Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
This provides a general paradigm for learning in systems governed by local symmetry, addressing a bottleneck in machine learning for fundamental physics.
The paper tackled the problem of learning under site-dependent symmetries in lattice gauge theories by introducing a gauge-equivariant graph neural network, which achieved validation across pure gauge, gauge-matter, and dynamical regimes.
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.