Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918462268375040 |
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| author | Rayat, Ali Li, Yaohang Chern, Gia-Wei |
| author_facet | Rayat, Ali Li, Yaohang Chern, Gia-Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20797 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories Rayat, Ali Li, Yaohang Chern, Gia-Wei Strongly Correlated Electrons Machine Learning High Energy Physics - Lattice 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. |
| title | Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories |
| topic | Strongly Correlated Electrons Machine Learning High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2604.20797 |