Lattice gauge equivariant convolutional neural networks

TL;DR

This paper introduces Lattice gauge equivariant CNNs (L-CNNs) that preserve gauge symmetry and can learn gauge covariant functions on lattices, outperforming traditional CNNs in gauge-invariant tasks.

Contribution

The paper presents a novel gauge-equivariant convolutional layer that forms Wilson loops and incorporates topological data, enabling neural networks to learn gauge covariant functions.

Findings

L-CNNs can learn gauge invariant quantities.

L-CNNs generalize better than traditional CNNs for gauge tasks.

The method preserves gauge symmetry throughout the network.

Abstract

We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.