against their claim that it is a real-world problem.<br />
<br />
2. This paper is only using static Google Street View images as its primary source of data. But the authors must at least complement this with other dynamic data like traffic and road blockage information for a realistic model of navigation in the world. Also, this is quite understandable not to use maps but is not clear why have they not used GPS to know their position and maybe even made up with a map. This can be something useful in an emergency or even for investigating places that are not known or there is no access to them. The resulting map could be easily compared with the real one and could also be used in training to achieve higher performance. The availability should not be a serious problem because if they are simulating a real city and the google images are available, why should not GPS be? What is the intuition? At lease a complementary description on this could be helpful.<br />
<br />
3. The 'Transfer in Multi-City Experiments' results could be strengthened significantly via cross-validation (only Wall Street, which covers the smallest area of the four regions, is used as the test case). Additionally, the results do not show true 'multi-city' transfer learning, since all regions are within New York City. It is stated in the paper that not having to re-learn visual representations when transferring between cities is one of the outcomes, but the tests do not actually check for this. There are likely significant differences in the features that would be learned in NYC vs. Waterloo, for example, and this type of transfer has not been evaluated.<br />
<br />
==Reference==<br />
[1] Espeholt, Lasse, Soyer, Hubert, Munos, Remi, Simonyan, Karen, Mnih, Volodymir, Ward, Tom, Doron, Yotam, Firoiu, Vlad, Harley, Tim, Dunning, Iain, Legg, Shane, and Kavukcuoglu, Koray. Impala: Scalable distributed deep-rl with importance weighted actor-learner architec- tures. arXiv preprint arXiv:1802.01561, 2018.<br />
<br />
[2] Mnih, Volodymyr, Badia, Adria Puigdomenech, Mirza, Mehdi, Graves, Alex, Lillicrap, Timothy, Harley, Tim, Silver, David, and Kavukcuoglu, Koray. Asynchronous methods for deep reinforcement learning. In Interna- tional Conference on Machine Learning, pp. 1928–1937, 2016.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Obfuscated_Gradients_Give_a_False_Sense_of_Security_Circumventing_Defenses_to_Adversarial_Examples&diff=40360Obfuscated Gradients Give a False Sense of Security Circumventing Defenses to Adversarial Examples2018-11-20T16:41:19Z<p>Npbhatt: /* The Attacks */ edited formula display</p>
<hr />
<div>= Introduction =<br />
Over the past few years, neural network models have been the source of major breakthroughs in a variety of computer vision problems. However, these networks have been shown to be susceptible to adversarial attacks. In these attacks, small humanly-imperceptible changes are made to images (that are originally correctly classified) which causes these models to misclassify with high confidence. These attacks pose a major threat that needs to be addressed before these systems can be deployed on a large scale, especially in safety-critical scenarios. <br />
<br />
The seriousness of this threat has generated major interest in both the design and defense against them. Recently, many new defenses have been proposed that claim robustness against iterative white-box adversarial attacks. This result is somewhat surprising, given that iterative white-box attacks are one of the most difficult classes of adversarial attacks. In this paper, the authors identify a common flaw, masked gradients, in many of these defenses that cause them to ''perceive'' a high accuracy on adversarial images. This flaw is so prevalent, that 7 out of the 9 defenses proposed in the ICLR 2018 conference were found to contain them. The authors develop three attacks, specifically targeting masked gradients, and show that the actual accuracy of these defenses is much lower than claimed. In fact, the majority of these attacks were found to be ineffective against true iterative white box attacks.<br />
<br />
= Methodology =<br />
<br />
The paper assumes a lot of familiarity with adversarial attack literature. The section below briefly explains some key concepts.<br />
<br />
== Background ==<br />
<br />
==== Adversarial Images Mathematically ====<br />
Given an image <math>x</math> and a classifier <math>f(x)</math>, an adversarial image <math>x'</math> satisfies two properties:<br />
# <math>D(x,x') < \epsilon </math><br />
# <math>c(x') \neq c^*(x) </math><br />
<br />
Where <math>D</math> is some distance metric, <math>\epsilon </math> is a small constant, <math>c(x')</math> is the output ''class'' predicted by the model, and <math>c^*(x)</math> is the true class for input x. In words, the adversarial image is a small distance from the original image, but the classifier classifies it incorrectly.<br />
<br />
==== Adversarial Attacks Terminology ====<br />
#Adversarial attacks can be either '''black''' or '''white-box'''. In black box attacks, the attacker has access to the network output only, while white-box attackers have full access to the network, including its gradients, architecture and weights. This makes white-box attackers much more powerful. Given access to gradients, white-box attacks use back propagation to modify inputs (as opposed to the weights) with respect to the loss function.<br />
#In '''untargeted''' attacks, the objective is to ''maximize'' the loss of the true class, <math>x'=x \mathbf{+} \lambda(sign(\nabla_xL(x,c^*(x))))</math>. While in '''targeted''' attacks, the objective is to ''minimize'' loss for a target class <math>c^t(x)</math> that is different from the true class, <math>x'=x \mathbf{-} \epsilon(sign(\nabla_xL(x,c^t(x))))</math>. Here, <math>\nabla_xL()</math> is the gradient of the loss function with respect to the input, <math>\lambda</math> is a small gradient step and <math>sign()</math> is the sign of the gradient.<br />
# An attacker may be allowed to use a single step of back-propagation ('''single step''') or multiple ('''iterative''') steps. Iterative attackers can generate more powerful adversarial images. Typically, to bound iterative attackers a distance measure is used.<br />
<br />
In this paper the authors focus on the more difficult attacks; white-box iterative targeted and untargeted attacks.<br />
<br />
== Obfuscated Gradients ==<br />
If gradients are masked, they cannot be followed to generate adversarial images, gradient masking is known to be an incomplete defense to adversarial images[Papernot et al., 2017; Tramer et al., 2018]. A defense method may appear to be providing robustness, but in reality, the gradients in the network cannot be followed to generate strong adversarial images. Generated adversarial images from these networks are much weaker and when used to evaluate the model robustness five a false sense of security against adversarial attacks. Defenses are designed in a way that the constructed defense inevitably leads to gradient masking as obfuscated gradients. In the defenses proposed in ICLR 2018, there are three ways which defense obfuscate gradients:<br />
<br />
# '''Shattered gradients''': Non-differentiable operations are introduced into the model, causing a gradient to be nonexistent or incorrect. Introduced by using operations where following the gradient doesn't maximize classification loss globally. <br />
# '''Stochastic gradients''': A stochastic process is added into the model at test time, causing the gradients to become randomized. Introduced by either randomly transforming inputs before feeding to the classifier, or randomly permuting the network itself. <br />
# '''Vanishing Gradients ''': Very deep neural networks or those with recurrent connections are used. Because of the vanishing or exploding gradient problem common in these deep networks, effective gradients at the input are small and not very useful. Introduced by using multiple iterations of neural network evaluation, where the output of one network is fed as the input to the next.<br />
<br />
'''Detecting Obfuscated Gradients''':<br />
<br />
The authors propose a number of tests that might help detect when a defense relies on obfuscated gradients.<br />
<br />
Iterative attacks should work better than single-step attacks, since iterative attacks are strictly stronger than single-step attacks.<br />
White-box attacks should perform better than black-box attacks, since the black-box threat model is a strict subset of the white-box threat model.<br />
Attacks with an unbounded distortion metric (e.g. L_2 norm) should find adversarial examples with 100% success.<br />
Optimization-based attacks should perform better than brute-force sampling of nearby inputs (sampling within an ϵ-ball).<br />
These tests may not cover all cases of obfuscated gradients, but they indicate when intuitive properties start to break down. All defenses with obfuscated gradients discussed by the authors fail at least one test.<br />
<br />
== The Attacks ==<br />
To circumvent these gradient masking techniques, the authors propose:<br />
# '''Backward Pass Differentiable Approximation (BPDA)''': For defenses that introduce non-differentiable components, the authors replace it with an approximate function that is differentiable on the backward pass. In a white-box setting, the attacker has full access to any added non-linear transformation and can find its approximation. <br />
# '''Expectation over Transformation [Athalye, 2017]''': For defenses that add some form of test time randomness, the authors propose to use expectation over transformation technique in the backward pass. Rather than moving along the gradient every step, several gradients are sampled and the step is taken in the average direction. This can help with any stochastic misdirection from individual gradients. The technique is similar to using mini-batch gradient descent but applied in the construction of adversarial images.<br />
# '''Re-parameterize the exploration space''': For very deep networks that rely on vanishing or exploding gradients, the authors propose to re-parameterize and search over the range where the gradient does not explode/vanish.<br />
They assume that given a classifier <math display = "inline">f(g(x))</math>, <math display = "inline">g(·)</math> performs some optimization loop to transform the input x to a new input <math display = "inline">\hat x</math>. Often times, differentiating through <math display = "inline">g(·)</math> yields exploding or vanishing gradients.<br />
<br />
To resolve this, they make a change-of-variable <math display = "inline">x = h(z)</math> for some function <math display = "inline">h(·)</math> such that <math display = "inline">g(h(z)) = h(z)</math> for all z, but <math display = "inline">h(·)</math> is differentiable. This allows them to compute gradients through f(h(z)) and hence circumvent the defense.<br />
<br />
= Main Results =<br />
[[File:Summary_Table.png|600px|center]]<br />
<br />
The table above summarizes the results of their attacks. Attacks are mounted on the same dataset each defense targeted. If multiple datasets were used, attacks were performed on the largest one. Two different distance metrics (<math>\ell_{\infty}</math> and <math>\ell_{2}</math>) were used in the construction of adversarial images. Distance metrics specify how much an adversarial image can vary from an original image. For <math>\ell_{\infty}</math> adversarial images, each pixel is allowed to vary by a maximum amount. For example, <math>\ell_{\infty}=0.031</math> specifies that each pixel can vary by <math>256*0.031=8</math> from its original value. <math>\ell_{2}</math> distances specify the magnitude of the total distortion allowed over all pixels. For MNIST and CIFAR-10, untargeted adversarial images were constructed using the entire test set, while for Imagenet, 1000 test images were randomly selected and used to generate targeted adversarial images. <br />
<br />
Standard models were used in evaluating the accuracy of defense strategies under the attacks,<br />
# MNIST: 5-layer Convolutional Neural Network (99.3% top-1 accuracy)<br />
# CIFAR-10: Wide-Resnet (95.0% top-1 accuracy)<br />
# Imagenet: InceptionV3 (78.0% top-1 accuracy)<br />
<br />
The last column shows the accuracies each defense method achieved over the adversarial test set. Except for [Madry, 2018], all defense methods could only achieve an accuracy of <10%. Furthermore, the accuracy of most methods was 0%. The results of [Samangoui,2018] (double asterisk), show that their approach was not as successful. The authors claim that is is a result of implementation imperfections but theoretically, the defense can be circumvented using their proposed method.<br />
<br />
==== The defense that worked - Adversarial Training [Madry, 2018] ====<br />
<br />
As a defense mechanism, [Madry, 2018] proposes training the neural networks with adversarial images. Although this approach is previously known [Szegedy, 2013] in their formulation, the problem is setup in a more systematic way using a min-max formulation:<br />
\begin{align}<br />
\theta^* = \arg \underset{\theta} \min \mathop{\mathbb{E_x}} \bigg{[} \underset{\delta \in [-\epsilon,\epsilon]}\max L(x+\delta,y;\theta)\bigg{]} <br />
\end{align}<br />
<br />
where <math>\theta</math> is the parameter of the model, <math>\theta^*</math> is the optimal set of parameters and <math>\delta</math> is a small perturbation to the input image <math>x</math> and is bounded by <math>[-\epsilon,\epsilon]</math>. <br />
<br />
Training proceeds in the following way. For each clean input image, a distorted version of the image is found by maximizing the inner maximization problem for a fixed number of iterations. Gradient steps are constrained to fall within the allowed range (projected gradient descent). Next, the classification problem is solved by minimizing the outer minimization problem.<br />
<br />
This approach was shown to provide resilience to all types of adversarial attacks.<br />
<br />
==== How to check for Obfuscated Gradients ====<br />
For future defense proposals, it is recommended to avoid using masked gradients. To assist with this, the authors propose a set of conditions that can help identify if a defense is relying on masked gradients:<br />
# If weaker one-step attacks are performing better than iterative attacks.<br />
# Black-box attacks can find stronger adversarial images compared with white-box attacks.<br />
# Unbounded iterative attacks do not reach 100% success.<br />
# If random brute force attempts are better than gradient-based methods at finding adversarial images.<br />
<br />
= Detailed Results =<br />
<br />
As a case study for evaluating the prevalence of obfuscated gradients, the authors studied the ICLR 2018 non-certified defenses that argue robustness in a white-box threat model. Each of these defenses argues a high robustness to adaptive, white box attacks. It is reported that seven of these nine defenses depend on this phenomenon, and the authors demonstrate that their techniques can completely circumvent six of those (and partially circumvent one) that depend on obfuscated gradients.<br />
<br />
== Non-obfuscated Gradients ==<br />
<br />
==== Cascade Adversarial Training, [Na, 2018] ====<br />
'''Defense''': Similar to the method of [Madry, 2018], the authors of [Na, 2018] propose adversarial training. The main difference is that instead of using iterative methods to generate adversarial examples at each mini-batch, a separate model is first trained and used to generate adversarial images. These adversarial images are used to augment the train set of another model.<br />
<br />
'''Attack''': The authors found that this technique does not use obfuscated gradients. They were not able to reduce the performance of this method. However, they point out that the claimed accuracy is much lower (%15) compared with [Madry, 2018] under the same perturbation setting.<br />
<br />
== Gradient Shattering ==<br />
<br />
==== Thermometer Coding, [Buckman, 2018] ====<br />
'''Defense''': Inspired by the observation that neural networks learn linear boundaries between classes [Goodfellow, 2014] , [Buckman, 2018] sought to break this linearity by explicitly adding a highly non-linear transform at the input of their model. The non-linear transformation they chose was quantizing inputs to binary vectors. The quantization performed was termed thermometer encoding,<br />
<br />
Given an image, for each pixel value <math>x_{i,j,c}</math>, if an <math>l</math> dimensional thermometer code, the <math>kth</math> bit is given by:<br />
\begin{align}<br />
\tau(x_{i,j,c})_k = \bigg{\{}\begin{array}{ll}<br />
1 \space if \thinspace x_{i,j,c} > \dfrac{k}{l} \\<br />
0 \space otherwise \\<br />
\end{array}<br />
\end{align}<br />
Here it is assumed <math>x_{i,j,c} \in [0, 1] </math> and <math>i, j, c</math> are the row, column and channel index of the pixel respectively. This encoding is like one-hot encoding, except all the points (not just one) greater than the target value are set to 1. This quantization technique preserves pairwise ordering between pixels.<br />
<br />
On CIFAR-10, the model gave 50% accuracy against <math>\ell_\infty</math> adversarial images with <math>\epsilon=0.031</math> attacks.<br />
<br />
'''Attack''': The authors attack this model using there BPDA approach. Given the non-linear transformation performed in the forward pass, <math>\tau(x)</math>, they develop a differentiable counterpart,<br />
\begin{align}<br />
\hat{\tau}(x_{i,j,c})_k = \min ( \max (x_{i,j,c} - \frac{k}{l}), 1 )<br />
\end{align}<br />
and use it in place of <math>\tau(x)</math> on the backward pass. With their modifications they were able to bring the accuracy of the model down to 0%.<br />
<br />
==== Input Transformation, [Guo, 2018] ====<br />
'''Defense''':[Gou, 2018] investigated the effect of including different input transformation on the robustness to adversarial images. In particular, they found two techniques provided the greatest resistance: total variance minimization and image quilting. Total variance minimization is a technique that removes high-frequency noise while preserving legitimate edges (good high-frequency components). In image quilting, a large database of image patches from clean images is collected. At test time, input patches, that contain a lot of noise, are replaced with similar but clean patches from the database.<br />
