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

Marc Finzi, Max Welling, Andrew Gordon Wilson
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:3318-3328, 2021.

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 $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik’s cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and modeling dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-finzi21a, title = {A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups}, author = {Finzi, Marc and Welling, Max and Wilson, Andrew Gordon Gordon}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {3318--3328}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/finzi21a/finzi21a.pdf}, url = {https://proceedings.mlr.press/v139/finzi21a.html}, 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 $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik’s cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and modeling dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary} }
Endnote
%0 Conference Paper %T A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups %A Marc Finzi %A Max Welling %A Andrew Gordon Wilson %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-finzi21a %I PMLR %P 3318--3328 %U https://proceedings.mlr.press/v139/finzi21a.html %V 139 %X 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 $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik’s cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and modeling dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary
APA
Finzi, M., Welling, M. & Wilson, A.G.. (2021). A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:3318-3328 Available from https://proceedings.mlr.press/v139/finzi21a.html.

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