Preserving gauge invariance in neural networks

TL;DR

This paper introduces lattice gauge equivariant convolutional neural networks (L-CNNs) that maintain gauge invariance in lattice gauge theory data processing, demonstrating their effectiveness over non-equivariant models.

Contribution

The paper presents a novel neural network architecture that exactly preserves gauge symmetry, enabling more accurate analysis of lattice gauge theory simulations.

Findings

L-CNNs can represent a wide class of gauge invariant functions.

Gauge invariance is preserved in L-CNNs but broken in non-equivariant networks.

L-CNNs outperform non-equivariant models in regression tasks.

Abstract

In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.