mlsanityData to 14 Oct 2026

Lattice gauge equivariant convolutional neural networks

arXiv 2012.12901 ↗First posted 23 Dec 2020hep-lat cs.LG hep-phcited by 45

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Abstract (arXiv)

We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.

Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Dec 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 10; 2022: 6; 2023: 6; 2024: 4; 2025: 9; 2026: 10.

45 papers.

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  1. 2021A Living Review of Machine Learning for Particle Physicscited by 78
  2. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 65
  3. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  4. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  5. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  6. 2021Homogeneous vector bundles and G-equivariant convolutional neural networkscited by 21
  7. 2022Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computingcited by 20
  8. 2021Generalization capabilities of translationally equivariant neural networkscited by 18
  9. 2021Quantum field-theoretic machine learningcited by 16
  10. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  11. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
  12. 2022Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learningcited by 10
33 more
  1. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  2. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 9
  3. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  4. 2021Deep Learning Hamiltonian Monte Carlocited by 7
  5. 2025Physics-Driven Learning for Inverse Problems in Quantum Chromodynamicscited by 7
  6. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  7. 2023Gauge-equivariant pooling layers for preconditioners in lattice QCDcited by 6
  8. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  9. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
  10. 2025AtlasD: Automatic Local Symmetry Discoverycited by 5
  11. 2021Machine Learning in Nuclear Physicscited by 4
  12. 2023mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networkscited by 4
  13. 2025Equivariant Neural Networks for General Linear Symmetries on Lie Algebrascited by 4
  14. 2023Fixed point actions from convolutional neural networkscited by 3
  15. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  16. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  17. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 3
  18. 2025Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networkscited by 2
  19. 2025Gauge Flow Modelscited by 2
  20. 2026Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theoriescited by 2
  21. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  22. 2024Optimal Symmetries in Binary Classificationcited by 1
  23. 2025Gauge-Equivariant Graph Networks via Self-Interference Cancellationcited by 1
  24. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  25. 2026How unconstrained machine-learning models learn physical symmetriescited by 1
  26. 2026Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networkscited by 1
  27. 2021Lattice gauge symmetry in neural networkscited by 0
  28. 2021Generalization capabilities of neural networks in lattice applicationscited by 0
  29. 2026Machine learning for four-dimensional SU(3) lattice gauge theoriescited by 0
  30. 2026Steerable Neural ODEs on Homogeneous Spacescited by 0
  31. 2026Adjusted Cup-Product Neural Layercited by 0
  32. 2026Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianccited by 0
  33. 2026Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discoverycited by 0