mlsanityData to 7 Oct 2026

Geometrical aspects of lattice gauge equivariant convolutional neural networks

arXiv 2303.11448 ↗First posted 20 Mar 2023hep-lat cs.LG stat.MLcited by 6

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Abstract (arXiv)

Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be equipped with global group equivariance. This allows us to extend the formulation to be equivariant not just under translations but under global lattice symmetries such as rotations and reflections. Additionally, we provide a geometric formulation of L-CNNs and show how convolutions in L-CNNs arise as a special case of gauge equivariant neural networks on SU(N) principal bundles.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 28 of its 46 references that are in the map. First posted on arXiv 20 Mar 2023.

Builds on

28 of 46 references.

References · 28

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  2. 2016Group Equivariant Convolutional Networkscited by 1,154
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
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  5. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
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16 more
  1. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  2. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  3. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  4. 2020Dense Steerable Filter CNNs for Exploiting Rotational Symmetry in Histology Imagescited by 33
  5. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 30
  6. 2021Flow-based sampling for fermionic lattice field theoriescited by 27
  7. 2021Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flowscited by 24
  8. 2022Equivariance versus Augmentation for Spherical Imagescited by 24
  9. 2021Homogeneous vector bundles and G-equivariant convolutional neural networkscited by 21
  10. 2021Generalization capabilities of translationally equivariant neural networkscited by 18
  11. 2021Quantum field-theoretic machine learningcited by 16
  12. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  13. 2019Covariance in Physics and Convolutional Neural Networkscited by 12
  14. 2020Towards Novel Insights in Lattice Field Theory with Explainable Machine Learningcited by 12
  15. 2022Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groupscited by 11
  16. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 8

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Cited by year

Citing papers per year: 2023: 3; 2024: 1; 2025: 2.

6 papers.

  1. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  2. 2025Physics-Driven Learning for Inverse Problems in Quantum Chromodynamicscited by 7
  3. 2023Gauge-equivariant pooling layers for preconditioners in lattice QCDcited by 5
  4. 2023Fixed point actions from convolutional neural networkscited by 3
  5. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  6. 2025Gauge Flow Modelscited by 2