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

by   Marc Finzi, et al.

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 to particle physics and dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary matrix groups.



There are no comments yet.


page 1

page 5


Orbital Graphs

We introduce orbital graphs and discuss some of their basic properties. ...

LieTransformer: Equivariant self-attention for Lie Groups

Group equivariant neural networks are used as building blocks of group i...

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data

The translation equivariance of convolutional layers enables convolution...

Design equivariant neural networks for 3D point cloud

This work seeks to improve the generalization and robustness of existing...

A formalization of Dedekind domains and class groups of global fields

Dedekind domains and their class groups are notions in commutative algeb...

Lazy caterer jigsaw puzzles: Models, properties, and a mechanical system-based solver

Jigsaw puzzle solving, the problem of constructing a coherent whole from...

Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron: The Haar Orthogonal Case

Free Probability Theory (FPT) provides rich knowledge for handling mathe...

Code Repositories

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.