Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
This paper uses the framework of Stone-Weiserstrass theorem to prove universal approximation of equivariant/invariant functions with respect to permutation groups by a family of single-hidden layer graph neural networks. Reviewers agreed that this work is technically sound, and offers a complementary perspective of known universal approximation results under (discrete) symmetries. Some reviewers were skeptical about the significance of this work, in the sense that it may feel incremental with respect to Maron et al.'19 which establish universal approximation in the invariant case. After discussions with reviewers and based on author feedback, ultimately the AC considers the positive aspects contributed in this work outweight its shortcomings, and therefore recommends acceptance.