Clarity: The paper is fairly dense because of the unfortunate 8-page limit, but well and carefully written. I think the most confusing part for readers ls likely to be the conjunction operation -- if there's an extra page in the camera-ready, the presentation here should be slowed down with some qualitative discussion. You should probably clarify early on that you're talking about undirected hypergraphs. Notation in section 2.1: I regard 52-53 as a commutation property, basically vertices(\bar{e}) \bar{vertices(e)}, where \bar lifts from variables or variable-tuples to their labels. I don't understand where the name "att" comes from ("attachment"?) or why you use the name "type" in the way you do.

We investigate adversarial learning in the case when only an unnormalized form of the density can be accessed, rather than samples. With insights so garnered, adversarial learning is extended to the case for which one has access to an unnormalized form u(x) of the target density function, but no samples. Further, new concepts in GAN regularization are developed, based on learning from samples or from u(x). The proposed method is compared to alternative approaches, with encouraging results demonstrated across a range of applications, including deep soft Q-learning.