LieTransformer: Equivariant self-attention for Lie Groups

TL;DR

The paper introduces LieTransformer, a novel self-attention architecture equivariant to Lie groups, enhancing group invariant neural networks and demonstrating competitive results across diverse tasks.

Contribution

It extends group equivariant neural networks to self-attention mechanisms, allowing equivariance to arbitrary Lie groups, which was previously limited mainly to convolutions.

Findings

Competitive performance on shape counting, molecular property regression, and particle trajectory modeling.

Demonstrates generality and effectiveness of LieSelfAttention layers.

Extends the scope of group equivariant neural networks beyond convolutions.

Abstract

Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics.