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Sampling using SU(N) gauge equivariant flows

arXiv 2008.05456 ↗First posted 12 Aug 2020hep-lat cs.LG stat.MLcited by 83

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Abstract (arXiv)

We develop a flow-based sampling algorithm for SU(N) lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an SU(N) variable (or on a U(N) variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.

Key facts. Cited by 83 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Aug 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 19; 2022: 15; 2023: 20; 2024: 9; 2025: 14; 2026: 6.

83 papers.

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  1. 2021E(n) Equivariant Normalizing Flowscited by 165
  2. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  3. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  4. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 74
  5. 2021Smooth Normalizing Flowscited by 52
  6. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  7. 2024Does equivariance matter at scale?cited by 49
  8. 2023Learning Interpolations between Boltzmann Densitiescited by 42
  9. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  10. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  11. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 35
  12. 2021Machine-learning hidden symmetriescited by 31
38 more
  1. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 28
  2. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  5. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  6. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  7. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  8. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  9. 2023Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processescited by 21
  10. 2021Topological Obstructions to Autoencodingcited by 20
  11. 2021Equivariant Manifold Flowscited by 20
  12. 2021Generalization capabilities of translationally equivariant neural networkscited by 18
  13. 2023Scaling Riemannian Diffusion Modelscited by 18
  14. 2021Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Modelscited by 17
  15. 2022Structure-preserving GANscited by 17
  16. 2021Group equivariant neural posterior estimationcited by 16
  17. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  18. 2022Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problemscited by 14
  19. 2023Sample Complexity of Probability Divergences under Group Symmetrycited by 13
  20. 2021Differentiable Physics: A Position Piececited by 12
  21. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  22. 2021Equivariant Finite Normalizing Flowscited by 11
  23. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
  24. 2021Continuous normalizing flows on manifoldscited by 10
  25. 2021Implicit Riemannian Concave Potential Mapscited by 10
  26. 2022Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learningcited by 10
  27. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  28. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion modelscited by 10
  29. 2025Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifoldscited by 10
  30. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  31. 2023Gauge-equivariant neural networks as preconditioners in lattice QCDcited by 8
  32. 2025A Tale of Two Symmetries: Exploring the Loss Landscape of Equivariant Modelscited by 8
  33. 2021Deep Learning Hamiltonian Monte Carlocited by 7
  34. 2023Learning Distributions on Manifolds with Free-Form Flowscited by 7
  35. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  36. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  37. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  38. 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6

50 most cited of 83 All 83 (JSON)