Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks

Efficient sampling of complicated high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo (MCMC) sampling, provide good approximations to such distributions, but suffer from either intrinsic bias or high variance. In this paper, we propose a novel 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, and we discuss the theoretical motivation of how they help implement the ergodicity of MCMC. We test our method on classical spin systems including the Ising model and a frustrated plaquette model with a first-order phase transition, showing it significantly reduces the autocorrelation time over previous unbiased sampling methods, and alleviates the issue of metastability for MCMC methods in first-order phase transitions.