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Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions

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arxiv 2207.08945 v3 pith:KSHV234J submitted 2022-07-18 hep-lat cs.LG

Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions

classification hep-lat cs.LG
keywords theoriesfieldlatticesamplingfermionicflowflow-basedgauge-equivariant
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as stochastic estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD. Methods by which flow-based sampling approaches can be improved via standard techniques such as even/odd preconditioning and the Hasenbusch factorization are also outlined. Numerical demonstrations in two-dimensional U(1) and SU(3) gauge theories with $N_f=2$ flavors of fermions are provided.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sampling the Schwinger Model with Gauge-Equivariant Diffusion

    hep-lat 2026-06 unverdicted novelty 7.0

    A gauge-equivariant diffusion model samples Schwinger model configurations, yielding unbiased observables matching MCMC and qualitatively less topological freezing than HMC.

  2. Higher-order hopping-parameter expansion by human-AI collaboration

    hep-lat 2026-06 accept novelty 6.5

    Trie-based algorithms evaluate the κ^8, κ^10 and κ^12 terms of Tr ln M on SU(Nc) configurations at costs of roughly 20, 460 and 8900 staple evaluations, verified against a reference implementation.

  3. Diffusion Models for Sampling Near Criticality in Lattice Field Theories

    hep-lat 2026-07 accept novelty 6.0

    Fully convolutional diffusion models trained on small lattices transfer to unseen larger volumes for 2D/3D phi^4 sampling across phases, matching or beating same-size training on most observables.

  4. Higher-order hopping-parameter expansion by human-AI collaboration

    hep-lat 2026-06 accept novelty 6.0

    Trie-based algorithms evaluate HPE coefficients through κ^12 on SU(Nc) configurations at roughly 20, 460, and 8900 staple costs, verified against a reference implementation.

  5. Normalizing flows for all-orders QED corrections in lattice field theory

    hep-lat 2026-05 unverdicted novelty 6.0

    Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.

  6. Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory

    hep-lat 2025-10 unverdicted novelty 6.0

    Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.

  7. Higher-order hopping-parameter expansion by human-AI collaboration

    hep-lat 2026-06 conditional novelty 5.0

    Trie-structured algorithms compute κ^8 to κ^12 terms in the hopping expansion of Tr ln M at costs scaling from 20x to 8900x a staple, verified by direct comparison to a reference calculation.

  8. Machine learning for four-dimensional SU(3) lattice gauge theories

    hep-lat 2026-04 unverdicted novelty 3.0

    Machine learning generative models and renormalization-group neural networks are used to enhance gauge field sampling and learn fixed-point actions in 4D SU(3) lattice gauge theories, with presented scaling results to...