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.
| Comments: | 11 pages, 5 figures |
| Subjects: | Strongly Correlated Electrons (cond-mat.str-el); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat) |
| Cite as: | arXiv:2604.20797 [cond-mat.str-el] |
| (or arXiv:2604.20797v1 [cond-mat.str-el] for this version) | |
| https://doi.org/10.48550/arXiv.2604.20797 arXiv-issued DOI via DataCite (pending registration) |
From: Gia-Wei Chern [view email]
[v1]
Wed, 22 Apr 2026 17:21:20 UTC (8,784 KB)
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