Lie groupoid equivariant CNNs are defined via lifting and convolution layers that specialize category-equivariant networks, shown equivalent to algebroid versions for suitable groupoids and as special cases of admissible category-equivariant layers via continuous natural transformations.
Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
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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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Introduces an adjusted cup-product neural layer whose output on closed cycles depends only on the adjustment coefficient and is exactly invariant under gauge transformations.
citing papers explorer
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Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
Lie groupoid equivariant CNNs are defined via lifting and convolution layers that specialize category-equivariant networks, shown equivalent to algebroid versions for suitable groupoids and as special cases of admissible category-equivariant layers via continuous natural transformations.
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Adjusted Cup-Product Neural Layer
Introduces an adjusted cup-product neural layer whose output on closed cycles depends only on the adjustment coefficient and is exactly invariant under gauge transformations.