Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
2026-04-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors created a new kind of neural network that respects local gauge symmetries, which are important in physics for describing fundamental forces and quantum materials. Their network uses special matrix features to pass messages in a way that naturally handles these local symmetries, even for complex nonlocal patterns. They tested this method in different physics scenarios and showed it works well for learning about systems with local gauge symmetry. This offers a new general approach for machine learning in physics models with such symmetries.
local gauge symmetrynon-Abelian symmetrygraph neural networksmessage passinggauge covariancequantum matterequivariant learninglattice gauge theorynonlocal observables
Authors
Ali Rayat, Yaohang Li, Gia-Wei Chern
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.