<br />
Both techniques, removed perturbations from adversarial images which provide some robustness to adversarial attacks. The best model achieved 60% accuracy on adversarial images with <math>l_{2}=0.05</math> perturbations. However, both approaches are non-differentiable and contain test time randomness as the modifications made are input dependent. Gradient flow to the input is non-differentiable and random.<br />
<br />
'''Attack''': The authors used the BPDA attack where the input transformations were replaced by an identity function. They were able to bring the accuracy of the model down to 0% under the same type of adversarial attacks.<br />
<br />
==== Local Intrinsic Dimensionality, [Ma, 2018] ====<br />
'''Defense''' Local intrinsic dimensionality (LID) is a distance-based metric that measures the similarity between points in a high dimensional space. Given a set of points, let the distance between sample <math>x</math> and its <math>ith</math> neighbor be <math>r_i(x)</math>, then the LID under the choose distance metric is given by,<br />
<br />
\begin{align}<br />
LID(x) = - \bigg{(} \frac{1}{k}\sum^k_{i=1}log \frac{r_i(x)}{r_k(x)} \bigg{)}^{-1}<br />
\end{align}<br />
where k is the number of nearest neighbors considered, <math>r_k(x)</math> is the maximum distance to any of the neighbors in the set k. <br />
<br />
First, <math>L_2</math> distances for all training and adversarial images. Next, the LID scores for each train and adversarial images were calculated. It was found that LID scores for adversarial images were significantly larger than those of clean images. Base on these results, the a separate classifier was created that can be used to detect adversarial inputs. [Ma, 2018] claim that this is not a defense method, but a method to study the properties of adversarial images.<br />
<br />
'''Attack''': Instead of attacking this method, the authors show that this method is not able to detect, and is therefore venerable to, attacks of the [Carlini and Wagner, 2017a] variety.<br />
<br />
== Stochastic Gradients ==<br />
<br />
==== Stochastic Activation Pruning, [Dhillon, 2018] ====<br />
'''Defense''': [Dhillon, 2018] use test time randomness in their model to guard against adversarial attacks. Because adversarial perturbations are like noises, randomly dropping activation can decrease their collective impact on the classifier. Within a layer, the activities of component nodes are randomly dropped with a probability proportional to its absolute value. The rest of the activation are scaled up to preserve accuracies. This is akin to test time drop-out. This technique was found to drop accuracy slightly on clean images, but improved performance on adversarial images.<br />
<br />
'''Attack''': The authors used the expectation over transformation attack to get useful gradients out of the model. With their attack, they were able to reduce the accuracy of this method down to 0% on CIFAR-10.<br />
<br />
==== Mitigation Through Randomization, [Xie, 2018] ====<br />
'''Defense''': [Xie, 2018] Add a randomization layer to their model to help defend against adversarial attacks. For an input image of size [299,299], first the image is randomly re-scaled to <math>r \in [299,331]</math>. Next, the image is zero-padded to fix the dimension of the modified input. This modified input is then fed into a regular classifier. The authors claim that is strategy can provide an accuracy of 32.8% against ensemble attack patterns (fixed distortions, but many of them which are picked randomly). Because of the introduced randomness, the authors claim the model builds some robustness to other types of attacks as well.<br />
<br />
'''Attack''': The EOT method was used to build adversarial images to attack this model. With their attack, the authors were able to bring the accuracy of this model down to 0% using <math>L_{\infty}(\epsilon=0.031)</math> perturbations.<br />
<br />
== Vanishing and Exploding Gradients ==<br />
<br />
==== Pixel Defend, [Song, 2018] ====<br />
'''Defense''': [Song, 2018] argues that adversarial images lie in low probability regions of the data manifold. Therefore, one way to handle adversarial attacks is to project them back into the high probability regions before feeding them into a classifier. They chose to do this by using a generative model (pixelCNN) in a denoising capacity. A PixelCNN model directly estimates the conditional probability of generating an image pixel by pixel [Van den Oord, 2016],<br />
<br />
\begin{align}<br />
p(\mathbf{x}= \prod_{i=1}^{n^2} p(x_i|x_0,x_1 ....x_{i-1}))<br />
\end{align}<br />
<br />
The reason for choosing this model is the long iterative process of generation. In the backward pass, following the gradient, all the way to the input would not be possible because of the vanishing/exploding gradient<br />
problem of deep networks. The proposed model was able to obtain an accuracy of 46% on CIFAR-10 images with <math>l_{\infty} (\epsilon=0.031) </math> perturbations.<br />
<br />
'''Attack''': The model was attacked using the BPDA technique where back-propagating though the pixelCNN was replaced with an identity function. With this approach, the authors were able to bring down the accuracy to 9% under the same kind of perturbations.<br />
<br />
==== Defense-GAN, [Samangouei, 2018] ====<br />
<br />
Before classifying the samples, Defense-GAN projects them onto the data manifold utilizing GAN. The intuition behind this approach is almost similar to that of PixelDefend. It uses GAN instead of pixel CNN.<br />
<br />
The authors used MNIST because CIFAR-10 is not argued secure. They found adversarial examples exist in the generator manifold, and they can construct an example. A perfect projector will not be able to modify this example, however, an imperfect gradient descent approach does not perfectly preserve manifold points. Therefore, the authors attacked DEFENSE-GAN using BPDA, but can only get a 45% success rate.<br />
<br />
<br />
= Conclusion =<br />
In this paper, it was found that gradient masking is a common flaw in many defenses claiming robustness against white box adversarial attacks. This leads to a perceived robustness against adversarial attacks when in reality it results in weaker adversarial image construction. The authors develop three attacks that can overcome gradient masking. With their attacks, they found that actual robustness of 7 out of the 9 defenses proposed in ICLR-2018, is significantly lower. In fact, many defenses were found to be completely ineffective.<br />
<br />
Some future work that can come out of this paper includes avoiding relying on obfuscated gradients for perceived robustness and use the evaluation approach to detect when the attack occurs. Early categorization of attacks using some supervised techniques can also help in critical evaluations of incoming data.<br />
<br />
= Critique =<br />
# The third attack method, reparameterization of the input distortion search space was presented very briefly and at a very high level. Moreover, the one defense proposal they chose to use it against, [Samangouei, 2018] prove to be resilient against the attack. The authors had to resort to one of their other methods to circumvent the defense.<br />
# The BPDA and reparameterization attacks require intrinsic knowledge of the networks. This information is not likely to be available to external users of a network. Most likely, the use-case for these attacks will be in-house to develop more robust networks. This also means that it is still possible to guard against adversarial attack using gradient masking techniques, provided the details of the network are kept secret. <br />
## A notable exception to this case could be applications that are built using open-source (or even published) models that are paired with model-agnostic defense mechanisms. For example, A ResNet-50 using the model-agnostic 'input transformations' technique by [Guo, 2018] may be used in many different image classification tasks, but could still be successfully attacked using BPDA. <br />
# The BPDA algorithm requires replacing a non-linear part of the model with a differentiable approximation. Since different networks are likely to use different transformations, this technique is not plug-and-play. For each network, the attack needs to be manually constructed.<br />
<br />
<br />
= Other Sources =<br />
# Their re-implementation of each of the defenses and implementations of the attacks are available [https://github.com/anishathalye/obfuscated-gradients here].<br />
<br />
= References =<br />
#'''[Madry, 2018]''' Madry, A., Makelov, A., Schmidt, L., Tsipras, D. and Vladu, A., 2017. Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083.<br />
#'''[Buckman, 2018]''' Buckman, J., Roy, A., Raffel, C. and Goodfellow, I., 2018. Thermometer encoding: One hot way to resist adversarial examples.<br />
#'''[Guo, 2018]''' Guo, C., Rana, M., Cisse, M. and van der Maaten, L., 2017. Countering adversarial images using input transformations. arXiv preprint arXiv:1711.00117.<br />
#'''[Xie, 2018]''' Xie, C., Wang, J., Zhang, Z., Ren, Z. and Yuille, A., 2017. Mitigating adversarial effects through randomization. arXiv preprint arXiv:1711.01991.<br />
#'''[song, 2018]''' Song, Y., Kim, T., Nowozin, S., Ermon, S. and Kushman, N., 2017. Pixeldefend: Leveraging generative models to understand and defend against adversarial examples. arXiv preprint arXiv:1710.10766.<br />
#'''[Szegedy, 2013]''' Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I. and Fergus, R., 2013. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199.<br />
#'''[Samangouei, 2018]''' Samangouei, P., Kabkab, M. and Chellappa, R., 2018. Defense-GAN: Protecting classifiers against adversarial attacks using generative models. arXiv preprint arXiv:1805.06605.<br />
#'''[van den Oord, 2016]''' van den Oord, A., Kalchbrenner, N., Espeholt, L., Vinyals, O. and Graves, A., 2016. Conditional image generation with pixelcnn decoders. In Advances in Neural Information Processing Systems (pp. 4790-4798).<br />
#'''[Athalye, 2017]''' Athalye, A. and Sutskever, I., 2017. Synthesizing robust adversarial examples. arXiv preprint arXiv:1707.07397.<br />
#'''[Ma, 2018]''' Ma, Xingjun, Bo Li, Yisen Wang, Sarah M. Erfani, Sudanthi Wijewickrema, Michael E. Houle, Grant Schoenebeck, Dawn Song, and James Bailey. "Characterizing adversarial subspaces using local intrinsic dimensionality." arXiv preprint arXiv:1801.02613 (2018).<br />
# '''[Na, 2018]''' Na, T., Ko, J.H. and Mukhopadhyay, S., 2017. Cascade Adversarial Machine Learning Regularized with a Unified Embedding. arXiv preprint arXiv:1708.02582.<br />
# '''[Papernot et al., 2017]''' Papernot, N., McDaniel, P., Goodfellow, I., Jha, S., Celik, Z. B., and Swami, A. Practical black-box attacks against machine learning. In Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security, ASIA CCS ’17, pp. 506–519, New York, NY, USA, 2017. ACM. ISBN 978-1-4503-4944-4.<br />
# '''[Tramer et al., 2018]''' Tramer, F., Kurakin, A., Papernot, N., Goodfellow, I., Boneh, D., and McDaniel, P. Ensemble adversarial training: Attacks and defenses. International Conference on Learning Representations, 2018.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Obfuscated_Gradients_Give_a_False_Sense_of_Security_Circumventing_Defenses_to_Adversarial_Examples&diff=40358Obfuscated Gradients Give a False Sense of Security Circumventing Defenses to Adversarial Examples2018-11-20T16:40:14Z<p>Npbhatt: /* The Attacks */ Technical contribution regarding reparametrization</p>
<hr />
<div>= Introduction =<br />
Over the past few years, neural network models have been the source of major breakthroughs in a variety of computer vision problems. However, these networks have been shown to be susceptible to adversarial attacks. In these attacks, small humanly-imperceptible changes are made to images (that are originally correctly classified) which causes these models to misclassify with high confidence. These attacks pose a major threat that needs to be addressed before these systems can be deployed on a large scale, especially in safety-critical scenarios. <br />
<br />
The seriousness of this threat has generated major interest in both the design and defense against them. Recently, many new defenses have been proposed that claim robustness against iterative white-box adversarial attacks. This result is somewhat surprising, given that iterative white-box attacks are one of the most difficult classes of adversarial attacks. In this paper, the authors identify a common flaw, masked gradients, in many of these defenses that cause them to ''perceive'' a high accuracy on adversarial images. This flaw is so prevalent, that 7 out of the 9 defenses proposed in the ICLR 2018 conference were found to contain them. The authors develop three attacks, specifically targeting masked gradients, and show that the actual accuracy of these defenses is much lower than claimed. In fact, the majority of these attacks were found to be ineffective against true iterative white box attacks.<br />
<br />
= Methodology =<br />
<br />
The paper assumes a lot of familiarity with adversarial attack literature. The section below briefly explains some key concepts.<br />
<br />
== Background ==<br />
<br />
==== Adversarial Images Mathematically ====<br />
Given an image <math>x</math> and a classifier <math>f(x)</math>, an adversarial image <math>x'</math> satisfies two properties:<br />
# <math>D(x,x') < \epsilon </math><br />
# <math>c(x') \neq c^*(x) </math><br />
<br />
Where <math>D</math> is some distance metric, <math>\epsilon </math> is a small constant, <math>c(x')</math> is the output ''class'' predicted by the model, and <math>c^*(x)</math> is the true class for input x. In words, the adversarial image is a small distance from the original image, but the classifier classifies it incorrectly.<br />
<br />
==== Adversarial Attacks Terminology ====<br />
#Adversarial attacks can be either '''black''' or '''white-box'''. In black box attacks, the attacker has access to the network output only, while white-box attackers have full access to the network, including its gradients, architecture and weights. This makes white-box attackers much more powerful. Given access to gradients, white-box attacks use back propagation to modify inputs (as opposed to the weights) with respect to the loss function.<br />
#In '''untargeted''' attacks, the objective is to ''maximize'' the loss of the true class, <math>x'=x \mathbf{+} \lambda(sign(\nabla_xL(x,c^*(x))))</math>. While in '''targeted''' attacks, the objective is to ''minimize'' loss for a target class <math>c^t(x)</math> that is different from the true class, <math>x'=x \mathbf{-} \epsilon(sign(\nabla_xL(x,c^t(x))))</math>. Here, <math>\nabla_xL()</math> is the gradient of the loss function with respect to the input, <math>\lambda</math> is a small gradient step and <math>sign()</math> is the sign of the gradient.<br />
# An attacker may be allowed to use a single step of back-propagation ('''single step''') or multiple ('''iterative''') steps. Iterative attackers can generate more powerful adversarial images. Typically, to bound iterative attackers a distance measure is used.<br />
<br />
In this paper the authors focus on the more difficult attacks; white-box iterative targeted and untargeted attacks.<br />
<br />
== Obfuscated Gradients ==<br />
If gradients are masked, they cannot be followed to generate adversarial images, gradient masking is known to be an incomplete defense to adversarial images[Papernot et al., 2017; Tramer et al., 2018]. A defense method may appear to be providing robustness, but in reality, the gradients in the network cannot be followed to generate strong adversarial images. Generated adversarial images from these networks are much weaker and when used to evaluate the model robustness five a false sense of security against adversarial attacks. Defenses are designed in a way that the constructed defense inevitably leads to gradient masking as obfuscated gradients. In the defenses proposed in ICLR 2018, there are three ways which defense obfuscate gradients:<br />
<br />
# '''Shattered gradients''': Non-differentiable operations are introduced into the model, causing a gradient to be nonexistent or incorrect. Introduced by using operations where following the gradient doesn't maximize classification loss globally. <br />
# '''Stochastic gradients''': A stochastic process is added into the model at test time, causing the gradients to become randomized. Introduced by either randomly transforming inputs before feeding to the classifier, or randomly permuting the network itself. <br />
# '''Vanishing Gradients ''': Very deep neural networks or those with recurrent connections are used. Because of the vanishing or exploding gradient problem common in these deep networks, effective gradients at the input are small and not very useful. Introduced by using multiple iterations of neural network evaluation, where the output of one network is fed as the input to the next.<br />
<br />
'''Detecting Obfuscated Gradients''':<br />
<br />
The authors propose a number of tests that might help detect when a defense relies on obfuscated gradients.<br />
<br />
Iterative attacks should work better than single-step attacks, since iterative attacks are strictly stronger than single-step attacks.<br />
White-box attacks should perform better than black-box attacks, since the black-box threat model is a strict subset of the white-box threat model.<br />
Attacks with an unbounded distortion metric (e.g. L_2 norm) should find adversarial examples with 100% success.<br />
Optimization-based attacks should perform better than brute-force sampling of nearby inputs (sampling within an ϵ-ball).<br />
These tests may not cover all cases of obfuscated gradients, but they indicate when intuitive properties start to break down. All defenses with obfuscated gradients discussed by the authors fail at least one test.<br />
<br />
== The Attacks ==<br />
