Universal Equivariant Multilayer Perceptrons
Abstract
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant MLPs with a single hidden layer. In particular, it is shown that having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance). A corollary is unconditional universality of equivariant MLPs for Abelian groups, such as CNNs with a single hidden layer. A second corollary is the universality of equivariant MLPs with a high-order hidden layer, where we give both group-agnostic bounds and means for calculating group-specific bounds on the order of hidden layer that guarantees universal equivariance (invariance).
Cite
@article{arxiv.2002.02912,
title = {Universal Equivariant Multilayer Perceptrons},
author = {Siamak Ravanbakhsh},
journal= {arXiv preprint arXiv:2002.02912},
year = {2020}
}