E3x: E(3)-Equivariant Deep Learning Made Easy

Abstract

This work introduces E3x, a software package for building neural networks that are equivariant with respect to the Euclidean group E(3), consisting of translations, rotations, and reflections of three-dimensional space. Compared to ordinary neural networks, E(3)-equivariant models promise benefits whenever input and/or output data are quantities associated with three-dimensional objects. This is because the numeric values of such quantities (e.g. positions) typically depend on the chosen coordinate system. Under transformations of the reference frame, the values change predictably, but the underlying rules can be difficult to learn for ordinary machine learning models. With built-in E(3)-equivariance, neural networks are guaranteed to satisfy the relevant transformation rules exactly, resulting in superior data efficiency and accuracy.

Authors

Oliver Unke, Hartmut Maennel

Venue

arXiv