A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups

Marc Finzi, Max Welling, Andrew Gordon Wilson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation, and permutation groups. In this work we provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before, including O(1, 3), O(5), Sp(n), and the Rubik's cube group. Our approach outperforms non-equivariant baselines, with applications including particle physics and dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary matrix groups.

Original languageEnglish (US)
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Pages3318-3328
Number of pages11
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: Jul 18 2021Jul 24 2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Electronic)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online
Period7/18/217/24/21

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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