mlsanityData to 14 Oct 2026

Multilevel Generative Samplers for Investigating Critical Phenomena

arXiv 2503.08918 ↗First posted 11 Mar 2025cs.LG hep-lat stat.MLcited by 6

Not on the map. Why?

Abstract (arXiv)

Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length -- known as scale invariance at criticality (SIC) in the renormalization group theory. SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS) -- a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site-wise-independent conditional HB sampling. Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers. RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for 128x128 two-dimensional Ising systems.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 35 of its 125 references that are in the map. First posted on arXiv 11 Mar 2025.

Builds on

35 of 125 references.

References · 35

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2015Variational Inference with Normalizing Flowscited by 2,170
  4. 2016WaveNet: A Generative Model for Raw Audiocited by 1,722
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  6. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
  7. 2016Pixel Recurrent Neural Networkscited by 816
  8. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 417
  9. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 307
  10. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 172
  11. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  12. 2014Neural Variational Inference and Learning in Belief Networkscited by 117
23 more
  1. 2016Why does deep and cheap learning work so well?cited by 100
  2. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
  3. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  4. 2018Neural Network Renormalization Groupcited by 48
  5. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  6. 2017Mutual Information, Neural Networks and the Renormalization Groupcited by 33
  7. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  8. 2023Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theoriescited by 25
  9. 2023Normalizing flows for lattice gauge theory in arbitrary space-time dimensioncited by 23
  10. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  11. 2019AR-Net: A simple Auto-Regressive Neural Network for time-seriescited by 20
  12. 2016Learning Thermodynamics with Boltzmann Machinescited by 16
  13. 2023Renormalizing Diffusion Modelscited by 16
  14. 2024Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defectscited by 13
  15. 2022Hierarchical autoregressive neural networks for statistical systemscited by 12
  16. 2023Sampling the lattice Nambu-Goto string using Continuous Normalizing Flowscited by 12
  17. 2020RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse priorcited by 11
  18. 2021Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulationscited by 10
  19. 2020Learning the Ising Model with Generative Neural Networkscited by 9
  20. 2021Universality of Winning Tickets: A Renormalization Group Perspectivecited by 8
  21. 2023The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systemscited by 8
  22. 2023ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulationcited by 8
  23. 2024MS3D: A RG Flow-Based Regularization for GAN Training with Limited Datacited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Sampling two-dimensional spin systems with transformerscited by 2
  2. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  3. 2026The critical slowing down in training diffusion modelscited by 1
  4. 2026Variational Autoregressive Networks with probability priorscited by 0
  5. 2026Renormalization Group Flow Matching for Scalable Local Generative Modelingcited by 0
  6. 2026Data Free Training of Diffusion Models for Lattice Field Theoriescited by 0