Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks

TL;DR

This paper introduces an unbiased Monte Carlo sampling method using autoregressive neural networks and physical symmetries, improving sampling accuracy for complex systems with phase transitions.

Contribution

It presents a novel approach combining autoregressive neural networks with symmetry-based cluster updates to achieve unbiased and low-variance sampling.

Findings

Successfully applied to classical spin systems at phase transitions

Effective in handling metastable states

Demonstrates viability for critical systems

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.