To circumvent these gradient masking techniques, the authors propose:<br />
# '''Backward Pass Differentiable Approximation (BPDA)''': For defenses that introduce non-differentiable components, the authors replace it with an approximate function that is differentiable on the backward pass. In a white-box setting, the attacker has full access to any added non-linear transformation and can find its approximation. <br />
# '''Expectation over Transformation [Athalye, 2017]''': For defenses that add some form of test time randomness, the authors propose to use expectation over transformation technique in the backward pass. Rather than moving along the gradient every step, several gradients are sampled and the step is taken in the average direction. This can help with any stochastic misdirection from individual gradients. The technique is similar to using mini-batch gradient descent but applied in the construction of adversarial images.<br />
# '''Re-parameterize the exploration space''': For very deep networks that rely on vanishing or exploding gradients, the authors propose to re-parameterize and search over the range where the gradient does not explode/vanish.<br />
They assume that given a classifier <math display = "inline">f(g(x))</math>, <math display = "inline">g(·)</math> performs some optimization loop to transform the input x to a new input <math display = "inline">\hat x \</math>. Often times, differentiating through <math display = "inline">g(·)</math> yields exploding or vanishing gradients.<br />
<br />
To resolve this, they make a change-of-variable <math display = "inline">x = h(z)</math> for some function <math display = "inline">h(·)</math> such that <math display = "inline">g(h(z)) = h(z)</math> for all z, but <math display = "inline">h(·)</math> is differentiable. This allows them to compute gradients through f(h(z)) and hence circumvent the defense.<br />
<br />
= Main Results =<br />
[[File:Summary_Table.png|600px|center]]<br />
<br />
The table above summarizes the results of their attacks. Attacks are mounted on the same dataset each defense targeted. If multiple datasets were used, attacks were performed on the largest one. Two different distance metrics (<math>\ell_{\infty}</math> and <math>\ell_{2}</math>) were used in the construction of adversarial images. Distance metrics specify how much an adversarial image can vary from an original image. For <math>\ell_{\infty}</math> adversarial images, each pixel is allowed to vary by a maximum amount. For example, <math>\ell_{\infty}=0.031</math> specifies that each pixel can vary by <math>256*0.031=8</math> from its original value. <math>\ell_{2}</math> distances specify the magnitude of the total distortion allowed over all pixels. For MNIST and CIFAR-10, untargeted adversarial images were constructed using the entire test set, while for Imagenet, 1000 test images were randomly selected and used to generate targeted adversarial images. <br />
<br />
Standard models were used in evaluating the accuracy of defense strategies under the attacks,<br />
# MNIST: 5-layer Convolutional Neural Network (99.3% top-1 accuracy)<br />
# CIFAR-10: Wide-Resnet (95.0% top-1 accuracy)<br />
# Imagenet: InceptionV3 (78.0% top-1 accuracy)<br />
<br />
The last column shows the accuracies each defense method achieved over the adversarial test set. Except for [Madry, 2018], all defense methods could only achieve an accuracy of <10%. Furthermore, the accuracy of most methods was 0%. The results of [Samangoui,2018] (double asterisk), show that their approach was not as successful. The authors claim that is is a result of implementation imperfections but theoretically, the defense can be circumvented using their proposed method.<br />
<br />
==== The defense that worked - Adversarial Training [Madry, 2018] ====<br />
<br />
As a defense mechanism, [Madry, 2018] proposes training the neural networks with adversarial images. Although this approach is previously known [Szegedy, 2013] in their formulation, the problem is setup in a more systematic way using a min-max formulation:<br />
\begin{align}<br />
\theta^* = \arg \underset{\theta} \min \mathop{\mathbb{E_x}} \bigg{[} \underset{\delta \in [-\epsilon,\epsilon]}\max L(x+\delta,y;\theta)\bigg{]} <br />
\end{align}<br />
<br />
where <math>\theta</math> is the parameter of the model, <math>\theta^*</math> is the optimal set of parameters and <math>\delta</math> is a small perturbation to the input image <math>x</math> and is bounded by <math>[-\epsilon,\epsilon]</math>. <br />
<br />
Training proceeds in the following way. For each clean input image, a distorted version of the image is found by maximizing the inner maximization problem for a fixed number of iterations. Gradient steps are constrained to fall within the allowed range (projected gradient descent). Next, the classification problem is solved by minimizing the outer minimization problem.<br />
<br />
This approach was shown to provide resilience to all types of adversarial attacks.<br />
<br />
==== How to check for Obfuscated Gradients ====<br />
For future defense proposals, it is recommended to avoid using masked gradients. To assist with this, the authors propose a set of conditions that can help identify if a defense is relying on masked gradients:<br />
# If weaker one-step attacks are performing better than iterative attacks.<br />
# Black-box attacks can find stronger adversarial images compared with white-box attacks.<br />
# Unbounded iterative attacks do not reach 100% success.<br />
# If random brute force attempts are better than gradient-based methods at finding adversarial images.<br />
<br />
= Detailed Results =<br />
<br />
As a case study for evaluating the prevalence of obfuscated gradients, the authors studied the ICLR 2018 non-certified defenses that argue robustness in a white-box threat model. Each of these defenses argues a high robustness to adaptive, white box attacks. It is reported that seven of these nine defenses depend on this phenomenon, and the authors demonstrate that their techniques can completely circumvent six of those (and partially circumvent one) that depend on obfuscated gradients.<br />
<br />
== Non-obfuscated Gradients ==<br />
<br />
==== Cascade Adversarial Training, [Na, 2018] ====<br />
'''Defense''': Similar to the method of [Madry, 2018], the authors of [Na, 2018] propose adversarial training. The main difference is that instead of using iterative methods to generate adversarial examples at each mini-batch, a separate model is first trained and used to generate adversarial images. These adversarial images are used to augment the train set of another model.<br />
<br />
'''Attack''': The authors found that this technique does not use obfuscated gradients. They were not able to reduce the performance of this method. However, they point out that the claimed accuracy is much lower (%15) compared with [Madry, 2018] under the same perturbation setting.<br />
<br />
== Gradient Shattering ==<br />
<br />
==== Thermometer Coding, [Buckman, 2018] ====<br />
'''Defense''': Inspired by the observation that neural networks learn linear boundaries between classes [Goodfellow, 2014] , [Buckman, 2018] sought to break this linearity by explicitly adding a highly non-linear transform at the input of their model. The non-linear transformation they chose was quantizing inputs to binary vectors. The quantization performed was termed thermometer encoding,<br />
<br />
Given an image, for each pixel value <math>x_{i,j,c}</math>, if an <math>l</math> dimensional thermometer code, the <math>kth</math> bit is given by:<br />
\begin{align}<br />
\tau(x_{i,j,c})_k = \bigg{\{}\begin{array}{ll}<br />
1 \space if \thinspace x_{i,j,c} > \dfrac{k}{l} \\<br />
0 \space otherwise \\<br />
\end{array}<br />
\end{align}<br />
Here it is assumed <math>x_{i,j,c} \in [0, 1] </math> and <math>i, j, c</math> are the row, column and channel index of the pixel respectively. This encoding is like one-hot encoding, except all the points (not just one) greater than the target value are set to 1. This quantization technique preserves pairwise ordering between pixels.<br />
<br />
On CIFAR-10, the model gave 50% accuracy against <math>\ell_\infty</math> adversarial images with <math>\epsilon=0.031</math> attacks.<br />
<br />
'''Attack''': The authors attack this model using there BPDA approach. Given the non-linear transformation performed in the forward pass, <math>\tau(x)</math>, they develop a differentiable counterpart,<br />
\begin{align}<br />
\hat{\tau}(x_{i,j,c})_k = \min ( \max (x_{i,j,c} - \frac{k}{l}), 1 )<br />
\end{align}<br />
and use it in place of <math>\tau(x)</math> on the backward pass. With their modifications they were able to bring the accuracy of the model down to 0%.<br />
<br />
==== Input Transformation, [Guo, 2018] ====<br />
'''Defense''':[Gou, 2018] investigated the effect of including different input transformation on the robustness to adversarial images. In particular, they found two techniques provided the greatest resistance: total variance minimization and image quilting. Total variance minimization is a technique that removes high-frequency noise while preserving legitimate edges (good high-frequency components). In image quilting, a large database of image patches from clean images is collected. At test time, input patches, that contain a lot of noise, are replaced with similar but clean patches from the database.<br />
<br />
Both techniques, removed perturbations from adversarial images which provide some robustness to adversarial attacks. The best model achieved 60% accuracy on adversarial images with <math>l_{2}=0.05</math> perturbations. However, both approaches are non-differentiable and contain test time randomness as the modifications made are input dependent. Gradient flow to the input is non-differentiable and random.<br />
<br />
'''Attack''': The authors used the BPDA attack where the input transformations were replaced by an identity function. They were able to bring the accuracy of the model down to 0% under the same type of adversarial attacks.<br />
<br />
==== Local Intrinsic Dimensionality, [Ma, 2018] ====<br />
'''Defense''' Local intrinsic dimensionality (LID) is a distance-based metric that measures the similarity between points in a high dimensional space. Given a set of points, let the distance between sample <math>x</math> and its <math>ith</math> neighbor be <math>r_i(x)</math>, then the LID under the choose distance metric is given by,<br />
<br />
\begin{align}<br />
LID(x) = - \bigg{(} \frac{1}{k}\sum^k_{i=1}log \frac{r_i(x)}{r_k(x)} \bigg{)}^{-1}<br />
\end{align}<br />
where k is the number of nearest neighbors considered, <math>r_k(x)</math> is the maximum distance to any of the neighbors in the set k. <br />
<br />
First, <math>L_2</math> distances for all training and adversarial images. Next, the LID scores for each train and adversarial images were calculated. It was found that LID scores for adversarial images were significantly larger than those of clean images. Base on these results, the a separate classifier was created that can be used to detect adversarial inputs. [Ma, 2018] claim that this is not a defense method, but a method to study the properties of adversarial images.<br />
<br />
'''Attack''': Instead of attacking this method, the authors show that this method is not able to detect, and is therefore venerable to, attacks of the [Carlini and Wagner, 2017a] variety.<br />
<br />
== Stochastic Gradients ==<br />
<br />
==== Stochastic Activation Pruning, [Dhillon, 2018] ====<br />
'''Defense''': [Dhillon, 2018] use test time randomness in their model to guard against adversarial attacks. Because adversarial perturbations are like noises, randomly dropping activation can decrease their collective impact on the classifier. Within a layer, the activities of component nodes are randomly dropped with a probability proportional to its absolute value. The rest of the activation are scaled up to preserve accuracies. This is akin to test time drop-out. This technique was found to drop accuracy slightly on clean images, but improved performance on adversarial images.<br />
<br />
'''Attack''': The authors used the expectation over transformation attack to get useful gradients out of the model. With their attack, they were able to reduce the accuracy of this method down to 0% on CIFAR-10.<br />
<br />
==== Mitigation Through Randomization, [Xie, 2018] ====<br />
'''Defense''': [Xie, 2018] Add a randomization layer to their model to help defend against adversarial attacks. For an input image of size [299,299], first the image is randomly re-scaled to <math>r \in [299,331]</math>. Next, the image is zero-padded to fix the dimension of the modified input. This modified input is then fed into a regular classifier. The authors claim that is strategy can provide an accuracy of 32.8% against ensemble attack patterns (fixed distortions, but many of them which are picked randomly). Because of the introduced randomness, the authors claim the model builds some robustness to other types of attacks as well.<br />
<br />
'''Attack''': The EOT method was used to build adversarial images to attack this model. With their attack, the authors were able to bring the accuracy of this model down to 0% using <math>L_{\infty}(\epsilon=0.031)</math> perturbations.<br />
<br />
== Vanishing and Exploding Gradients ==<br />
<br />
==== Pixel Defend, [Song, 2018] ====<br />
'''Defense''': [Song, 2018] argues that adversarial images lie in low probability regions of the data manifold. Therefore, one way to handle adversarial attacks is to project them back into the high probability regions before feeding them into a classifier. They chose to do this by using a generative model (pixelCNN) in a denoising capacity. A PixelCNN model directly estimates the conditional probability of generating an image pixel by pixel [Van den Oord, 2016],<br />
<br />
\begin{align}<br />
p(\mathbf{x}= \prod_{i=1}^{n^2} p(x_i|x_0,x_1 ....x_{i-1}))<br />
\end{align}<br />
<br />
The reason for choosing this model is the long iterative process of generation. In the backward pass, following the gradient, all the way to the input would not be possible because of the vanishing/exploding gradient<br />
problem of deep networks. The proposed model was able to obtain an accuracy of 46% on CIFAR-10 images with <math>l_{\infty} (\epsilon=0.031) </math> perturbations.<br />
<br />
'''Attack''': The model was attacked using the BPDA technique where back-propagating though the pixelCNN was replaced with an identity function. With this approach, the authors were able to bring down the accuracy to 9% under the same kind of perturbations.<br />
<br />
==== Defense-GAN, [Samangouei, 2018] ====<br />
<br />
Before classifying the samples, Defense-GAN projects them onto the data manifold utilizing GAN. The intuition behind this approach is almost similar to that of PixelDefend. It uses GAN instead of pixel CNN.<br />
<br />
The authors used MNIST because CIFAR-10 is not argued secure. They found adversarial examples exist in the generator manifold, and they can construct an example. A perfect projector will not be able to modify this example, however, an imperfect gradient descent approach does not perfectly preserve manifold points. Therefore, the authors attacked DEFENSE-GAN using BPDA, but can only get a 45% success rate.<br />
<br />
<br />
= Conclusion =<br />
In this paper, it was found that gradient masking is a common flaw in many defenses claiming robustness against white box adversarial attacks. This leads to a perceived robustness against adversarial attacks when in reality it results in weaker adversarial image construction. The authors develop three attacks that can overcome gradient masking. With their attacks, they found that actual robustness of 7 out of the 9 defenses proposed in ICLR-2018, is significantly lower. In fact, many defenses were found to be completely ineffective.<br />
<br />
Some future work that can come out of this paper includes avoiding relying on obfuscated gradients for perceived robustness and use the evaluation approach to detect when the attack occurs. Early categorization of attacks using some supervised techniques can also help in critical evaluations of incoming data.<br />
<br />
= Critique =<br />
# The third attack method, reparameterization of the input distortion search space was presented very briefly and at a very high level. Moreover, the one defense proposal they chose to use it against, [Samangouei, 2018] prove to be resilient against the attack. The authors had to resort to one of their other methods to circumvent the defense.<br />
# The BPDA and reparameterization attacks require intrinsic knowledge of the networks. This information is not likely to be available to external users of a network. Most likely, the use-case for these attacks will be in-house to develop more robust networks. This also means that it is still possible to guard against adversarial attack using gradient masking techniques, provided the details of the network are kept secret. <br />
## A notable exception to this case could be applications that are built using open-source (or even published) models that are paired with model-agnostic defense mechanisms. For example, A ResNet-50 using the model-agnostic 'input transformations' technique by [Guo, 2018] may be used in many different image classification tasks, but could still be successfully attacked using BPDA. <br />
# The BPDA algorithm requires replacing a non-linear part of the model with a differentiable approximation. Since different networks are likely to use different transformations, this technique is not plug-and-play. For each network, the attack needs to be manually constructed.<br />
<br />
<br />
= Other Sources =<br />
# Their re-implementation of each of the defenses and implementations of the attacks are available [https://github.com/anishathalye/obfuscated-gradients here].<br />
<br />
= References =<br />
#'''[Madry, 2018]''' Madry, A., Makelov, A., Schmidt, L., Tsipras, D. and Vladu, A., 2017. Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083.<br />
#'''[Buckman, 2018]''' Buckman, J., Roy, A., Raffel, C. and Goodfellow, I., 2018. Thermometer encoding: One hot way to resist adversarial examples.<br />
