Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 8: Accept
review_content: This is an interesting, timely study.  CycleGAN has attracted a lot of attention in unpaired image-to-image translation. Although the basic idea of CycleGAN seem sensible, its precise behavior is not totally clear--can one really avoid mismatch with CycleGAN? Do we need additional constraints? This paper provides a nice answer the the first question.

Overall I enjoyed reading this paper. The addressed issue is important, the investigation is reasonable, and the results are intuitive and plausible, with clear practical implications. I think it is a good paper.

 I acknowledge I read the authors' response and other reviews and would like to keep my original rating.
review_title: Official Blind Review #3

final_score: rating: 6: Weak Accept
review_content: This paper focuses on CycleGAN method to show theoretically when the exact solution space is invariant with respect to authomorphisms of the underlying probability spaces for unpaired image-to-image translation. 

- The paper provides interesting theoretical results on identifying conditions under which CycleGAN admits nontrivial symmetries and has a natural structure of a principal homogeneous space.  Proposition 2.1 provides interesting insights into the invariance of the kernel space. 

- Propositions 2.5 and 2.6 are interesting in that they show that the existence of authomorphisms can worsen the performance of CycleGAN, however, it is unclear that in practice, how could one verify the conditions efficiently before applying CycleGAN.

- The experimental results are interesting, however, they are very limited. Having a toy experiment is a good sanity check, but it would be more interesting to see the performance on a real-world applications, such as medical images or other use-cases brought in the introduction. Also, more discussion on the results provided in Fig 3, confusion matrices, would be very helpful. Are there any intuitions behind the large and low values in the table? It could be interesting to see what are the effects of other parameters such as alpha in producing the results. 

- Overall this paper presents interesting results regarding the theory of CycleGANs, however, the numerical results are very limited, and do not justify the motivations discussed in the introduction and the abstract. Moreover, although the paper introduces novel attempts and theoretically analyzing the CycleGAN, the scope of the work seems to be limited, and thus, it does not have a sufficient significance to be published in ICLR. I strongly suggest the authors to expand and provide more experimental evaluations.

** update:
Thanks for your comments! I found the additional experiment useful and better aligned with the purpose of the model. The discussion added clarified the confusion about the automorphism. That is why I decided to change my score. 
review_title: Official Blind Review #1

final_score: rating: 3: Weak Reject
review_content: I have read the rebuttal of the authors . Thank you for you answer and for addressing some concerns.  While the question addressed is important, the theory presented here does not seem to hint to a solution, hence I am keeping my score.    

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Summary of the paper: 

This paper shows that the cycle GAN loss suffers from the presence of lot of symmetries that make the existence of a unique solution not possible , and moreover adding a regularizer that uses the identity loss is not enough to make the problem less prone to those invariances. 

Review of the paper: 

The notations and the formalism  in the paper are heavy and cumbersome and don't come with any surprising result, since the transforms between unpaired spaces will be found always up to   symmetries since we have the composition of one map with another. The use of the identity loss is also shown to not to help either in fixing this invariance issue. 

Experiments are not interesting since without any structure on the map of F and G , the source domain and the target domain, one is expected to get permutations.

The paper points in the conclusion  that the use of skipconnection in F and G has the major influence.

 The study of cycle GAN might need some assessment of what is the mutual information between the domains , as on what  information needs be preserved , and information needs to match , skip connection maintain the content in image generation as the information is kept from lower layer and its modified to target the style of the target images. 

An information theoretic analysis of cycle gan is needed using for example the objective of "MISO: Mutual Information Loss with Stochastic Style Representations for Multimodal Image-to-Image Translation". 
or by using a radically new approach  for cycle gan such as the Gromov Wasserstein distance as done in " Learning Generative Models Across Incomparable Spaces"

review_title: Official Blind Review #2

Meta-review: This paper theoretically studied one of the fundamental issue in CycleGAN (recently gained much attention for image-to-image translation). The authors analyze the space of exact and approximated solutions under automorphisms.

Reviewers mostly agree with theoretical value of the paper. Some concerns on practical values are also raised, e.g., limited or no-surprising experimental results. In overall, I think this is a boarderline paper. But, I am a bit toward acceptance as the theoretical contribution is solid, and potentially beneficial to many future works on unpaired image-to-image translation.


Decision: Accept (Poster)