Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories

2026-04-22

AI Summary

This work addresses the absence of a general framework in existing machine learning approaches for handling local gauge symmetries, particularly in non-Abelian settings and for non-local observables. It introduces Gauge Equivariant Graph Neural Networks, which extend equivariant learning from global to fully local gauge symmetries for the first time. By embedding matrix-valued, gauge-covariant features and symmetry-compatible update rules into message passing, the method explicitly models non-Abelian local gauge symmetry, enabling non-local correlations and loop-like structures to emerge naturally from purely local operations. The approach demonstrates consistent efficacy across pure gauge theories, gauge-matter coupled systems, and dynamical settings, thereby establishing the generality and feasibility of gauge-equivariant learning for systems governed by local symmetries.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Security and privacy of machine learning and AI applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• gauge symmetry
• graph neural networks
• nonlocal observables
• equivariant learning
• lattice gauge theories

Innovation

• gauge-equivariant
• graph neural networks
• local gauge symmetry
• non-Abelian symmetry
• message passing