mlsanityData to 7 Oct 2026

Solving Statistical Mechanics Using Variational Autoregressive Networks

arXiv 1809.10606 ↗First posted 27 Sep 2018cond-mat.stat-mech cond-mat.dis-nn cs.LGcited by 99

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Abstract (arXiv)

We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variational free energy, estimates physical quantities such as entropy, magnetizations and correlations, and generates uncorrelated samples all at once. Training of the network employs the policy gradient approach in reinforcement learning, which unbiasedly estimates the gradient of variational parameters. We apply our approach to several classic systems, including 2D Ising models, the Hopfield model, the Sherrington-Kirkpatrick model, and the inverse Ising model, for demonstrating its advantages over existing variational mean-field methods. Our approach sheds light on solving statistical physics problems using modern deep generative neural networks.

Key facts. Cited by 99 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Sep 2018.

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Citing papers per year: 2021: 12; 2022: 16; 2023: 14; 2024: 10; 2025: 27; 2026: 20.

99 papers.

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  1. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 58
  2. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  3. 2021Variational Neural Annealingcited by 45
  4. 2025LEAPS: A discrete neural sampler via locally equivariant networkscited by 30
  5. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  6. 2021NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systemscited by 27
  7. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  8. 2023Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspectivecited by 26
  9. 2022Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flowscited by 22
  10. 2021Local-Global MCMC kernels: the best of both worldscited by 21
  11. 2023Variational Annealing on Graphs for Combinatorial Optimizationcited by 21
  12. 2021Tensor networks for unsupervised machine learningcited by 20
38 more
  1. 2021Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networkscited by 17
  2. 2021Ab-initio study of interacting fermions at finite temperature with neural canonical transformationcited by 16
  3. 2023Controlling Continuous Relaxation for Combinatorial Optimizationcited by 16
  4. 2021Efficient Bayesian Sampling Using Normalizing Flows to Assist Markov Chain Monte Carlo Methodscited by 15
  5. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  6. 2022Precision Machine Learningcited by 14
  7. 2024A theoretical perspective on mode collapse in variational inferencecited by 14
  8. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  9. 2022Hierarchical autoregressive neural networks for statistical systemscited by 12
  10. 2025Reinforcement Fine-Tuning for Materials Designcited by 11
  11. 2021Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulationscited by 10
  12. 2021Machine Learning of Thermodynamic Observables in the Presence of Mode Collapsecited by 10
  13. 2022Path-Gradient Estimators for Continuous Normalizing Flowscited by 10
  14. 2025Artificial intelligence for representing and characterizing quantum systemscited by 9
  15. 2022Neural-network solutions to stochastic reaction networkscited by 8
  16. 2023The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systemscited by 8
  17. 2023qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformerscited by 8
  18. 2022m^ast of two-dimensional electron gas: a neural canonical transformation studycited by 7
  19. 2025Rethinking Losses for Diffusion Bridge Samplerscited by 7
  20. 2022Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problemscited by 6
  21. 2022Deep Variational Free Energy Approach to Dense Hydrogencited by 6
  22. 2023eVAE: Evolutionary Variational Autoencodercited by 6
  23. 2022Simulating first-order phase transition with hierarchical autoregressive networkscited by 5
  24. 2024Message Passing Variational Autoregressive Network for Solving Intractable Ising Modelscited by 5
  25. 2025Multilevel Generative Samplers for Investigating Critical Phenomenacited by 5
  26. 2025Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimationcited by 5
  27. 2025Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics modelscited by 5
  28. 2025Quantum computing and artificial intelligence: status and perspectivescited by 5
  29. 2025Boltzmann generators for amorphous particle systemscited by 5
  30. 2021Scaling of neural-network quantum states for time evolutioncited by 4
  31. 2021A Bayesian generative neural network framework for epidemic inference problemscited by 4
  32. 2023Mutual information of spin systems from autoregressive neural networkscited by 4
  33. 2023Balanced Training of Energy-Based Models with Adaptive Flow Samplingcited by 4
  34. 2023Empirical Sample Complexity of Neural Network Mixed State Reconstructioncited by 4
  35. 2023Generative Marginalization Modelscited by 4
  36. 2022Estimating the Euclidean quantum propagator with deep generative modeling of Feynman pathscited by 3
  37. 2024CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solvercited by 3
  38. 2025Lattice Protein Folding with Variational Annealingcited by 3

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