Generative Adversarial Symmetry Discovery

TL;DR

LieGAN is a novel framework that automatically discovers symmetries in data using adversarial training, enabling the use of equivariant neural networks without prior symmetry knowledge.

Contribution

It introduces a Lie algebra-based approach for automatic symmetry discovery, applicable to various groups, improving neural network performance without pre-specified symmetries.

Findings

Successfully discovers multiple symmetry groups including SO(n) and Lorentz groups.

Enhances neural network accuracy and generalization by incorporating learned symmetries.

Demonstrates applicability in trajectory prediction and particle physics tasks.

Abstract

Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.