#'''[Guo, 2018]''' Guo, C., Rana, M., Cisse, M. and van der Maaten, L., 2017. Countering adversarial images using input transformations. arXiv preprint arXiv:1711.00117.<br />
#'''[Xie, 2018]''' Xie, C., Wang, J., Zhang, Z., Ren, Z. and Yuille, A., 2017. Mitigating adversarial effects through randomization. arXiv preprint arXiv:1711.01991.<br />
#'''[song, 2018]''' Song, Y., Kim, T., Nowozin, S., Ermon, S. and Kushman, N., 2017. Pixeldefend: Leveraging generative models to understand and defend against adversarial examples. arXiv preprint arXiv:1710.10766.<br />
#'''[Szegedy, 2013]''' Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I. and Fergus, R., 2013. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199.<br />
#'''[Samangouei, 2018]''' Samangouei, P., Kabkab, M. and Chellappa, R., 2018. Defense-GAN: Protecting classifiers against adversarial attacks using generative models. arXiv preprint arXiv:1805.06605.<br />
#'''[van den Oord, 2016]''' van den Oord, A., Kalchbrenner, N., Espeholt, L., Vinyals, O. and Graves, A., 2016. Conditional image generation with pixelcnn decoders. In Advances in Neural Information Processing Systems (pp. 4790-4798).<br />
#'''[Athalye, 2017]''' Athalye, A. and Sutskever, I., 2017. Synthesizing robust adversarial examples. arXiv preprint arXiv:1707.07397.<br />
#'''[Ma, 2018]''' Ma, Xingjun, Bo Li, Yisen Wang, Sarah M. Erfani, Sudanthi Wijewickrema, Michael E. Houle, Grant Schoenebeck, Dawn Song, and James Bailey. "Characterizing adversarial subspaces using local intrinsic dimensionality." arXiv preprint arXiv:1801.02613 (2018).<br />
# '''[Na, 2018]''' Na, T., Ko, J.H. and Mukhopadhyay, S., 2017. Cascade Adversarial Machine Learning Regularized with a Unified Embedding. arXiv preprint arXiv:1708.02582.<br />
# '''[Papernot et al., 2017]''' Papernot, N., McDaniel, P., Goodfellow, I., Jha, S., Celik, Z. B., and Swami, A. Practical black-box attacks against machine learning. In Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security, ASIA CCS ’17, pp. 506–519, New York, NY, USA, 2017. ACM. ISBN 978-1-4503-4944-4.<br />
# '''[Tramer et al., 2018]''' Tramer, F., Kurakin, A., Papernot, N., Goodfellow, I., Boneh, D., and McDaniel, P. Ensemble adversarial training: Attacks and defenses. International Conference on Learning Representations, 2018.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Countering_Adversarial_Images_Using_Input_Transformations&diff=40351Countering Adversarial Images Using Input Transformations2018-11-20T16:02:45Z<p>Npbhatt: Technical Contribution: elaborated important conclusions from the paper; minor grammar edits.</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.<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 />
[[File:Attack.PNG|200px |]],<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 />
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.<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 defences. 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 defence 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 />
In particular, total variation minimization involves performing complex minimization on a function which is random, inherently. Image quilting involves a discrete variable that conducts selection of a patch from the database, which is a non-differentiable operation.<br />
<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 random selection of a particular K<br />
nearest neighbor uniformly, but in a random manner. This inherent randomness makes it<br />
difficult to attack the model. The implication here is that the adversary must find a perturbation that alters<br />
the prediction for the entire distribution of images that could be used as input. This is<br />
harder than perturbing a single image.<br />
<br />
<br />
Thus, it is also concluded that randomness is particularly important in developing strong defenses. 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 />
=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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Robot_Learning_in_Homes:_Improving_Generalization_and_Reducing_Dataset_Bias&diff=40233Robot Learning in Homes: Improving Generalization and Reducing Dataset Bias2018-11-20T03:42:22Z<p>Npbhatt: Grammar and formatting edits.</p>
<hr />
<div>==Introduction==<br />
<br />
<br />
Using data-driven approaches in robotics has increased in the last decade. Instead of using hand-designed models, these data-driven approaches work on large-scale datasets and learn appropriate policies that map from high-dimensional observations to actions. Since collecting data using an actual robot in real-time is very expensive, most of the data-driven approaches in robotics use simulators in order to collect simulated data. The concern which arises here is whether these approaches have the capability to be robust enough to domain shift and to be used for real-world data. It is an undeniable fact that there is a wide reality gap between simulators and the real world.<br />
<br />
This has motivated the robotics community to increase their efforts in collecting real-world physical interaction data for a variety of tasks. This effort has been accelerated by the declining costs of hardware. This approach has been quite successful at tasks such as grasping, pushing, poking and imitation learning. However, the major problem is that the performance of these learning models is not good enough and tends to plateau fast. Furthermore, robotic action data did not lead to similar gains in other areas such as computer vision and natural language processing. As the paper claimed, the solution for all of these obstacles is using “real data”. Current robotic datasets lack diversity of environment. Learning-based approaches need to move out of simulators in the labs and go to real environments such as real homes so that they can learn from real datasets. <br />
<br />
Like every other process, the process of collecting real world data is made difficult by a number of problems. First, there is a need for cheap and compact robots to collect data in homes but current industrial robots (i.e. Sawyer and Baxter) are too expensive. Secondly, cheap robots are not accurate enough to collect reliable data. Also, there is a lack of constant supervision of data collection in homes. Finally, there is also a circular dependency problem in home-robotics: there is lack of real-world data which are needed to improve current robots, but current robots are not good enough to collect reliable data in homes. These challenges in addition to some other external factors will likely result in noisy data collection. In this paper, a first systematic effort has been presented for collecting a dataset inside homes. In accomplishing this goal, the authors: <br />
<br />
1. Build a cheap robot costing less than USD 3K which is appropriate for use in homes<br />
<br />
2. Collect training data in 6 different homes and testing data in 3 homes<br />
<br />
3. Propose a method for modeling the noise in the labeled data<br />
<br />
4. Demonstrate that the diversity in the collected data provides superior performance and requires little-to-no domain adaptation<br />
<br />
[[File:aa1.PNG|600px|thumb|center|]]<br />
<br />
==Overview==<br />
<br />
This paper emphasizes the importance of diversifying the data for robotic learning in order to have a greater generalization, by focusing on the task of grasping. A diverse dataset also allows for removing biases in the data. By considering these facts, the paper argues that even for simple tasks like grasping, datasets which are collected in labs suffer from strong biases such as simple backgrounds and same environment dynamics. Hence, the learning approaches cannot generalize the models and work well on real datasets.<br />
<br />
As a future possibility, there would be a need for having a low-cost robot to collect large-scale data inside a huge number of homes. For this reason, they introduced a customized mobile manipulator. They used a Dobot Magician which is a robotic arm mounted on a Kobuki which is a low-cost mobile robot base equipped with sensors such as bumper contact sensors and wheel encoders. The resulting robot arm has five degrees of freedom (DOF) (x, y, z, roll, pitch). The gripper is a two-fingered electric gripper with a 0.3kg payload. They also add an Intel R200 RGBD camera to their robot which is at a height of 1m above the ground. An Intel Core i5 processor is also used as an on-board laptop to perform all the processing. The whole system can run for 1.5 hours with a single charge.<br />
<br />
As there is always a trade-off, when we gain a low-cost robot, we are actually losing accuracy for controlling it. So, the low-cost robot which is built from cheaper components than the expensive setups such as Baxter and Sawyer suffers from higher calibration errors and execution errors. This means that the dataset collected with this approach is diverse and huge but it has noisy labels. To illustrate, consider when the robot wants to grasp at location <math> {(x, y)}</math>. Since there is a noise in the execution, the robot may perform this action in the location <math> {(x + \delta_{x}, y+ \delta_{y})}</math> which would assign the success or failure label of this action to a wrong place. Therefore, to solve the problem, they used an approach to learn from noisy data. They modeled noise as a latent variable and used two networks, one for predicting the noise and one for predicting the action to execute.<br />
<br />
==Learning on low-cost robot data==<br />
<br />
This paper uses patch grasping framework in its proposed architecture. Also, as mentioned before, there is a high tendency for noisy labels in the datasets which are collected by inaccurate and cheap robots. The cause of the noise in the labels could be due to the hardware execution error, inaccurate kinematics, camera calibration, proprioception, wear, and tear, etc. Here are more explanations about different parts of the architecture in order to disentangle the noise of the low-cost robot’s actual and commanded executions.<br />
<br />
===Grasping Formulation===<br />
<br />
Planar grasping is the object of interest in this architecture. It means that all the objects are grasped at the same height and vertical to the ground (ie: a fixed end-effector pitch). The final goal is to find <math>{(x, y, \theta)}</math> given an observation <math> {I}</math> of the object, where <math> {x}</math> and <math> {y}</math> are the translational degrees of freedom and <math> {\theta}</math> is the rotational degrees of freedom (roll of the end-effector). For the purpose of comparison, they used a model which does not predict the <math>{(x, y, \theta)}</math> directly from the image <math> {I}</math>, but samples several smaller patches <math> {I_{P}}</math> at different locations <math>{(x, y)}</math>. Thus, the angle of grasp <math> {\theta}</math> is predicted from these patches. Also, in order to have multi-modal predictions, discrete steps of the angle <math> {\theta}</math>, <math> {\theta_{D}}</math> is used. <br />
<br />
Hence, each datapoint consists of an image <math> {I}</math>, the executed grasp <math>{(x, y, \theta)}</math> and the grasp success/failure label g. Then, the image <math> {I}</math> and the angle <math> {\theta}</math> are converted to image patch <math> {I_{P}}</math> and angle <math> {\theta_{D}}</math>. Then, to minimize the classification error, a binary cross entropy loss is used which minimizes the error between the predicted and ground truth label <math> g </math>. A convolutional neural network with weight initialization from pre-training on Imagenet is used for this formulation.<br />
<br />
===Modeling noise as latent variable===<br />
<br />
In order to tackle the problem of inaccurate position control and calibration due to cheap robot, they found a structure in the noise which is dependent on the robot and the design. They modeled this structure of noise as a latent variable and decoupled during training. The approach is shown in figure 2: <br />
<br />
<br />
[[File:aa2.PNG|600px|thumb|center|]]<br />
<br />
<br />
The grasp success probability for image patch <math> {I_{P}}</math> at angle <math> {\theta_{D}}</math> is represented as <math> {P(g|I_{P},\theta_{D}; \mathcal{R} )}</math> where <math> \mathcal{R}</math> represents environment variables that can add noise to the system.<br />
<br />
The conditional probability of grasping for this model is computed by:<br />
<br />
<br />
\[ { P(g|I_{P},\theta_{D}, \mathcal{R} ) = ∑_{( \widehat{I_P} \in \mathcal{P})} P(g│z=\widehat{I_P},\theta_{D},\mathcal{R}) \cdot P(z=\widehat{I_P} | \theta_{D},I_P,\mathcal{R})} \]<br />
<br />
<br />
Here, <math> {z}</math> models the latent variable of the actual patch executed, and <math>\widehat{I_P}</math> belongs to a set of possible neighboring patches <math> \mathcal{P}</math>.<math> P(z=\widehat{I_P}|\theta_D,I_P,\mathcal{R})</math> shows the noise which can be caused by <math>\mathcal{R}</math> variables and is implemented as the Noise Modelling Network (NMN). <math> {P(g│z=\widehat{I_P},\theta_{D}, \mathcal{R} )}</math> shows the grasp prediction probability given the true patch and is implemented as the Grasp Prediction Network (GPN). The overall Robust-Grasp model is computed by marginalizing GPN and NMN.<br />
<br />
===Learning the latent noise model===<br />
<br />
They assume that <math> {z}</math> is conditionally independent of the local patch-specific variables <math> {(I_{P}, \theta_{D})}</math>. To estimate the latent variable <math> {z}</math> given the global information <math>\mathcal{R}</math>, i.e <math> P(z=\widehat{I_P}|\theta_D,I_P,\mathcal{R}) \equiv P(z=\widehat{I_P}|\mathcal{R})</math>. They used direct optimization to learn both NMN and GPN with noisy labels. The entire image of the scene and the environment information are the inputs of the NMN, as well as robot ID and raw-pixel grasp location.. The output of the NMN is the probability distribution of the actual patches where the grasps are executed. Finally, a binary cross entropy loss is applied to the marginalized output of these two networks and the true grasp label g.<br />
<br />
===Training details===<br />
<br />
They implemented their model in PyTorch using a pretrained ResNet-18 model. They concatenated 512 dimensional ResNet feature with a 1-hot vector of robot ID and the raw pixel location of the grasp for their NMN. Also, the inputs of the GPN are the original noisy patch plus 8 other equidistant patches from the original one.<br />
Their training process starts with training only GPN over 5 epochs of the data. Then, the NMN and the marginalization operator are added to the model. So, they train NMN and GPN simultaneously for the other 25 epochs.<br />
<br />
==Results==<br />
<br />
In the results part of the paper, they show that collecting dataset in homes is essential for generalizing learning from unseen environments. They also show that modelling the noise in their Low-Cost Arm (LCA) can improve grasping performance.<br />
They collected data in parallel using multiple robots in 6 different homes, as shown in Figure 3. They used an object detector (tiny-YOLO) as the input data were unstructured due to LCA limited memory and computational capabilities. With an object location detected, class information was discarded, and a grasp was attempted. The grasp location in 3D was computed using PointCloud data. They scattered different objects in homes within 2m area to prevent collision of the robot with obstacles and let the robot move randomly and grasp objects. Finally, they collected a dataset with 28K grasp results.<br />
<br />
[[File:aa3.PNG|600px|thumb|center|]]<br />
<br />
To evaluate their approach in a more quantitative way, they used three test settings:<br />
<br />
- The first one is a binary classification or held-out data. The test set is collected by performing random grasps on objects. They measure the performance of binary classification by predicting the success or failure of grasping, given a location and the angle. Using binary classification allows for testing a lot of models without running them on real robots. They collected two held-out datasets using LCA in lab and homes and the dataset for Baxter robot.<br />
<br />
- The second one is Real Low-Cost Arm (Real-LCA). Here, they evaluate their model by running it in three unseen homes. They put 20 new objects in these three homes in different orientations. Since the objects and the environments are completely new, this tests could measure the generalization of the model.<br />
<br />
- The third one is Real Sawyer (Real-Sawyer). They evaluate the performance of their model by running the model on the Sawyer robot which is more accurate than the LCA. They tested their model in the lab environment to show that training models with the datasets collected from homes can improve the performance of models even in lab environments.<br />
<br />
They used baselines for both their data which is collected in homes and their model which is Robust-Grasp. They used two datasets for the baseline. The dataset collected by (Lab-Baxter) and the dataset collected by their LCA in the lab (Lab-LCA).<br />
They compared their Robust-Grasp model with the noise independent patch grasping model (Patch-Grasp) [4]. They also compared their data and model with DexNet-3.0 (DexNet) for a strong real-world grasping baseline.<br />
<br />
===Experiment 1: Performance on held-out data===<br />
<br />
Table 1 shows that the models trained on lab data cannot generalize to the Home-LCA environment. However, the model trained on Home-LCA has a good performance on both lab data and home environment.<br />
<br />
[[File:aa4.PNG|600px|thumb|center|]]<br />
<br />
===Experiment 2: Performance on Real LCA Robot===<br />
<br />
In table 2, the performance of the Home-LCA is compared against a pre-trained DexNet and the model trained on the Lab-Baxter. Training on the Home-LCA dataset performs 43.7% better than training on the Lab-Baxter dataset and 33% better than DexNet. The low performance of DexNet can be described by the possible noise in the depth images that are caused by the natural light. DexNet, which requires high quality depth sensing, cannot perform well. By using cheap commodity RGBD cameras in LCA, the noise in the depth images is not a matter of concern, as the model has no expectation of high quality.<br />
