Lattice gauge symmetry in neural networks

TL;DR

This paper introduces Lattice Gauge Equivariant CNNs (L-CNNs), a neural network architecture that preserves gauge symmetry explicitly, demonstrating improved accuracy and generalizability in lattice gauge theory tasks.

Contribution

The paper presents the design of gauge equivariant convolutional and bilinear layers, enabling neural networks to maintain gauge symmetry exactly in lattice gauge theory applications.

Findings

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

L-CNNs demonstrate better generalization and accuracy.

The architecture explicitly preserves gauge symmetry.

Abstract

We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge symmetry. We discuss the concept of gauge equivariance which we use to explicitly construct a gauge equivariant convolutional layer and a bilinear layer. The performance of L-CNNs and non-equivariant CNNs is compared using seemingly simple non-linear regression tasks, where L-CNNs demonstrate generalizability and achieve a high degree of accuracy in their predictions compared to their non-equivariant counterparts.