Venue: ICLR 2017 workshop

Reviews:

final_score: rating: 7: Good paper, accept
review_content: Summary: This paper proposed a novel method for training Markov chains using the indistinguishability framework popularized by generative adversarial networks. Experiments on MNIST are promising. The experiments show a clear improvement of quality as the chain size increases.

Novelty: The idea has been featured in prior work but only amongst other ideas mixed in, but this is the first paper which describes and validates this idea alone.

Clarity: The paper is very clearly written, and the experiments are appropriate for a workshop paper.

Quality: Neat execution of idea. However, it's not clear whether the Markov chain is actually refining the same digit or whether the improvement is just due to more computation that a large chain can perform. Is the improvement due to the new objective, or is this just a recurrent neural network? The authors need to show a chain of the sample size from 0 to 50 to prove the refinement.

Pros: Independent atomic description and evaluation of a significant idea.
Cons: It's not 100% clear whether it's the MCMC that works, or just recurrent computation.
review_title: Review

final_score: rating: 6: Marginally above acceptance threshold
review_content: The authors propose to use an adversarial objective to train a transition operator for a Markov chain such that the stationary distribution is indistinguishable from the training data. Samples are either generated by starting from some fixed distribution \pi^0 and applying the operator multiple times, or by starting from a training set sample. The idea is simple, intuitively appealing and seems to be  mathematically correct.

In the experimental section the authors apply their approach to MNIST and show results for three differently parameterized transition operators: a DCGAN based architecture, a convolutional- and a fully connected neural neural network. The corresponding samples in Figs. 1-3 look decent, although not obviously better than those of other GAN based models.
A surprising (and potentially disappointing?) property apparent from Figs. 1-4 is, that even applying the transition operator only once, typically changes the digit-class and style completely. It therefore seems, the model uses the current state of the chain merely as a source randomness. It has not learned to “refine” the current state. Phrased more positively: the learned MC mixes extraordinary fast. 
  
Positive: 
Simple idea; straightforward implementation.
Combines ideas from GSNs (generative stochastic networks) and adversarial training.

Negative:
No objective way to compare model quality; no clear improvement over std. GANs.
Might use the current state merely as source of randomness: taking 5 or 10 steps does not provide obvious improvement over taking 2 steps.

review_title: Simple, appealing idea but no clear improvement over std. GANs

Decision: Accept