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Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks

arXiv 2105.05650 ↗First posted 12 May 2021cond-mat.stat-mech cond-mat.dis-nn cs.LGcited by 17

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Abstract (arXiv)

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions, but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 13 of its 72 references that are in the map. First posted on arXiv 12 May 2021.

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13 of 72 references.

References · 13

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Multi-Scale Context Aggregation by Dilated Convolutionscited by 1,128
  3. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  4. 2016Pixel Recurrent Neural Networkscited by 814
  5. 2018Neural Importance Samplingcited by 154
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  7. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 99
  8. 2016Neural Autoregressive Distribution Estimationcited by 94
  9. 2017Generalizing Hamiltonian Monte Carlo with Neural Networkscited by 52
  10. 2018Neural Network Renormalization Groupcited by 48
  11. 2017A-NICE-MC: Adversarial Training for MCMCcited by 36
  12. 2016Accelerate Monte Carlo Simulations with Restricted Boltzmann Machinescited by 21
1 more
  1. 2017The Lov'asz Theta Function for Random Regular Graphs and Community Detection in the Hard Regimecited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 3; 2024: 5; 2025: 3; 2026: 1.

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  1. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 58
  2. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  5. 2021Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulationscited by 10
  6. 2023The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systemscited by 8
  7. 2024Message Passing Variational Autoregressive Network for Solving Intractable Ising Modelscited by 5
  8. 2025IsingFormer: Augmenting Parallel Tempering With Learned Proposalscited by 2
  9. 2025Nonlocal Monte Carlo via Reinforcement Learningcited by 1
  10. 2022An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum Statescited by 0
  11. 2022Neural network quantum state with proximal optimization: a ground-state searching scheme based on variational Monte Carlocited by 0
  12. 2023High-precision regressors for particle physicscited by 0
5 more
  1. 2023Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulationscited by 0
  2. 2024Statistical Mechanics Calculations Using Variational Autoregressive Networks and Quantum Annealingcited by 0
  3. 2024A method for quantifying the generalization capabilities of generative models for solving Ising modelscited by 0
  4. 2024Machine learning the Ising transition: A comparison between discriminative and generative approachescited by 0
  5. 2026Enhanced Neural Quantum State via Annealed Gradient Descentcited by 0