Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Sampling

TL;DR

This paper introduces saVANt, an improved VAN-based method for statistical mechanics that corrects sampling errors using neural network-based MCMC and importance sampling, leading to unbiased estimators and broader applicability.

Contribution

It proposes a modification to existing VAN methods by incorporating importance and MCMC sampling, leveraging VANs' property of providing exact sample probabilities.

Findings

Sampling error correction improves estimator accuracy.

Unbiased estimators are achieved through neural network-based MCMC.

Potential for greater impact in physics fields like statistical mechanics.

Abstract

In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be corrected by using neural network-based MCMC or importance sampling which leads to asymptotically unbiased estimators for physical quantities. This modification is possible due to a singular property of VANs, namely that they provide the exact sample probability. With these modifications, we believe that their method could have a substantially greater impact on various important fields of physics, including strongly-interacting field theories and statistical physics.