Applications of Lattice Gauge Equivariant Neural Networks

TL;DR

This paper explores the development and application of Lattice Gauge Equivariant Neural Networks (L-CNNs), which incorporate gauge symmetries into neural network layers to improve performance and generalization in lattice gauge theory simulations.

Contribution

The paper introduces L-CNNs that are gauge equivariant and can be applied to lattice gauge theories, extending their use to Wilson flow and continuous normalizing flow with neural ODEs.

Findings

L-CNNs generalize better to different lattice sizes.

L-CNNs are equivariant under lattice gauge transformations.

Initial tests on toy models show promising results.

Abstract

The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge symmetries, which are incorporated into the network layers of our recently proposed Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs). L-CNNs can generalize better to differently sized lattices than traditional neural networks and are by construction equivariant under lattice gauge transformations. In these proceedings, we present our progress on possible applications of L-CNNs to Wilson flow or continuous normalizing flow. Our methods are based on neural ordinary differential equations which allow us to modify link configurations in a gauge equivariant manner. For simplicity, we focus on simple toy models to test these ideas in practice.