<br />
[[File:aa5.PNG|600px|thumb|center|]]<br />
<br />
===Performance on Real Sawyer===<br />
<br />
To compare the performance of the Robust-Grasp model against the Patch-Grasp model without collecting noise-free data, they used Lab-Baxter for bench-marking, which is an accurate and better calibrated robot. The Sawyer robot is used for testing to ensure that the testing robot is different from both training robots. As shown in Table 3, the Robust-Grasp model trained on Home-LCA outperforms the Patch-Grasp model and achieves 77.5% accuracy. This accuracy is similar to several recent papers, however, this model was trained and tested in different environment. The Robust-Grasp model also outperforms the Patch-Grasp by about 4% on binary classification. Furthermore, the visualizations of predicted noise corrections in Figure 4 shows that the corrections depend on both the pixel locations of the noisy grasp and the robot.<br />
<br />
[[File:aa6.PNG|600px|thumb|center|]]<br />
<br />
[[File:aa7.PNG|600px|thumb|center|]]<br />
<br />
==Related work==<br />
<br />
Over the last few years, the interest of scaling up robot learning with large scale datasets has been increased. Hence, many papers were published in this area. A hand annotated grasping dataset, a self-supervised grasping dataset, and grasping using reinforcement learning are some examples of using large scale datasets for grasping. The work mentioned above used high-cost hardware and data labeling mechanisms. There were also many papers that worked on other robotic tasks like material recognition, pushing objects and manipulating a rope. However, none of these papers worked on real data in real environments like homes, they all used lab data.<br />
<br />
Furthermore, since grasping is one of the basic problems of robotic, there were some efforts to improve grasping. Classic approaches focused on physics-based issues of grasping and required 3D models of the objects. However, recent works focused on data-driven approaches which learn from visual observations to grasp objects. Simulation and real-world robots are both required for large-scale data collection. A versatile grasping model was proposed to achieve a 90% performance for a bin-picking task. The point here is that they usually require high quality depth as input which seems to be a barrier for practical use of robots in real environments.<br />
<br />
Most labs use industrial robots or standard collaborative hardware for their experiments. Therefore, there is few research that used low cost robots. One of the examples is learning using a cheap inaccurate robot for stack multiple blocks, although it is not clear whether learning approaches are used in it alongside mapping and planning.<br />
<br />
Learning from noisy inputs is another challenge specifically in computer vision. A controversial question which is often raised in this area is whether learning from noise can improve the performance. Some works show it could have bad effects on the performance; however, some other works find it valuable when the noise is dependent on the environment. In this paper, they used a model that can exploit the noise and learn a better grasping model.<br />
<br />
==Conclusion==<br />
<br />
All in all, the paper presents an approach for collecting large-scale robot data in real home environments. They implemented their approach by using a mobile manipulator which is a lot cheaper than the existing industrial robots. They collected a dataset of 28K grasps in six different homes. In order to solve the problem of noisy labels which were caused by their inaccurate robots, they presented a framework to factor out the noise in the data. They tested their model by physically grasping 20 new objects in three new homes and in the lab. The model trained with home dataset showed 43.7% improvement over the models trained with lab data. Their results also showed that their model can improve the grasping performance even in lab environments. They also demonstrated that their architecture for modeling the noise improved the performance by about 10%.<br />
<br />
==Critiques==<br />
<br />
This paper does not contain a significant algorithmic contribution. They are just combining a large number of data engineering techniques for the robot learning problem. The authors claim that they have obtained 43.7% more accuracy than baseline models, but it does not seem to be a fair comparison as the data collection happened in simulated settings in the lab for other methods, whereas the authors use the home dataset. The authors must have also discussed safety issues when training robots in real environments as against simulated environments like labs. The authors are encouraging other researchers to look outside the labs, but are not discussing the critical safety issues in this approach.<br />
<br />
Another strange finding is that the paper mentions that they "follow a model architecture similar to [Pinto and Gupta [4]]," however, the proposed model is in fact a fine tuned resnet-18 architecture. Pinto and Gupta, implement a version similar to AlexNet as shown below in Figure 5.<br />
<br />
[[File:Figure_5_PandG.JPG | 450px|thumb|center|Figure 5: AlexNet architecture implemented in Pinto and Gupta [4].]]<br />
<br />
<br />
The paper argues that the dataset collected by the LCA is noisy, since the robot is cheap and inaccurate. It further asserts that in order to handle the noise in the dataset, they can model the noise as a latent variable and their model can improve the performance of grasping. Although learning from noisy data and achieving a good performance is valuable, it is better that they test their noise modeling network for other robots as well. Since their noise modelling network takes robot information as an input, it would be a good idea to generalize it by testing it using different inaccurate robots to ensure that it would perform well.<br />
<br />
They did not mention other aspects of their comparison, for example they could mention their training time compared to other models or the size of other datasets.<br />
<br />
==References==<br />
<br />
#Josh Tobin, Rachel Fong, Alex Ray, Jonas Schneider, Wojciech Zaremba, and Pieter Abbeel. "Domain randomization for transferring deep neural networks from simulation to the real world." 2017. URL https://arxiv.org/abs/1703.06907.<br />
#Xue Bin Peng, Marcin Andrychowicz, Wojciech Zaremba, and Pieter Abbeel. "Sim-to-real transfer of robotic control with dynamics randomization." arXiv preprint arXiv:1710.06537,2017.<br />
#Lerrel Pinto, Marcin Andrychowicz, Peter Welinder, Wojciech Zaremba, and Pieter Abbeel. "Asymmetric actor critic for image-based robot learning." Robotics Science and Systems, 2018.<br />
#Lerrel Pinto and Abhinav Gupta. "Supersizing self-supervision: Learning to grasp from 50k tries and 700 robot hours." CoRR, abs/1509.06825, 2015. URL http://arxiv.org/abs/1509. 06825.<br />
#Adithyavairavan Murali, Lerrel Pinto, Dhiraj Gandhi, and Abhinav Gupta. "CASSL: Curriculum accelerated self-supervised learning." International Conference on Robotics and Automation, 2018.<br />
# Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. "End-to-end training of deep visuomotor policies." The Journal of Machine Learning Research, 17(1):1334–1373, 2016.<br />
#Sergey Levine, Peter Pastor, Alex Krizhevsky, and Deirdre Quillen. "Learning hand-eye coordination for robotic grasping with deep learning and large scale data collection." CoRR, abs/1603.02199, 2016. URL http://arxiv.org/abs/1603.02199.<br />
#Pulkit Agarwal, Ashwin Nair, Pieter Abbeel, Jitendra Malik, and Sergey Levine. "Learning to poke by poking: Experiential learning of intuitive physics." 2016. URL http://arxiv.org/ abs/1606.07419<br />
#Chelsea Finn, Ian Goodfellow, and Sergey Levine. "Unsupervised learning for physical interaction through video prediction." In Advances in neural information processing systems, 2016.<br />
#Ashvin Nair, Dian Chen, Pulkit Agrawal, Phillip Isola, Pieter Abbeel, Jitendra Malik, and Sergey Levine. "Combining self-supervised learning and imitation for vision-based rope manipulation." International Conference on Robotics and Automation, 2017.<br />
#Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. "Revisiting unreasonable effectiveness of data in deep learning era." ICCV, 2017.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Robot_Learning_in_Homes:_Improving_Generalization_and_Reducing_Dataset_Bias&diff=40230Robot Learning in Homes: Improving Generalization and Reducing Dataset Bias2018-11-20T03:33:16Z<p>Npbhatt: Techincal Contribution - Added critique regarding model architecture.</p>
<hr />
<div>==Introduction==<br />
<br />
<br />
Using data-driven approaches in robotics has increased in the last decade. Instead of using hand-designed models, these data-driven approaches work on large-scale datasets and learn appropriate policies that map from high-dimensional observations to actions. Since collecting data using an actual robot in real-time is very expensive, most of the data-driven approaches in robotics use simulators in order to collect simulated data. The concern which arises here is whether these approaches have the capability to be robust enough to domain shift and to be used for real-world data. It is an undeniable fact that there is a wide reality gap between simulators and the real world.<br />
<br />
This has motivated the robotics community to increase their efforts in collecting real-world physical interaction data for a variety of tasks. This effort has been accelerated by the declining costs of hardware. This approach has been quite successful at tasks such as grasping, pushing, poking and imitation learning. However, the major problem is that the performance of these learning models is not good enough and tends to plateau fast. Furthermore, robotic action data did not lead to similar gains in other areas such as computer vision and natural language processing. As the paper claimed, the solution for all of these obstacles is using “real data”. Current robotic datasets lack diversity of environment. Learning-based approaches need to move out of simulators in the labs and go to real environments such as real homes so that they can learn from real datasets. <br />
<br />
Like every other process, the process of collecting real world data is made difficult by a number of problems. First, there is a need for cheap and compact robots to collect data in homes but current industrial robots (i.e. Sawyer and Baxter) are too expensive. Secondly, cheap robots are not accurate enough to collect reliable data. Also, there is a lack of constant supervision of data collection in homes. Finally, there is also a circular dependency problem in home-robotics: there is lack of real-world data which are needed to improve current robots, but current robots are not good enough to collect reliable data in homes. These challenges in addition to some other external factors will likely result in noisy data collection. In this paper, a first systematic effort has been presented for collecting a dataset inside homes. In accomplishing this goal, the authors: <br />
<br />
-Build a cheap robot costing less than USD 3k which is appropriate for use in homes<br />
<br />
-Collect training data in 6 different homes and testing data in 3 homes<br />
<br />
-Propose a method for modeling the noise in the labeled data<br />
<br />
-Demonstrate that the diversity in the collected data provides superior performance and requires little-to-no domain adaptation<br />
<br />
[[File:aa1.PNG|600px|thumb|center|]]<br />
<br />
==Overview==<br />
<br />
<br />
This paper emphasizes the importance of diversifying the data for robotic learning in order to have a greater generalization, by focusing on the task of grasping. A diverse dataset also allows for removing biases in the data. By considering these facts, the paper argues that even for simple tasks like grasping, datasets which are collected in labs suffer from strong biases such as simple backgrounds and same environment dynamics. Hence, the learning approaches cannot generalize the models and work well on real datasets.<br />
<br />
As a future possibility, there would be a need for having a low-cost robot to collect large-scale data inside a huge number of homes. For this reason, they introduced a customized mobile manipulator. They used a Dobot Magician which is a robotic arm mounted on a Kobuki which is a low-cost mobile base. The resulting robot arm has five degrees of freedom (DOF) (x, y, z, roll, pitch). The gripper is a two-fingered electric gripper with a 0.3kg payload. They also add an Intel R200 RGBD camera to their robot which is at a height of 1m above the ground. An Intel Core i5 processor is also used as an onboard laptop to perform all the processing. The whole system can run for 1.5 hours with a single charge.<br />
<br />
As there is always a trade-off, when we gain a low-cost robot, we are actually losing accuracy for controlling it. So, the low-cost robot which is built from cheaper components than the expensive setups such as Baxter and Sawyer suffers from higher calibration errors and execution errors. This means that the dataset collected with this approach is diverse and huge but it has noisy labels. To illustrate, consider when the robot wants to grasp at location <math> {(x, y)}</math>. Since there is a noise in the execution, the robot may perform this action in the location <math> {(x + \delta_{x}, y+ \delta_{y})}</math> which would assign the success or failure label of this action to a wrong place. Therefore, to solve the problem, they used an approach to learn from noisy data. They modeled noise as a latent variable and used two networks, one for predicting the noise and one for predicting the action to execute.<br />
<br />
==Learning on low-cost robot data==<br />
<br />
This paper uses patch grasping framework in its proposed architecture. Also, as mentioned before, there is a high tendency for noisy labels in the datasets which are collected by inaccurate and cheap robots. The cause of the noise in the labels could be due to the hardware execution error, inaccurate kinematics, camera calibration, proprioception, wear, and tear, etc. Here are more explanations about different parts of the architecture in order to disentangle the noise of the low-cost robot’s actual and commanded executions.<br />
<br />
<br />
===Grasping Formulation===<br />
<br />
Planar grasping is the object of interest in this architecture. It means that all the objects are grasped at the same height and vertical to the ground (ie: a fixed end-effector pitch). The final goal is to find <math>{(x, y, \theta)}</math> given an observation <math> {I}</math> of the object, where <math> {x}</math> and <math> {y}</math> are the translational degrees of freedom and <math> {\theta}</math> is the rotational degrees of freedom (roll of the end-effector). For the purpose of comparison, they used a model which does not predict the <math>{(x, y, \theta)}</math> directly from the image <math> {I}</math>, but samples several smaller patches <math> {I_{P}}</math> at different locations <math>{(x, y)}</math>. Thus, the angle of grasp <math> {\theta}</math> is predicted from these patches. Also, in order to have multimodal predictions, discrete steps of the angle <math> {\theta}</math>, <math> {\theta_{D}}</math> is used. <br />
<br />
Hence, each datapoint consists of an image <math> {I}</math>, the executed grasp <math>{(x, y, \theta)}</math> and the grasp success/failure label g. Then, the image <math> {I}</math> and the angle <math> {\theta}</math> are converted to image patch <math> {I_{P}}</math> and angle <math> {\theta_{D}}</math>. Then, to minimize the classification error, a binary cross entropy loss is used which minimizes the error between the predicted and ground truth label <math> g </math>. A convolutional neural network with weight initialization from pre-training on Imagenet is used for this formulation.<br />
<br />
===Modeling noise as latent variable===<br />
<br />
In order to tackle the problem of inaccurate position control and calibration due to cheap robot, they found a structure in the noise which is dependent on the robot and the design. They modelled this structure of noise as a latent variable and decoupled during training. The approach is shown in figure 2: <br />
<br />
<br />
[[File:aa2.PNG|600px|thumb|center|]]<br />
<br />
<br />
<br />
The grasp success probability for image patch <math> {I_{P}}</math> at angle <math> {\theta_{D}}</math> is represented as <math> {P(g|I_{P},\theta_{D}; \mathcal{R} )}</math> where <math> \mathcal{R}</math> represents environment variables that can add noise to the system.<br />
<br />
The conditional probability of grasping for this model is computed by:<br />
<br />
<br />
\[ { P(g|I_{P},\theta_{D}, \mathcal{R} ) = ∑_{( \widehat{I_P} \in \mathcal{P})} P(g│z=\widehat{I_P},\theta_{D},\mathcal{R}) \cdot P(z=\widehat{I_P} | \theta_{D},I_P,\mathcal{R})} \]<br />
<br />
<br />
<br />
<br />
Here, <math> {z}</math> models the latent variable of the actual patch executed, and <math>\widehat{I_P}</math> belongs to a set of possible neighboring patches <math> \mathcal{P}</math>.<math> P(z=\widehat{I_P}|\theta_D,I_P,\mathcal{R})</math> shows the noise which can be caused by <math>\mathcal{R}</math> variables and is implemented as the Noise Modelling Network (NMN). <math> {P(g│z=\widehat{I_P},\theta_{D}, \mathcal{R} )}</math> shows the grasp prediction probability given the true patch and is implemented as the Grasp Prediction Network (GPN). The overall Robust-Grasp model is computed by marginalizing GPN and NMN.<br />
<br />
===Learning the latent noise model===<br />
<br />
<br />
