deep Generative Stochastic Networks Trainable by Backprop

Introduction

The Deep Learning boom that has been seen in recent years was spurred initially by research in unsupervised learning techniques. However, most of the major successes over the last few years have mostly been based on supervised techniques. A drawback for the unsupervised methods stems from their need for too many calculations and intractable sums in their models (inference, learning, sampling and partition functions). The paper presented puts forth an idea for a network that creates a model of a conditional distribution, [math]\displaystyle{ P(X|\bar{X}) }[/math], which can be seen as a local (usually) unimodal representation of [math]\displaystyle{ P(X) }[/math]. [math]\displaystyle{ \bar{X} }[/math] is a corrupted example of the original data [math]\displaystyle{ X }[/math]. The Generative Stochastic Network (GSN) combines arbitrary latent variables [math]\displaystyle{ H }[/math] that serve as input for a Markov chain which build in layers that eventually create a representation of the original data. Training of the network does not need Gibb's sampling or large partition functions but is trained with backpropagation and all the tools that come with it.

Unsupervised learning is attractive because the quantity of unlabelled data far exceeds that of labelled data

Avoiding intractable sums or maximization that is inherent in many unsupervised techniques

Generalize autoencoders

GSN parametrize transition operators of Markov chain rather than P(X). Allows for training of unsupervised methods by gradient descent and ML no partition functions, just backprop

graphical models have too many computations (inference, sampling, learning) MCMC can be used for estimation if only a few terms dominate the weighted sum that is being calculated.

Generative Stochastic Network (GSN)

GSN relies on estimating the transition operator of a Markov chain.

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Figure 1

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Figure 2

Experimental Results

Some initial experimental results were created without extensive parameter alteration. This was done to maintain consistency over the tests and likely to show that even without optimization that the results approached the performance of more established unsupervised learning networks. The main comparison was made to Deep Boltzmann Machines.

MNIST

The non-linearity for the units in the GSN was applied as [math]\displaystyle{ h_i = \eta_{out} + \tanh (\eta_{in} + a_i) }[/math], with a_i as the linear activation for unit i and \eta_{in} and \eta_{out} are both zero mean Gaussian noise. Sampling of unfinished or incomplete data can be done in a similar manner to DBM, where representations can propagate upwards and downwards in the network. This allows for pattern completion similar to that achieved by DBM. The third image in Figure 3 demonstrates the GSN's ability to move from only half an image (where the rest is noise) and complete the digit, showing it has a internal representation of the digit that can be sampled to complete the digit.

[math]\displaystyle{ \sum_{i=0}^\infty 2^{-i} }[/math]

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Figure 3

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Faces

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Figure 4

Critique

Mentions SPN