Generative Adversarial Nets
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1 2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
Review of submission 1384:Generative Adversarial NetsSummary: There are two "adversarial" MLPs G and D. G gets random inputs, and should learn to generate samples of a given data distribution. D is trained to learn the probability that something like G's output stems from the original distribution instead of G, while G is trained "to maximize the probability of D making a mistake." First experimental results are described. Comments:Sections 1 and 2:I find the basic ideas quite interesting and appealing.The discussion of related work, however, could be a bit more balanced. Example:"So far, the most striking successes in deep learning have involved discriminative models, usually those that map a high-dimensional, rich sensory input to a class label [14, 21]."References [14, 21] are about discriminative models for speech recognition and Imagenet. But [14] does not yet include the current state of the art of discriminative models for speech - compare instead the work of Graves et al, e.g., IJCAI 2007, ICASSP 2013, ICML 2014. And [21] is not any longer state of the art for Imagenet - compare instead work of Zeiler and Fergus http://arxiv.org/abs/1311.2901  Also, the cited survey of 2009 [1] on "rich, hierarchical models [1]" does not mention numerous original papers on deep learning with hierarchical models since the 1960s, many of them listed in a recent comprehensive overview http://arxiv.org/abs/1404.7828 In the context of "generalized denoising auto-encoders [4]", one should also cite the earlier, closely related work of Behnke at IJCAI 2001 and ICANN 2003.In the context of backpropagation "into a stochastic network with continuous activations (so that gradients can be back-propagated)," one should also cite the much older original papers on this, in particular those by Williams (e.g., Machine Learning, 1992), who adjusted mean and variance of probabilistic continuous units by backpropagation through random number generators.Finally, how is the submission related to the first work on "adversarial" MLPs for modeling data distributions through estimating conditional probabilities, which was called "predictability minimisation" or PM (Schmidhuber, NECO 1992)? The new approach seems similar in many ways. Both approaches use "adversarial" MLPs to estimate certain probabilities and to learn to encode distributions. A difference is that the new system learns to generate a non-trivial distribution in response to statistically independent, random inputs, while good old PM learns to generate statistically independent, random outputs in response to a non-trivial distribution (by extracting mutually independent, factorial features encoding the distribution). Hence the new system essentially inverts the direction of PM - is this the main difference? Should it perhaps be called "inverse PM"?Sections 4 and 6 - convergence:Interesting theorem: Under certain assumptions the algorithm will converge:"If G and D have enough capacity, and at each step of Algorithm 1, D is allowed to approximately track its optimum given G, and each update of G improves its criterion, then Algorithm 1 converges to the global optimum."Here I seem to stumble about a possibly irrelevant or trivial issue. Is it really enough that each update of G improves its criterion? Could it not be that those improvements get exponentially smaller over time in some weird way, such that even infinitely many of them might converge to a suboptimal point? My intuition tells me that this is not the case, and probably this is just a minor technical issue, but has this really been shown, or is it trivial for some reason - if so, is there a reference for this?As was to be expected, some of the drawbacks mentioned by the authors are similar to those of adversarial PM for distribution modeling: "G must not be trained too much without updating D ..."Section 5 - experimentsExperimental results and graphical visualizations are interesting. They seem a bit hard to judge tough, for lack of direct comparisons to the state of the art, although at least for one of the experiments (Parzen density) the authors cautiously write: "This method of estimating the likelihood has somewhat high variance and does not perform well in high dimensional spaces but it is the best method available to our knowledge."The authors comment on the experimental results with some handwaving:"While we make no claim that these samples are better than samples generated by existing methods, we believe that these samples are at least competitive with the better generative models in the literature and highlight the potential of the adversarial framework."Section 7 - a somewhat half-hearted conclusion:"This paper has demonstrated the viability of the adversarial modeling framework, suggesting that these research directions could prove useful."