They assume that <math> {z}</math> is conditionally independent of the local patch-specific variables <math> {(I_{P}, \theta_{D})}</math>. To estimate the latent variable <math> {z}</math> given the global information <math>\mathcal{R}</math>, i.e <math> P(z=\widehat{I_P}|\theta_D,I_P,\mathcal{R}) \equiv P(z=\widehat{I_P}|\mathcal{R})</math>. They used direct optimization to learn both NMN and GPN with noisy labels. The entire image of the scene and the environment information are the inputs of the NMN, as well as robot ID and raw-pixel grasp location.. The output of the NMN is the probability distribution of the actual patches where the grasps are executed. Finally, a binary cross entropy loss is applied to the marginalized output of these two networks and the true grasp label g.<br />
<br />
===Training details===<br />
<br />
<br />
They implemented their model in PyTorch using a pretrained ResNet-18 model. They concatenated 512 dimensional ResNet feature with a 1-hot vector of robot ID and the raw pixel location of the grasp for their NMN. Also, the inputs of the GPN are the original noisy patch plus 8 other equidistant patches from the original one.<br />
Their training process starts with training only GPN over 5 epochs of the data. Then, the NMN and the marginalization operator are added to the model. So, they train NMN and GPN simultaneously for the other 25 epochs.<br />
<br />
==Results==<br />
<br />
<br />
In the results part of the paper, they show that collecting dataset in homes is essential for generalizing learning from unseen environments. They also show that modelling the noise in their Low-Cost Arm (LCA) can improve grasping performance.<br />
They collected data in parallel using multiple robots in 6 different homes, as shown in Figure 3. They used an object detector (tiny-YOLO) as the input data were unstructured due to LCA limited memory and computational capabilities. With an object location detected, class information was discarded, and a grasp was attempted. The grasp location in 3D was computed using PointCloud data. They scattered different objects in homes within 2m area to prevent collision of the robot with obstacles and let the robot move randomly and grasp objects. Finally, they collected a dataset with 28K grasp results.<br />
<br />
[[File:aa3.PNG|600px|thumb|center|]]<br />
<br />
<br />
To evaluate their approach in a more quantitative way, they used three test settings:<br />
<br />
- The first one is a binary classification or held-out data. The test set is collected by performing random grasps on objects. They measure the performance of binary classification by predicting the success or failure of grasping, given a location and the angle. Using binary classification allows for testing a lot of models without running them on real robots. They collected two held-out datasets using LCA in lab and homes and the dataset for Baxter robot.<br />
<br />
- The second one is Real Low-Cost Arm (Real-LCA). Here, they evaluate their model by running it in three unseen homes. They put 20 new objects in these three homes in different orientations. Since the objects and the environments are completely new, this tests could measure the generalization of the model.<br />
<br />
- The third one is Real Sawyer (Real-Sawyer). They evaluate the performance of their model by running the model on the Sawyer robot which is more accurate than the LCA. They tested their model in the lab environment to show that training models with the datasets collected from homes can improve the performance of models even in lab environments.<br />
<br />
They used baselines for both their data which is collected in homes and their model which is Robust-Grasp. They used two datasets for the baseline. The dataset collected by (Lab-Baxter) and the dataset collected by their LCA in the lab (Lab-LCA).<br />
They compared their Robust-Grasp model with the noise independent patch grasping model (Patch-Grasp) [4]. They also compared their data and model with DexNet-3.0 (DexNet) for a strong real-world grasping baseline.<br />
<br />
<br />
<br />
===Experiment 1: Performance on held-out data===<br />
<br />
<br />
Table 1 shows that the models trained on lab data cannot generalize to the Home-LCA environment. However, the model trained on Home-LCA hasa good performance on both lab data and home environment.<br />
<br />
[[File:aa4.PNG|600px|thumb|center|]]<br />
<br />
<br />
<br />
===Experiment 2: Performance on Real LCA Robot===<br />
<br />
<br />
In table 2, the performance of the Home-LCA is compared against a pre-trained DexNet and the model trained on the Lab-Baxter. Training on the Home-LCA dataset performs 43.7% better than training on the Lab-Baxter dataset and 33% better than DexNet. The low performance of DexNet can be described by the possible noise in the depth images that are caused by the natural light. DexNet, which requires high quality depth sensing, cannot perform well. By using cheap commodity RGBD cameras in LCA, the noise in the depth images is not a matter of concern, as the model has no expectation of high quality.<br />
<br />
[[File:aa5.PNG|600px|thumb|center|]]<br />
<br />
===Performance on Real Sawyer===<br />
<br />
<br />
To compare the performance of the Robust-Grasp model against the Patch-Grasp model without collecting noise-free data, they used Lab-Baxter for benchmarking, which is an accurate and better calibrated robot. The Sawyer robot is used for testing to ensure that the testing robot is different from both training robots. As shown in Table 3, the Robust-Grasp model trained on Home-LCA outperforms the Patch-Grasp model and achieves 77.5% accuracy. This accuracy is similar to sevelral recent papers, however, this model was trained and tested in different environment. The Robust-Grasp model also outperforms the Patch-Grasp by about 4% on binary classification. Furthermore, the visualizations of predicted noise corrections in Figure 4 shows that the corrections depend on both the pixel locations of the noisy grasp and the robot.<br />
<br />
<br />
[[File:aa6.PNG|600px|thumb|center|]]<br />
<br />
[[File:aa7.PNG|600px|thumb|center|]]<br />
<br />
==Related work==<br />
<br />
<br />
Over the last few years, the interest of scaling up robot learning with large scale datasets has been increased. Hence, many papers were published in this area. A hand annotated grasping dataset, a self-supervised grasping dataset, and grasping using reinforcement learning are some examples of using large scale datasets for grasping. The work mentioned above used high-cost hardware and data labelling mechanisms. There were also many papers that worked on other robotic tasks like material recognition, pushing objects and manipulating a rope. However, none of these papers worked on real data in real environments like homes, they all used lab data.<br />
<br />
<br />
Furthermore, since grasping is one of the basic problems of robotic, there were some efforts to improve grasping. Classic approaches focused on physics-based issues of grasping and required 3D models of the objects. However, recent works focused on data-driven approaches which learn from visual observations to grasp objects. Simulation and real-world robots are both required for large-scale data collection. A versatile grasping model was proposed to achieve a 90% performance for a bin-picking task. The point here is that they usually require high quality depth as input which seems to be a barrier for practical use of robots in real environments.<br />
<br />
<br />
Most labs use industrial robots or standard collaborative hardware for their experiments. Therefore, there is few research that used low cost robots. One of the examples is learning using a cheap inaccurate robot for stack multiple blocks, although it is not clear whether learning approaches are used in it alongside mapping and planning.<br />
<br />
<br />
Learning from noisy inputs is another challenge specifically in computer vision. A controversial question which is often raised in this area is whether learning from noise can improve the performance. Some works show it could have bad effects on the performance; however, some other works find it valuable when the noise is dependent on the environment. In this paper, they used a model that can exploit the noise and learn a better grasping model.<br />
<br />
==Conclusion==<br />
<br />
All in all, the paper presents an approach for collecting large-scale robot data in real home environments. They implemented their approach by using a mobile manipulator which is a lot cheaper than the existing industrial robots. They collected a dataset of 28K grasps in six different homes. In order to solve the problem of noisy labels which were caused by their inaccurate robots, they presented a framework to factor out the noise in the data. They tested their model by physically grasping 20 new objects in three new homes and in the lab. The model trained with home dataset showed 43.7% improvement over the models trained with lab data. Their results also showed that their model can improve the grasping performance even in lab environments. They also demonstrated that their architecture for modeling the noise improved the performance by about 10%.<br />
<br />
==Critiques==<br />
<br />
This paper does not contain a significant algorithmic contribution. They are just combining a large number of data engineering techniques for the robot learning problem. The authors claim that they have obtained 43.7% more accuracy than baseline models, but it does not seem to be a fair comparison as the data collection happened in simulated settings in the lab for other methods, whereas the authors use the home dataset. The authors must have also discussed safety issues when training robots in real environments as against simulated environments like labs. The authors are encouraging other researchers to look outside the labs, but are not discussing the critical safety issues in this approach.<br />
<br />
Another strange finding is that the paper mentions that they "follow a model architecture similar to [Pinto and Gupta [4]]," however, the proposed model is in fact a fine tuned resnet-18 architecture. Pinto and Gupta, implement a version similar to AlexNet as shown below in Figure 5.<br />
<br />
[[File:Figure_5_PandG.JPG | 450px|thumb|center|Figure 5: AlexNet architecture implemented in Pinto and Gupta [4].]]<br />
<br />
<br />
The paper argues that the dataset collected by the LCA is noisy, since the robot is cheap and inaccurate. It further asserts that in order to handle the noise in the dataset, they can model the noise as a latent variable and their model can improve the performance of grasping. Although learning from noisy data and achieving a good performance is valuable, it is better that they test their noise modeling network for other robots as well. Since their noise modelling network takes robot information as an input, it would be a good idea to generalize it by testing it using different inaccurate robots to ensure that it would perform well.<br />
<br />
<br />
They did not mention other aspects of their comparison, for example they could mention their training time compared to other models or the size of other datasets.<br />
<br />
==References==<br />
<br />
#Josh Tobin, Rachel Fong, Alex Ray, Jonas Schneider, Wojciech Zaremba, and Pieter Abbeel. "Domain randomization for transferring deep neural networks from simulation to the real world." 2017. URL https://arxiv.org/abs/1703.06907.<br />
#Xue Bin Peng, Marcin Andrychowicz, Wojciech Zaremba, and Pieter Abbeel. "Sim-to-real transfer of robotic control with dynamics randomization." arXiv preprint arXiv:1710.06537,2017.<br />
#Lerrel Pinto, Marcin Andrychowicz, Peter Welinder, Wojciech Zaremba, and Pieter Abbeel. "Asymmetric actor critic for image-based robot learning." Robotics Science and Systems, 2018.<br />
#Lerrel Pinto and Abhinav Gupta. "Supersizing self-supervision: Learning to grasp from 50k tries and 700 robot hours." CoRR, abs/1509.06825, 2015. URL http://arxiv.org/abs/1509. 06825.<br />
#Adithyavairavan Murali, Lerrel Pinto, Dhiraj Gandhi, and Abhinav Gupta. "CASSL: Curriculum accelerated self-supervised learning." International Conference on Robotics and Automation, 2018.<br />
# Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel. "End-to-end training of deep visuomotor policies." The Journal of Machine Learning Research, 17(1):1334–1373, 2016.<br />
#Sergey Levine, Peter Pastor, Alex Krizhevsky, and Deirdre Quillen. "Learning hand-eye coordination for robotic grasping with deep learning and large scale data collection." CoRR, abs/1603.02199, 2016. URL http://arxiv.org/abs/1603.02199.<br />
#Pulkit Agarwal, Ashwin Nair, Pieter Abbeel, Jitendra Malik, and Sergey Levine. "Learning to poke by poking: Experiential learning of intuitive physics." 2016. URL http://arxiv.org/ abs/1606.07419<br />
#Chelsea Finn, Ian Goodfellow, and Sergey Levine. "Unsupervised learning for physical interaction through video prediction." In Advances in neural information processing systems, 2016.<br />
#Ashvin Nair, Dian Chen, Pulkit Agrawal, Phillip Isola, Pieter Abbeel, Jitendra Malik, and Sergey Levine. "Combining self-supervised learning and imitation for vision-based rope manipulation." International Conference on Robotics and Automation, 2017.<br />
#Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta. "Revisiting unreasonable effectiveness of data in deep learning era." ICCV, 2017.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Figure_5_PandG.JPG&diff=40228File:Figure 5 PandG.JPG2018-11-20T03:30:12Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=MULTI-VIEW_DATA_GENERATION_WITHOUT_VIEW_SUPERVISION&diff=39384MULTI-VIEW DATA GENERATION WITHOUT VIEW SUPERVISION2018-11-15T17:37:55Z<p>Npbhatt: just made the content and view information in the Figure 4 and 5 clear by adding a description.</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. An implementation of the models presented in this paper is available here[https://github.com/mickaelChen/GMV]<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 (i.e. methods based on unlabeled samples), 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. The conditionality of a CGAN is determined by defining a generator function G which takes a noise vector z and a condition y as inputs. 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. A target X from a given input y can be obtained by first sampling the latent vector <math>z ∼ p_z</math>, then by computing G(y, z). The discriminator takes both the condition y and the datapoint x as inputs.<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 encoder E is similar to D with the only differences being the batch-normalization in the first layer and the last layer which doesn't have a non-linearity. The Adam optimizer 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 (generator, encoder and discriminator).<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. In the left hand block of Figure 5, each row shows different views generated given the same content. <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). Again, in the left and right hand block of Figure 6, each row shows different views generated given the same content. 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. In the future, they are planning to use the method of this paper for data augmentation which can enrich training dataset.<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 />
The method that the paper presented is novel and the paper is easy to follow. However, the authors only show a comparison between the proposed method and several baselines: DCGAN and CGAN and do not compare with the methods from Mathieu et al. 2016. In addition, the experiment result is empirical, we do not know the performance of this method in practice in the real word.<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>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Reinforcement_Learning_of_Theorem_Proving&diff=39379Reinforcement Learning of Theorem Proving2018-11-15T16:50:45Z<p>Npbhatt: Figure numbers fixed and minor edits</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|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. 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|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 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|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 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|450px|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|450px|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|450px|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|450px|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|center]Figure 5a. Experimental result on Mizar40 dataset]<br />
[[file:atp_result1.jpg|frame|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.<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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:ANNOTATING_OBJECT_INSTANCES_NEEL_BHATT.pdf&diff=38354File:ANNOTATING OBJECT INSTANCES NEEL BHATT.pdf2018-11-08T15:46:17Z<p>Npbhatt: Npbhatt uploaded a new version of File:ANNOTATING OBJECT INSTANCES NEEL BHATT.pdf</p>
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<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18&diff=38331stat946F182018-11-08T13:42:13Z<p>Npbhatt: Uploaded Presentation Slides - Neel Bhatt</p>
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<div>== [[F18-STAT946-Proposal| Project Proposal ]] ==<br />
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=Paper presentation=<br />
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[https://goo.gl/forms/8NucSpF36K6IUZ0V2 Your feedback on presentations]<br />
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= Record your contributions here [https://docs.google.com/spreadsheets/d/1SxkjNfhOg_eXWpUnVHuIP93E6tEiXEdpm68dQGencgE/edit?usp=sharing]=<br />
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Use the following notations:<br />
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{| class="wikitable"<br />
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|width="60pt"|Date<br />
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|Feb 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946w18/Unsupervised_Machine_Translation_Using_Monolingual_Corpora_Only Summary]]<br />
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|Oct 25 || Dhruv Kumar || 1 || Beyond Word Importance: Contextual Decomposition to Extract Interactions from LSTMs || [https://openreview.net/pdf?id=rkRwGg-0Z Paper] || <br />
