mlsanityData to 14 Oct 2026

Variational Neural Annealing

arXiv 2101.10154 ↗First posted 25 Jan 2021cond-mat.dis-nn cond-mat.stat-mech cs.LGcited by 47

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Abstract (arXiv)

Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for groundstate solutions of a target Hamiltonian. While powerful, simulated annealing is known to have prohibitively slow sampling dynamics when the optimization landscape is rough or glassy. Here we show that by generalizing the target distribution with a parameterized model, an analogous annealing framework based on the variational principle can be used to search for groundstate solutions. Modern autoregressive models such as recurrent neural networks provide ideal parameterizations since they can be exactly sampled without slow dynamics even when the model encodes a rough landscape. We implement this procedure in the classical and quantum settings on several prototypical spin glass Hamiltonians, and find that it significantly outperforms traditional simulated annealing in the asymptotic limit, illustrating the potential power of this yet unexplored route to optimization.

Key facts. Cited by 47 papers in the map (data through 14 Oct 2026). Builds on 19 of its 106 references that are in the map. First posted on arXiv 25 Jan 2021.

Builds on

19 of 106 references.

References · 19

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  4. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
  5. 2013Ising formulations of many NP problemscited by 207
  6. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 200
  7. 2013Minimizing Finite Sums with the Stochastic Average Gradientcited by 164
  8. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  9. 2019Deep neural network solution of the electronic Schr"odinger equationcited by 127
  10. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
  11. 2017Dilated Recurrent Neural Networkscited by 83
  12. 2019Deep autoregressive models for the efficient variational simulation of many-body quantum systemscited by 64
7 more
  1. 2016Discovering Phase Transitions with Unsupervised Learningcited by 49
  2. 2016Accelerate Monte Carlo Simulations with Restricted Boltzmann Machinescited by 21
  3. 2016Learning Thermodynamics with Boltzmann Machinescited by 16
  4. 2020Controlled Online Optimization Learning (COOL): Finding the ground state of spin Hamiltonians with reinforcement learningcited by 14
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 6; 2024: 9; 2025: 12; 2026: 10.

47 papers.

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  1. 2021Combinatorial Optimization with Physics-Inspired Graph Neural Networkscited by 108
  2. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 59
  3. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 29
  4. 2023Variational Annealing on Graphs for Combinatorial Optimizationcited by 21
  5. 2022From Tensor Network Quantum States to Tensorial Recurrent Neural Networkscited by 14
  6. 2022Neural-network solutions to stochastic reaction networkscited by 8
  7. 2023Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superpositioncited by 8
  8. 2023The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systemscited by 8
  9. 2024Recurrent neural network wave functions for Rydberg atom arrays on kagome latticecited by 8
  10. 2022Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problemscited by 6
  11. 2022Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracycited by 6
  12. 2023Investigating Topological Order using Recurrent Neural Networkscited by 6
35 more
  1. 2023Efficient Training of Multi-task Neural Solver for Combinatorial Optimizationcited by 6
  2. 2024Message Passing Variational Autoregressive Network for Solving Intractable Ising Modelscited by 6
  3. 2021A Bayesian generative neural network framework for epidemic inference problemscited by 5
  4. 2025Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimizationcited by 5
  5. 2023Quantum approximate optimization via learning-based adaptive optimizationcited by 4
  6. 2024Retentive Neural Quantum States: Efficient Ans"atze for Ab Initio Quantum Chemistrycited by 4
  7. 2025Distributionally Robust Free Energy Principle for Decision-Makingcited by 4
  8. 2026Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixturescited by 4
  9. 2021Quantum Approximate Optimization Algorithm applied to the binary perceptroncited by 3
  10. 2022Estimating the Euclidean quantum propagator with deep generative modeling of Feynman pathscited by 3
  11. 2022Toward Neural Network Simulation of Variational Quantum Algorithmscited by 3
  12. 2025Lattice Protein Folding with Variational Annealingcited by 3
  13. 2025LMask: Learn to Solve Constrained Routing Problems with Lazy Maskingcited by 3
  14. 2025IsingFormer: Augmenting Parallel Tempering With Learned Proposalscited by 3
  15. 2025Diffusion-Augmented Markov Decision Processes for Maximum Entropy Reinforcement Learningcited by 3
  16. 2025A Generative Neural Annealer for Black-Box Combinatorial Optimizationcited by 2
  17. 2026Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlocited by 2
  18. 2026Scalable Physics-Inspired Transformers for Spin Glassescited by 2
  19. 2024Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraintscited by 1
  20. 2024Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learningcited by 1
  21. 2024Scalable Quantum-Inspired Optimization through Dynamic Qubit Compressioncited by 1
  22. 2024PearSAN: A Machine Learning Method for Inverse Design using Pearson Correlated Surrogate Annealingcited by 1
  23. 2025Adaptive Neural Quantum States: A Recurrent Neural Network Perspectivecited by 1
  24. 2025Nonlocal Monte Carlo via Reinforcement Learningcited by 1
  25. 2025Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistrycited by 1
  26. 2026Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum Statescited by 1
  27. 2022CITS: Coherent Ising Tree Search Algorithm Towards Solving Combinatorial Optimization Problemscited by 0
  28. 2024A method for quantifying the generalization capabilities of generative models for solving Ising modelscited by 0
  29. 2025Large-scale portfolio optimization with variational neural annealingcited by 0
  30. 2026Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machinescited by 0
  31. 2026Enhanced Neural Quantum State via Annealed Gradient Descentcited by 0
  32. 2026Neural Fourier Surrogates for Data Reuploading Quantum Neural Networkscited by 0
  33. 2026Fixed-point neural samplers on discrete spacescited by 0
  34. 2026Autoregressive Differentiable Method for Integer Programmingcited by 0
  35. 2026Probabilistic Algorithms for Ising Machines from Optimization to Generative AIcited by 0