Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks

Abstract

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.

arXiv comment12 pages, 9 figures

References in corpus (19)

• Machine learning and the physical sciences
• Self-Learning Monte Carlo Method
• Walking, Weak first-order transitions, and Complex CFTs
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Event-chain Monte Carlo algorithms for hard-sphere systems
• Statistical physics-based reconstruction in compressed sensing
• Neural networks-based variationally enhanced sampling
• Neural Network Renormalization Group
• Hiding Quiet Solutions in Random Constraint Satisfaction Problems
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Asymptotically unbiased estimation of physical observables with neural samplers
• Self-learning Monte Carlo with Deep Neural Networks
• A-NICE-MC: Adversarial Training for MCMC
• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• Flow-based sampling for multimodal and extended-mode distributions in lattice field theory
• Generative models for sampling of lattice field theories
• First order phase transition of the q-state Potts model in two dimensions

Cited by in corpus (12)

• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems
• Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations
• Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation
• Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Machine Learning Wavefunction
• Sample generation for the spin-fermion model using neural networks
• Using Markov transition matrices to generate trial configurations in Markov chain Monte Carlo simulations
• An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States