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|Oct 25 || Amirpasha Ghabussi || 2 || DCN+: Mixed Objective And Deep Residual Coattention for Question Answering || [https://openreview.net/pdf?id=H1meywxRW Paper] ||<br />
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|Oct 25 || Juan Carrillo || 3 || Hierarchical Representations for Efficient Architecture Search || [https://arxiv.org/abs/1711.00436 Paper] || <br />
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|Oct 30 || Manpreet Singh Minhas || 4 || End-to-end Active Object Tracking via Reinforcement Learning || [http://proceedings.mlr.press/v80/luo18a/luo18a.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=End_to_end_Active_Object_Tracking_via_Reinforcement_Learning Summary]<br />
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|Oct 30 || Marvin Pafla || 5 || Fairness Without Demographics in Repeated Loss Minimization || [http://proceedings.mlr.press/v80/hashimoto18a.html Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Fairness_Without_Demographics_in_Repeated_Loss_Minimization Summary]<br />
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|Oct 30 || Glen Chalatov || 6 || Pixels to Graphs by Associative Embedding || [http://papers.nips.cc/paper/6812-pixels-to-graphs-by-associative-embedding Paper] ||<br />
[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Pixels_to_Graphs_by_Associative_Embedding Summary]<br />
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|Nov 1 || Sriram Ganapathi Subramanian || 7 ||Differentiable plasticity: training plastic neural networks with backpropagation || [http://proceedings.mlr.press/v80/miconi18a.html Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946F18/differentiableplasticity Summary]<br />
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|Nov 1 || Henry Chen || 9 || DeepVO: Towards end-to-end visual odometry with deep Recurrent Convolutional Neural Networks || [https://ieeexplore.ieee.org/abstract/document/7989236 Paper] || <br />
[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=DeepVO_Towards_end_to_end_visual_odometry_with_deep_RNN Summary]<br />
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|Nov 6 || Nargess Heydari || 10 ||Wavelet Pooling For Convolutional Neural Networks Networks || [https://openreview.net/pdf?id=rkhlb8lCZ Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946w18/Wavelet_Pooling_For_Convolutional_Neural_Networks Summary] [https://wiki.math.uwaterloo.ca/statwiki/images/1/1a/Wavelet_Pooling_for_Convolutional_Neural_Networks.pptx Slides]<br />
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|Nov 6 || Aravind Ravi || 11 || Towards Image Understanding from Deep Compression Without Decoding || [https://openreview.net/forum?id=HkXWCMbRW Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat946w18/Towards_Image_Understanding_From_Deep_Compression_Without_Decoding Summary]<br />
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|Nov 8 || Neel Bhatt || 13 || Annotating Object Instances with a Polygon-RNN || [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN Summary] [https://wiki.math.uwaterloo.ca/statwiki/images/a/af/ANNOTATING_OBJECT_INSTANCES_NEEL_BHATT.pdf Slides]<br />
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|Nov 8 || Jacob Manuel || 14 || Co-teaching: Robust Training Deep Neural Networks with Extremely Noisy Labels || [https://arxiv.org/pdf/1804.06872.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Co-Teaching Summary]<br />
|-<br />
|Nov 8 || Charupriya Sharma|| 15 || A Bayesian Perspective on Generalization and Stochastic Gradient Descent|| [https://openreview.net/pdf?id=BJij4yg0Z Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=A_Bayesian_Perspective_on_Generalization_and_Stochastic_Gradient_Descent Summary]<br />
|-<br />
|NOv 13 || Sagar Rajendran || 16 || Zero-Shot Visual Imitation || [https://openreview.net/pdf?id=BkisuzWRW Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Zero-Shot_Visual_Imitation Summary]<br />
|-<br />
<br />
|Nov 13 || Ruijie Zhang || 17 || Searching for Efficient Multi-Scale Architectures for Dense Image Prediction || [https://arxiv.org/pdf/1809.04184.pdf Paper]||<br />
|-<br />
|Nov 13 || Neil Budnarain || 18 || Predicting Floor Level For 911 Calls with Neural Networks and Smartphone Sensor Data || [https://openreview.net/pdf?id=ryBnUWb0b Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Predicting_Floor_Level_For_911_Calls_with_Neural_Network_and_Smartphone_Sensor_Data Summary]<br />
|-<br />
|NOv 15 || Zheng Ma || 19 || Reinforcement Learning of Theorem Proving || [https://arxiv.org/abs/1805.07563 Paper] || <br />
|-<br />
|Nov 15 || Abdul Khader Naik || 20 || Multi-View Data Generation Without View Supervision || [https://openreview.net/pdf?id=ryRh0bb0Z Paper] ||<br />
|-<br />
|Nov 15 || Johra Muhammad Moosa || 21 || Attend and Predict: Understanding Gene Regulation by Selective Attention on Chromatin || [https://papers.nips.cc/paper/7255-attend-and-predict-understanding-gene-regulation-by-selective-attention-on-chromatin.pdf Paper] || <br />
|-<br />
|NOv 20 || Zahra Rezapour Siahgourabi || 22 ||Robot Learning in Homes: Improving Generalization and Reducing Dataset Bias ||[https://arxiv.org/pdf/1807.07049 Paper] || <br />
|-<br />
|Nov 20 || Shubham Koundinya || 23 || TBD || || <br />
|-<br />
|Nov 20 || Salman Khan || 24 || Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples || [http://proceedings.mlr.press/v80/athalye18a.html paper] || <br />
|-<br />
|NOv 22 ||Soroush Ameli || 25 || Learning to Navigate in Cities Without a Map || [https://arxiv.org/abs/1804.00168 paper] || <br />
|-<br />
|Nov 22 ||Ivan Li || 26 || Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction || [https://arxiv.org/pdf/1802.05451v3.pdf Paper] ||<br />
|-<br />
|Nov 22 ||Sigeng Chen || 27 || || ||<br />
|-<br />
|Nov 27 || Aileen Li || 28 || Spatially Transformed Adversarial Examples ||[https://openreview.net/pdf?id=HyydRMZC- Paper] || <br />
|-<br />
|NOv 27 ||Xudong Peng || 29 || Multi-Scale Dense Networks for Resource Efficient Image Classification || [https://openreview.net/pdf?id=Hk2aImxAb Paper] || <br />
|-<br />
|Nov 27 ||Xinyue Zhang || 30 || An Inference-Based Policy Gradient Method for Learning Options || [http://proceedings.mlr.press/v80/smith18a/smith18a.pdf Paper] || <br />
|-<br />
|NOv 29 ||Junyi Zhang || 31 || Autoregressive Convolutional Neural Networks for Asynchronous Time Series || [http://proceedings.mlr.press/v80/binkowski18a/binkowski18a.pdf Paper] ||<br />
|-<br />
|Nov 29 ||Travis Bender || 32 || Automatic Goal Generation for Reinforcement Learning Agents || [http://proceedings.mlr.press/v80/florensa18a/florensa18a.pdf Paper] ||<br />
|-<br />
|Nov 29 ||Patrick Li || 33 || Matrix Capsules with EM Routing || [https://openreview.net/pdf?id=HJWLfGWRb Paper] ||<br />
|-<br />
|Makeup || Jiazhen Chen || 34 || || || <br />
|-<br />
|Makeup || Ahmed Afify || 35 ||Don't Decay the Learning Rate, Increase the Batch Size || [https://openreview.net/pdf?id=B1Yy1BxCZ Paper]||<br />
|-<br />
|Makeup || Gaurav Sahu || 36 || TBD || ||<br />
|-<br />
|Makeup || Kashif Khan || 37 || Wasserstein Auto-Encoders || [https://arxiv.org/pdf/1711.01558.pdf Paper] ||<br />
|-<br />
|Makeup || Shala Chen || 38 || A NEURAL REPRESENTATION OF SKETCH DRAWINGS || ||<br />
|-<br />
|Makeup || Ki Beom Lee || 39 || Detecting Statistical Interactions from Neural Network Weights|| [https://openreview.net/forum?id=ByOfBggRZ Paper] ||<br />
|-<br />
|Makeup || Wesley Fisher || 40 || Deep Reinforcement Learning in Continuous Action Spaces: a Case Study in the Game of Simulated Curling || [http://proceedings.mlr.press/v80/lee18b/lee18b.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Reinforcement_Learning_in_Continuous_Action_Spaces_a_Case_Study_in_the_Game_of_Simulated_Curling Summary]</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:ANNOTATING_OBJECT_INSTANCES_NEEL_BHATT.pdf&diff=38330File:ANNOTATING OBJECT INSTANCES NEEL BHATT.pdf2018-11-08T13:38:59Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38306Annotating Object Instances with a Polygon RNN2018-11-08T05:26:23Z<p>Npbhatt: spell check</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 />
<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''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <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 />
<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 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, 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 the first vertex. 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.<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 />
== 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 />
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 />
== 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38275Annotating Object Instances with a Polygon RNN2018-11-08T03:06:22Z<p>Npbhatt: /* Quantitative Results */ divided results into qualitative and quantitative</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
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 />
== 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 5: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38274Annotating Object Instances with a Polygon RNN2018-11-08T03:05:04Z<p>Npbhatt: /* Quatitative Results */ spell check</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
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 />
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 5: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38273Annotating Object Instances with a Polygon RNN2018-11-08T03:04:27Z<p>Npbhatt: /* Baseline Techniques */ more formatting</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
== Quatitative Results ==<br />
<br />
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 />
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 5: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38272Annotating Object Instances with a Polygon RNN2018-11-08T03:04:07Z<p>Npbhatt: /* Baseline Techniques = */ formatting</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
2. '''DeepMask''': a build-up on the 50 layer ResNet with an addition of another CNN.<br />
3. '''Dilation10''': another simple technique using purely convolutional operations.<br />
4. '''SquareBox''': a simple technique where an entire bounding box is labeled as an object<br />
<br />
== Quatitative Results ==<br />
<br />
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 />
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 5: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38271Annotating Object Instances with a Polygon RNN2018-11-08T03:03:27Z<p>Npbhatt: /* Quatitative Results */ figure caption changed</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
2. '''DeepMask''': a build-up on the 50 layer ResNet with an addition of another CNN.<br />
3. '''Dilation10''': another simple technique using purely convolutional operations.<br />
4. '''SquareBox''': a simple technique where an entire bounding box is labeled as an object<br />
<br />
== Quatitative Results ==<br />
<br />
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 />
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 5: Qualitative results: comparison with human annotator.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38270Annotating Object Instances with a Polygon RNN2018-11-08T03:01:04Z<p>Npbhatt: few changes to the conclusion</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 signoid 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, 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 the first vertex. 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.<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 />
== 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 />
2. '''DeepMask''': a build-up on the 50 layer ResNet with an addition of another CNN.<br />
3. '''Dilation10''': another simple technique using purely convolutional operations.<br />
4. '''SquareBox''': a simple technique where an entire bounding box is labeled as an object<br />
<br />
== Quatitative Results ==<br />
<br />
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 />
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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Table_0_Neel.JPG&diff=38269File:Table 0 Neel.JPG2018-11-08T03:00:30Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38253Annotating Object Instances with a Polygon RNN2018-11-08T01:23:41Z<p>Npbhatt: moved equation to center</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first 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 signoid 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 />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38249Annotating Object Instances with a Polygon RNN2018-11-08T01:21:15Z<p>Npbhatt: added standard ConvLSTM equations</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first 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 />
<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 />
<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 signoid 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 />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38242Annotating Object Instances with a Polygon RNN2018-11-07T22:06:13Z<p>Npbhatt: /* Architecture */ CNN Skip Connections grammar edits</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: 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 4). 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38239Annotating Object Instances with a Polygon RNN2018-11-07T21:03:25Z<p>Npbhatt: /* Model */ minor changes in prose</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<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 4: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<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 feature fused together in a tensor that can feed into the RNN (refer to Figure 2). Namely, the last max-pool layer 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 passing through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38238Annotating Object Instances with a Polygon RNN2018-11-07T20:59:00Z<p>Npbhatt: Fixed figure captions</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 2: 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 3: Illustration of the superpixel idea.]] <br />
<br />
<br />
= Model =<br />
<br />
As an input to the model, an annotator or perhaps another neural network provides a ground-truth 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 4: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<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 feature fused together in a tensor that can feed into the RNN (refer to Figure 2). Namely, the last max-pool layer 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 passing through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 5: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 6: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38237Annotating Object Instances with a Polygon RNN2018-11-07T20:56:17Z<p>Npbhatt: Added some images for visual illustration (Related Work Section)</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
Some of the techniques used in semi-automatic annotation are as follows:<br />
<br />
1. '''GrabCut''': Some researchers use multiple scribbles from users to aid the model in defining the foreground and background. <br />
<br />
[[File:GrabCut_Example.png | 450px|thumb|center|Figure 1: Different levels of detection in an image.]]<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 1: Different levels of detection in an image.]] <br />
<br />
<br />
= Model =<br />
<br />
As an input to the model, an annotator or perhaps another neural network provides a ground-truth 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<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 feature fused together in a tensor that can feed into the RNN (refer to Figure 2). Namely, the last max-pool layer 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 passing through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 3: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 4: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Superpixel_idea.jpg&diff=38236File:Superpixel idea.jpg2018-11-07T20:53:34Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:GrabCut_Example.png&diff=38235File:GrabCut Example.png2018-11-07T20:53:18Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38150Annotating Object Instances with a Polygon RNN2018-11-07T04:27:25Z<p>Npbhatt: /* Results */ made results a main heading rather than sub-heading</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
The related works are related to the fields of semi-automatic image annotation and object instance segmentation. <br />
<br />
The critical advances in the field of semi-automatic annotation are as follows: <br />
<br />
1) Some researchers use scribbles as seeds to model the appearance of foreground and background. <br />
<br />
2) Other works use multiple scribbles on the object and exploit motion cues to annotate an object in a video. <br />
<br />
3) Scribbles are also used to train CNNs for semantic image segmentation. <br />
<br />
4) Some methods exploit annotations in the form of 2D bounding boxes and perform per-pixel labeling with foreground/background models using EM. <br />
<br />
The following are the critical advances in the field of Object instance segmentation: <br />
<br />
1) Most of the approaches operate on pixel-level and exploit a CNN inside a box or a patch to perform the labeling. <br />
<br />
2) Some approaches aim to produce a polygon around an object. These approaches start by detecting edge fragments and find an optimal cycle that links the edges into a coherent region.<br />
<br />
3) One particular work uses superpixels in the form of small polygons which is combined into object regions with the aim to label aerial images. <br />
<br />
<br />
= Model =<br />
<br />
As an input to the model, an annotator or perhaps another neural network provides a ground-truth 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<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 feature fused together in a tensor that can feed into the RNN (refer to Figure 2). Namely, the last max-pool layer 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 passing through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
