Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Sampling
This incremental improvement could enhance the method's impact on physics fields like strongly-interacting field theories and statistical physics.
This comment addresses sampling error in Variational Autoregressive Networks (VANs) for statistical mechanics by proposing neural network-based MCMC or importance sampling corrections, resulting in asymptotically unbiased estimators for physical quantities.
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.