Complete Neural Networks for Complete Euclidean Graphs

arXiv:2301.13821v3 Announce Type: replace
Abstract: Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model with polynomial complexity is known to be complete, that is, able to distinguish between any pair of non-isomorphic point clouds. We fill this theoretical gap by showing that point clouds can be completely determined, up to permutation and rigid motion, by …

abstract arxiv complexity cs.lg dynamics graphs modeling molecular dynamics natural networks neural networks polynomial recommender systems success systems type