MatrixNet: Learning over symmetry groups using learned group representations

TL;DR

MatrixNet is a neural network architecture that learns matrix representations of symmetry group elements, improving sample efficiency and generalization in tasks involving geometric data and group transformations.

Contribution

It introduces a novel approach where the network learns group representations directly, unlike traditional methods that use predefined representations.

Findings

MatrixNet outperforms standard baselines in prediction tasks.

It generalizes to larger group elements beyond training data.

Respects group relations for better generalization.

Abstract

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use known symmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.