Paper:
Despite their success, generative adversarial networks (GANs) cannot easily generate structured objects like molecules or game maps. The issue is that such objects must satisfy structural requirements (e.g., molecules must be chemically valid, game maps must guarantee reachability of the end goal) that are difficult to capture with examples alone. As a remedy, we propose constrained adversarial networks (CANs), which embed the constraints into the model during training by penalizing the generator whenever it outputs invalid structures. As in unconstrained GANs, new objects can be sampled straightforwardly from the generator, but in addition they satisfy the constraints with high probability. Our approach handles arbitrary logical constraints and leverages knowledge compilation techniques to efficiently evaluate the expected disagreement between the model and the constraints. This setup is further extended to hybrid logical-neural constraints for capturing complex requirements like graph reachability. An extensive empirical analysis on constrained images, molecules, and video game levels shows that CANs efficiently generate valid structures that are both high-quality and novel.

Review:
In this paper the authors present a Generative Adversarial Neural Networks with Xu et al.’s semantic loss applied to the generator. They call this GAN a Constrained Adversarial Network or (CAN) and identify it as a new class of GAN. The authors present three different problem domains for their experiments focused on the generation of constrained images, chunks of Super Mario Bros.-style levels, and molecules. For each domain they include particular constraints for the semantic loss, which biases the generator towards creating valid content according to these constraints. 
The paper at present has a number of issues holding it back. First, I am not convinced by the author’s claims that the application of an existing loss function to the generator is sufficient to identify a new class of GAN. Second, there is a lack of technical detail in the experiments necessary to replicate them. Third, there is a lack of discussion of the experimental results to place them in context for readers. Finally following from the earlier points, there seems to be a lack of technical contributions in the paper. 
I certainly agree with the authors about the inability of GANs to learn structural constraints with insufficient training data, as this has been demonstrated in many examples of prior work. I also agree that particular problem domains, as identified by the authors, have stronger structural requirements. However, it is unclear to me why in these instances one would use GANs and not some alternative approach such as constraint-based solvers. Or even if one wanted to employ GANs, what the benefit of adapting the constraints into a loss function is compared to say constraining generated output in a post-hoc process.
The descriptions of the two of the three experiments do not include any discussion of the GAN architectures or hyperparameters. While this is not strictly necessary in the paper text some discussion in an appendix or a citation to a prior application of the architecture(s) would be appropriate. Without this, it is impossible for future researchers to replicate these results. Further, it is difficult for readers to place the results in context. For individual experiments, such as the Super Mario Bros. experiment, it is unclear why certain choices were made. For example, why train a GAN on just level 1-3 or 3-3, and not train a single model on multiple levels as is common in the field of procedural content generation via machine learning. 
There is a lack of discussion in the paper on the results of each experiment. For example, the output of the GANs for all the experiments seems quite low, and the differences in terms of the results between the GAN and the CAN across the experiments do not seem to be substantial. Some discussion to put this into context for readers would be helpful.
As far as I can understand the primary technical contributions of the paper are: (1) the application of Xu et al.’s semantic loss to GANS, (2) the constraints developed for the three experiments, and (3) the results of the three experiments. I am unconvinced of the utility of these contributions to a general machine learning audience.
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Updated my review as the authors included extra detail regarding the experiments in a new draft, which helped with the reproducibility issue. However, I am still unconvinced in the contributions of the paper outside of what I previously listed. While I am also unfamiliar with any prior example demonstrating that GANs produce invalid structure, this is not a surprising result. Especially as validity can be defined in an arbitrary, domain-specific manner.