Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories

TL;DR

This paper introduces a gauge-equivariant graph neural network that embeds local gauge symmetries directly into message passing, enabling effective learning of nonlocal observables in lattice gauge theories.

Contribution

It extends equivariant learning to fully local gauge symmetries by embedding non-Abelian symmetry into message passing with gauge-covariant features.

Findings

Successfully models nonlocal correlations and loop structures from local operations.

Validates the approach across pure gauge, gauge-matter, and dynamical regimes.

Establishes gauge-equivariant message passing as a general paradigm for systems with local symmetry.

Abstract

Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for intrinsically nonlocal observables. Here we introduce a gauge-equivariant graph neural network that embeds non-Abelian symmetry directly into message passing via matrix-valued, gauge-covariant features and symmetry-compatible updates, extending equivariant learning from global to fully local symmetries. In this formulation, message passing implements gauge-covariant transport across the lattice, allowing nonlocal correlations and loop-like structures to emerge naturally from local operations. We validate the approach across pure gauge, gauge-matter, and dynamical regimes, establishing gauge-equivariant message passing as a general paradigm for learning in systems governed by local symmetry.