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Symmetries and equivariance are fundamental to the generalization of neuralnetworks on domains such as images, graphs, and point clouds. Existing work hasprimarily focused on a small number of groups, such as the translation,rotation, and permutation groups. In this work we provide a completely generalalgorithm for solving for the equivariant layers of matrix groups. In additionto recovering solutions from other works as special cases, we constructmultilayer perceptrons equivariant to multiple groups that have never beentackled 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 dynamical systems. We release oursoftware library to enable researchers to construct equivariant layers forarbitrary matrix groups.

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