The paper attempts make progress in the problem of learning mappings from sets of vectors to (hyper) graphs. In this regard, authors propose to learn a sequence of functions mapping a set to a tuple of k-edges. The reviewers find this formulation to be interesting. This formulation is shown to be universal as well as claimed to be parameter efficient and practical. The reviewers find the universality result to be novel, meaningful, and presented nicely, but only involved fairly standard techniques. Overall, the reviewers are happy with current version of the draft. Thus, I would be happy to recommend acceptance to NeurIPS. For the final version of the paper, please incorporate all reviewer suggested changes with the extra one page (e.g. figure size, timing results etc.). Also maybe add an remark that psi network has to be sufficiently powerful depending on the problem, which will guide other people when applying set2graph.