Relaxed Equivariant Graph Neural Networks

TL;DR

This paper introduces a framework for relaxed E(3) graph equivariant neural networks that can learn and control symmetry breaking, enhancing modeling of physical systems with symmetry deviations.

Contribution

It extends the e3nn framework by incorporating relaxed weights to enable learned symmetry breaking within continuous groups.

Findings

Relaxed weights effectively learn the appropriate degree of symmetry breaking.

The framework demonstrates improved modeling of physical systems with symmetry deviations.

Empirical results validate the ability to control symmetry breaking in neural networks.

Abstract

3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry breaking within continuous groups. Building on the existing e3nn framework, we propose the use of relaxed weights to allow for controlled symmetry breaking. We show empirically that these relaxed weights learn the correct amount of symmetry breaking.