mlsanityData to 7 Oct 2026

Learning Lattice Quantum Field Theories with Equivariant Continuous Flows

arXiv 2207.00283 ↗First posted 1 Jul 2022hep-lat cond-mat.stat-mech cs.LGcited by 37

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Abstract (arXiv)

We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test our model on the φ4 theory, showing that it systematically outperforms previously proposed flow-based methods in sampling efficiency, and the improvement is especially pronounced for larger lattices. Furthermore, we demonstrate that our model can learn a continuous family of theories at once, and the results of learning can be transferred to larger lattices. Such generalizations further accentuate the advantages of machine learning methods.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 14 of its 49 references that are in the map. First posted on arXiv 1 Jul 2022.

Builds on

14 of 49 references.

References · 14

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  5. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  6. 2020Normalizing Flows on Tori and Spherescited by 117
  7. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  8. 2020Sampling using SU(N) gauge equivariant flowscited by 83
  9. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  10. 2020Towards Novel Insights in Lattice Field Theory with Explainable Machine Learningcited by 12
  11. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  12. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 10
2 more
  1. 2017Towards reduction of autocorrelation in HMC by machine learningcited by 9
  2. 2019Classifying Topological Charge in SU(3) Yang-Mills Theory with Machine Learningcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 10; 2024: 9; 2025: 12; 2026: 4.

37 papers.

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  1. 2024Does equivariance matter at scale?cited by 49
  2. 2023Learning Interpolations between Boltzmann Densitiescited by 42
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  5. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  6. 2024Efficient mapping of phase diagrams with conditional Boltzmann Generatorscited by 18
  7. 2023Renormalizing Diffusion Modelscited by 16
  8. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  9. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  10. 2024On learning higher-order cumulants in diffusion modelscited by 10
  11. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
  12. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
25 more
  1. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributionscited by 7
  2. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6
  3. 2023Fluctuation without dissipation: Microcanonical Langevin Monte Carlocited by 6
  4. 2024Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flowscited by 6
  5. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  6. 2025Neural Flow Samplers with Shortcut Modelscited by 5
  7. 2025Multilevel Generative Samplers for Investigating Critical Phenomenacited by 5
  8. 2025Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusioncited by 4
  9. 2023Fixed point actions from convolutional neural networkscited by 3
  10. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  11. 2025Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimizationcited by 3
  12. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  13. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  14. 2025SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flowscited by 2
  15. 2026Generative Models and Statistical Validationcited by 2
  16. 2022Deformations of Boltzmann Distributionscited by 1
  17. 2024Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flowscited by 1
  18. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  19. 2025Viability of perturbative expansion for quantum field theories on neuronscited by 1
  20. 2026The critical slowing down in training diffusion modelscited by 1
  21. 2023Fourier Neural Differential Equations for learning Quantum Field Theoriescited by 0
  22. 2025Studying Effective String Theory using deep generative modelscited by 0
  23. 2025Particle Monte Carlo methods for Lattice Field Theorycited by 0
  24. 2026Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theoriescited by 0
  25. 2026What Neural Network Field Theory Can and Cannot Realise on a Computercited by 0