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Normalizing flows for lattice gauge theory in arbitrary space-time dimension

arXiv 2305.02402 ↗First posted 3 May 2023hep-lat cond-mat.stat-mech cs.LGcited by 23

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Abstract (arXiv)

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow architectures facilitating the generalization to higher-dimensional lattice geometries. Specifically, we discuss masked autoregressive transformations with tractable and unbiased Jacobian determinants, a key ingredient for scalable and asymptotically exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) lattice gauge theory in four space-time dimensions are reported.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 0 of its 13 references that are in the map. First posted on arXiv 3 May 2023.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 6; 2025: 8; 2026: 6.

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  1. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  2. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generationcited by 55
  3. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  4. 2024Bayesian RG Flow in Neural Network Field Theoriescited by 9
  5. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  6. 2024Practical applications of machine-learned flows on gauge fieldscited by 6
  7. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  8. 2025Multilevel Generative Samplers for Investigating Critical Phenomenacited by 5
  9. 2024Non-Perturbative Trivializing Flows for Lattice Gauge Theoriescited by 3
  10. 2025Hierarchical autoregressive neural networks in three-dimensional statistical systemcited by 3
  11. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  12. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
11 more
  1. 2025Path Gradients after Flow Matchingcited by 2
  2. 2026Sampling two-dimensional spin systems with transformerscited by 2
  3. 2026Generative Models and Statistical Validationcited by 2
  4. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  5. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  6. 2024A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equationcited by 0
  7. 2024Stochastic normalizing flows for Effective String Theorycited by 0
  8. 2025Studying Effective String Theory using deep generative modelscited by 0
  9. 2026Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillationcited by 0
  10. 2026Machine learning for four-dimensional SU(3) lattice gauge theoriescited by 0
  11. 2026Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Samplingcited by 0