Venue: ICLR 2018 conference

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: 
In this paper, the authors interpret the training of GAN by potential field and inspired from which to provide new training procedure for GAN. They claim that under the condition that global optima are achieved for discriminator and generator in each iteration, the Coulomb GAN converges to the global solution. 

I think there are several points need to be addressed. 

1, I agree that the "model collapsing" is due to converging to a local Nash Equilibrium. However, there are more reasons besides the drawback of the loss function, which is emphasized in the paper. Leave the stochastic gradient descent optimization algorithm apart (since most of the neural networks are trained in this way), the parametrization and the richness of discriminator family play a vital role in the model collapsing issue. In fact, even with KL-divergence in which log operation is involved, if one can select reasonable parametrization, e.g., directly handling in function space, the saddle point optimization is convex-concave, which means under the same assumption made in the paper, there is only one global Nash Equilibrium. On the other hand, the richness of the discriminator also important in the training of GAN. I did not get the point about the drawback of III. If indeed as the paper considered in the ideal case, the discriminator is rich enough, III cannot happen. 

The model collapsing is not just because loss function in training GAN. It is caused by the twist of these three issues listed above. Modifying the loss can avoid partially model collapsing, however, it is not appropriate to claim that the proposed algorithm is 'provable'. The assumption in this paper is too restricted, and the discussion is unfair to the existing variants of GAN, e.g., GMMN or Wasserstein GAN, which under some assumptions, there is also only one global Nash Equilibrium. 

2, In the training procedure, the discriminator family is important as we discussed. The paper claims that the reason to introduce the extra discriminator is reducing variance. However, such parametrization will introduce bias too. The bias and variance tradeoff should be explicitly discussed here. Ideally, it should contain all the functions formed with Plummer kernel, but not too large (otherwise, it will increase the sample complexity.). Which function family used in the paper is not clear. 


3, As the authors already realized, the GMMN is one closely related model. It will be more convincing to add the comparison with GMMN. 

In sum, this paper provides an interesting perspective modeling GAN from the potential field, however, there are several issues need to be addressed. I expect to see the reply of the authors regarding the mentioned issues. 
review_title: Several points should be clarified

final_score: rating: 7: Good paper, accept
review_content: The authors draw from electrical field dynamics and propose to formulate the GAN learning problem in a way such that generated samples are attracted to training set samples, but repel each other. Optimizing this formulation using gradient descent can be proven to yield only one optimal global Nash equilibrium, which the authors claim allows Coulomb GANs to overcome the "mode collapse" issue. Experimental results are reported on image and language modeling tasks, and show that the model can produce very diverse samples, although some samples can consist of somewhat nonsensical interpolations.

This is a good, well-written paper. It is technically rigorous and empirically convincing. Overall, it presents an interesting approach to overcome the mode collapse problem with GANs. 

The image samples presented -- although of high variability -- are not of very high quality, though, and I somewhat disagree with the claim that "Coulomb GAN was able to efficiently learn the whole distribution" (Sec 3.1). At best, it seems to me that the new objective does in fact force the generator to concentrate efforts on learning over the full support of the data distribution, but the lower quality samples and sometimes somewhat bad interpolations seem to suggest to me that it is *not* yet doing so very "efficiently". 

Nonetheless, I think this is an important step forward in improving GANs, and should be accepted for publication.

Note: I did not check all the proofs in the appendix.
review_title: Good step forward in improving GANs

final_score: rating: 7: Good paper, accept
review_content: The paper takes an interesting approach to solve the existing problems of GAN training, using Coulomb potential for addressing the learning problem. It is also well written with a clear presentation of the motivation of the problems it is trying to address, the background and proves the optimality of the suggested solution. My understanding and validity of the proof is still an educated guess. I have been through section A.2 , but I'm unfamiliar with the earlier literature on the similar topics so I would not be able to comment on it. 

Overall, I think this is a good paper that provides a novel way of looking at and solving problems in GANs. I just had a couple of points in the paper that I would like some clarification on : 

* In section 2.2.1 : The notion of the generated a_i not disappearing is something I did not follow. What does it mean for a generated sample to "not disappear" ? and this directly extends to the continuity equation in (2). 

* In section 1 : in the explanation of the 3rd problem that GANs exhibit i.e.  the generator not being able to generalize the distribution of the input samples, I was hoping if you could give a bit more motivation as to why this happens. I don't think this needs to be included in the paper, but would like to have it for a personal clarification. 
review_title:  The paper introduces a new way to address GAN training problems, equating it to potential fields and taking inspiration from electrostatics. 

Meta-review: The paper provides an interesting take on GAN training based on Coulomb dynamics. The proposed formulation is theoretically well motivated and authors provide guarantees for convergence. Reviewers agree that the theoretical analysis is interesting but are not completely impressed by the results. The method addresses mode collapse issue but still lacks in sample quality. Nevertheless, reviewers agree that this is a good step towards the understanding of GAN training. 
Decision: Accept (Poster)