= Results =<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 3: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 4: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=38149Annotating Object Instances with a Polygon RNN2018-11-07T04:26:11Z<p>Npbhatt: minor information highlighting and organization</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, here, is to not only to assign pixel-level categorical labels, but also 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 />
<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 />
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 />
= Related Works =<br />
<br />
The related works are related to the fields of semi-automatic image annotation and object instance segmentation. <br />
<br />
The critical advances in the field of semi-automatic annotation are as follows: <br />
<br />
1) Some researchers use scribbles as seeds to model the appearance of foreground and background. <br />
<br />
2) Other works use multiple scribbles on the object and exploit motion cues to annotate an object in a video. <br />
<br />
3) Scribbles are also used to train CNNs for semantic image segmentation. <br />
<br />
4) Some methods exploit annotations in the form of 2D bounding boxes and perform per-pixel labeling with foreground/background models using EM. <br />
<br />
The following are the critical advances in the field of Object instance segmentation: <br />
<br />
1) Most of the approaches operate on pixel-level and exploit a CNN inside a box or a patch to perform the labeling. <br />
<br />
2) Some approaches aim to produce a polygon around an object. These approaches start by detecting edge fragments and find an optimal cycle that links the edges into a coherent region.<br />
<br />
3) One particular work uses superpixels in the form of small polygons which is combined into object regions with the aim to label aerial images. <br />
<br />
<br />
= Model =<br />
<br />
As an input to the model, an annotator or perhaps another neural network provides a ground-truth 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<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 feature fused together in a tensor that can feed into the RNN (refer to Figure 2). Namely, the last max-pool layer 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 passing through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 as well as boundary/semantic information about the instances. 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 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 encodingof 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 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, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross-entropy is used for the RNN cost function.<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 />
=== 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". The typical inference time as quoted by the paper is 250ms per object.<br />
<br />
== Results ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection over Union (IoU) measure is used for comparison. 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 />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. 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_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 3: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 4: 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 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. 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 />
2. The method outperforms other methods only in the three categories mentioned but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=37611Annotating Object Instances with a Polygon RNN2018-11-02T15:17:44Z<p>Npbhatt: Formatting</p>
<hr />
<div>Summary of the CVPR '17 best [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf ''paper'']<br />
<br />
= Introduction =<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 besides a street light. This ability to decompose objects in scenes into separate entities is key to understanding what is around us and it helps 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." The term object detection has been used interchangeably, however, 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 of 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 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: The goal, here, is to not only to assign pixel-level categorical labels, but also 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 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 />
<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. Thus, the main goal of the paper is to enable '''semi-automatic''' annotation of object instances.<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 small number of clicks (30 - 40) compared to other methods; this approach works as silhouette of an object is typically connected without holes. Thus, the authors intuition behind the success of this method is the sparse nature of these polygons that allow representation of an object through a cluster of pixels rather than a pixel level description.<br />
<br />
= Model =<br />
<br />
As an input to the the model, an annotator or perhaps another neural network provides a ground-truth 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 they 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 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<br />
<br />
1. '''CNN with skip connections''':<br />
<br />
The authors have adopted the VGG16 feature extractor architecture with a few modifications pertaining to preservation of feature fused together in a tensor than can feed into the RNN (refer to Figure 2). Namely,the last max-pool layer 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 pass through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 allows the CNN to extract low-level edge and corner features as well as boundary/semantic information about the instances. Finally, a 3x3 convolution applied alongwith 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 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.<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 addition 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 creation of the polygon. Coming back to the prediction of the first vertex, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross entropy is used for the RNN cost function.<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 />
=== Human Annotator in the Loop ===<br />
<br />
The model is 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.<br />
<br />
<br />
== Results ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection of Union (IoU) measure (a measure that effectively measures overlap of predictions with the ground truth) is used for comparison.<br />
<br />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. In addition, with the help of the annotator, the speed up factor was 7.3 times with under 5 clicks which the authors claim is the main advantage of this method.<br />
<br />
[[File:Table_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 3: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 4: 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 that works on different unseen datasets. <br />
<br />
2. Significant improvement in annotation time can be achieved with the Polygon-RNN method itself.<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 training of the CNN for the first vertex.<br />
<br />
=Critique=<br />
<br />
1. 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 />
2. The method outperforms other methods only in the three categories mentioned, but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=37607Annotating Object Instances with a Polygon RNN2018-11-02T04:46:51Z<p>Npbhatt: </p>
<hr />
<div>Summary of the CVPR '17 best [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf ''paper'']<br />
<br />
= Introduction =<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 besides a street light. This ability to decompose objects in scenes into separate entities is key to understanding what is around us and it helps 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." The term object detection has been used interchangeably, however, 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 of 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 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: The goal, here, is to not only to assign pixel-level categorical labels, but also 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 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 />
<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. Thus, the main goal of the paper is to enable '''semi-automatic''' annotation of object instances.<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 small number of clicks (30 - 40) compared to other methods; this approach works as silhouette of an object is typically connected without holes. Thus, the authors intuition behind the success of this method is the sparse nature of these polygons that allow representation of an object through a cluster of pixels rather than a pixel level description.<br />
<br />
= Model =<br />
<br />
As an input to the the model, an annotator or perhaps another neural network provides a ground-truth 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 they 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 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<br />
<br />
1. '''CNN with skip connections''':<br />
<br />
The authors have adopted the VGG16 feature extractor architecture with a few modifications pertaining to preservation of feature fused together in a tensor than can feed into the RNN (refer to Figure 2). Namely,the last max-pool layer 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 pass through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 allows the CNN to extract low-level edge and corner features as well as boundary/semantic information about the instances. Finally, a 3x3 convolution applied alongwith 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 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.<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 addition 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 creation of the polygon. Coming back to the prediction of the first vertex, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross entropy is used for the RNN cost function.<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 />
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 />
=== Human Annotator in the Loop ===<br />
<br />
The model is 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.<br />
<br />
<br />
== Results ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection of Union (IoU) measure (a measure that effectively measures overlap of predictions with the ground truth) is used for comparison.<br />
<br />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. In addition, with the help of the annotator, the speed up factor was 7.3 times with under 5 clicks which the authors claim is the main advantage of this method.<br />
<br />
[[File:Table_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<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 3: Qualitative results without human annotator in the loop.|alt=alt language<br />
File:Figure_4_Neel.JPG|Figure 4: 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. Significant improvement in annotation time can be achieved with the Polygon-RNN method itself.<br />
<br />
2. However, the flexibility of having inputs from a human annotator helps increase the IoU for a certain range of clicks.<br />
<br />
3. The model architecture has a down-sampling factor of 16 and the final output resolution and accuracy is sensitive to object size.<br />
<br />
4. Another downside of the model architecture is that training time is increased due to training of the CNN for the first vertex.<br />
<br />
=Critique=<br />
<br />
1. 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 />
2. The method outperforms other methods only in the three categories mentioned, but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Figure_4_Neel.JPG&diff=37606File:Figure 4 Neel.JPG2018-11-02T04:25:07Z<p>Npbhatt: </p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Figure_3_Neel.JPG&diff=37605File:Figure 3 Neel.JPG2018-11-02T04:24:44Z<p>Npbhatt: Npbhatt uploaded a new version of File:Figure 3 Neel.JPG</p>
<hr />
<div></div>Npbhatthttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Annotating_Object_Instances_with_a_Polygon_RNN&diff=37604Annotating Object Instances with a Polygon RNN2018-11-02T04:19:35Z<p>Npbhatt: /* Critique */</p>
<hr />
<div>Summary of the CVPR '17 best [https://www.cs.utoronto.ca/~fidler/papers/paper_polyrnn.pdf ''paper'']<br />
<br />
= Introduction =<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 besides a street light. This ability to decompose objects in scenes into separate entities is key to understanding what is around us and it helps 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." The term object detection has been used interchangeably, however, 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 of 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 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: The goal, here, is to not only to assign pixel-level categorical labels, but also 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 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 />
<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. Thus, the main goal of the paper is to enable '''semi-automatic''' annotation of object instances.<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 small number of clicks (30 - 40) compared to other methods; this approach works as silhouette of an object is typically connected without holes. Thus, the authors intuition behind the success of this method is the sparse nature of these polygons that allow representation of an object through a cluster of pixels rather than a pixel level description.<br />
<br />
= Model =<br />
<br />
As an input to the the model, an annotator or perhaps another neural network provides a ground-truth 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 they 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 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 2: Model architecture for Polygon-RNN depicting a CNN with skip connections feeding into a 2 layer ConvLSTM (One-to-many type).]]<br />
<br />
1. '''CNN with skip connections''':<br />
<br />
The authors have adopted the VGG16 feature extractor architecture with a few modifications pertaining to preservation of feature fused together in a tensor than can feed into the RNN (refer to Figure 2). Namely,the last max-pool layer 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 pass through 2 pooling layers with 128 and 2 convolutional layers. At each of these four steps, the idea is to have a width of 512 and 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 allows the CNN to extract low-level edge and corner features as well as boundary/semantic information about the instances. Finally, a 3x3 convolution applied alongwith 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 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.<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 addition 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 creation of the polygon. Coming back to the prediction of the first vertex, 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 the first vertex.<br />
<br />
== Training ==<br />
<br />
The training of the model is done as follows:<br />
<br />
1. Cross entropy is used for the RNN cost function.<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 />
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 />
=== Human Annotator in the Loop ===<br />
<br />
The model is 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.<br />
<br />
<br />
== Results ==<br />
<br />
The evaluation of the model performance was conducted based on the Cityscapes and KITTI Datasets. The standard Intersection of Union (IoU) measure (a measure that effectively measures overlap of predictions with the ground truth) is used for comparison.<br />
<br />
[[File:Table_1_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
Compared to other instance segmentation techniques, the Polygon-RNN method performs significantly better in the person, car, and rider categories and above average in other categories. In addition, with the help of the annotator, the speed up factor was 7.3 times with under 5 clicks which the authors claim is the main advantage of this method.<br />
<br />
[[File:Table_2_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
In addition, most of the comparisons with human annotators show that the method is at par with human level annotation.<br />
<br />
[[File:Figure_3_Neel.JPG | 800px|thumb|center|Table 1: IoU performance on Cityscapes data without any annotator intervention.]]<br />
<br />
=Conclusion=<br />
<br />
The important conclusions from this paper are:<br />
<br />
1. Significant improvement in annotation time can be achieved with the Polygon-RNN method itself.<br />
<br />
2. However, the flexibility of having inputs from a human annotator helps increase the IoU for a certain range of clicks.<br />
<br />
3. The model architecture has a down-sampling factor of 16 and the final output resolution and accuracy is sensitive to object size.<br />
<br />
4. Another downside of the model architecture is that training time is increased due to training of the CNN for the first vertex.<br />
<br />
=Critique=<br />
<br />
1. 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 />
2. The method outperforms other methods only in the three categories mentioned, but isn't a significant improvement in other categories.<br />
<br />
3. 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 />
4. 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 />
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.</div>Npbhatt