A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
This work addresses the need for more flexible equivariant models in machine learning, enabling researchers to handle symmetries in diverse domains, though it is incremental in extending existing methods to broader groups.
The paper tackles the problem of constructing equivariant neural networks for arbitrary matrix groups, which had been limited to a few specific groups, by providing a general algorithm that recovers known solutions and enables new applications like particle physics and dynamical systems, outperforming non-equivariant baselines.
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 dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary matrix groups.