mlsanityData to 14 Oct 2026

Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories

arXiv 2604.20797 ↗First posted 22 Apr 2026cond-mat.str-el cs.LG hep-latcited by 3

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 25 of its 67 references that are in the map. First posted on arXiv 22 Apr 2026.

Builds on

25 of 67 references.

References · 25

  1. 2017Inductive Representation Learning on Large Graphscited by 6,320
  2. 2018How Powerful are Graph Neural Networks?cited by 4,393
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2016Group Equivariant Convolutional Networkscited by 1,165
  5. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  7. 2018Invariant and Equivariant Graph Networkscited by 346
  8. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  9. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 256
  10. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  11. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  12. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
13 more
  1. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 101
  2. 2020Sampling using SU(N) gauge equivariant flowscited by 84
  3. 2021Machine Learning in the Search for New Fundamental Physicscited by 50
  4. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  5. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 31
  6. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 28
  7. 2022Equivariant Networks for Crystal Structurescited by 24
  8. 2020Machine Learning for Condensed Matter Physicscited by 22
  9. 2021Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Modelscited by 18
  10. 2021Generalization capabilities of translationally equivariant neural networkscited by 18
  11. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 9
  12. 2023Gauge-equivariant pooling layers for preconditioners in lattice QCDcited by 6
  13. 2024Deep learning lattice gauge theoriescited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networkscited by 1
  2. 2026Adjusted Cup-Product Neural Layercited by 0
  3. 2026Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networkscited by 0