TY - GEN
T1 - A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
AU - Finzi, Marc
AU - Welling, Max
AU - Wilson, Andrew Gordon
N1 - Publisher Copyright:
Copyright © 2021 by the author(s)
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85161319707
T3 - Proceedings of Machine Learning Research
SP - 3318
EP - 3328
BT - Proceedings of the 38th International Conference on Machine Learning, ICML 2021
PB - ML Research Press
T2 - 38th International Conference on Machine Learning, ICML 2021
Y2 - 18 July 2021 through 24 July 2021
ER -