Analysis of autocorrelation times in Neural Markov Chain Monte Carlo simulations

In case of complicated probability distributions most formulations resort to the construction of an associated Markov chain of consecutive proposals. The statistical uncertainty of any outcome of Monte Carlo simulation depends directly on the number of statistically independent configurations used to estimate it. Hence, the effectiveness of simulation algorithms is measured by autocorrelation time which quantify how many configurations are produced by the algorithm before a new, statistically independent configuration appears. Increasing autocorrelation times, a phenomenon called critical slowing down, is usually the main factor which limits the statistical precision of outputs. In the context of field theory simulations in elementary particle physics several proposals were advanced in order to alleviate that problem, in particular metadynamics [3, 4], instanton updates [5] or multiscale thermalization [6]. The recent great interest in machine learning techniques has also provided new ideas in the domain of Monte Carlo simulations which aim at reducing the autocorrelation times. The ability of artificial neural networks to approximate a very wide class of probability distributions was used in Ref.[7] to propose a variational estimate of free energy of statistical systems. Subsequently the idea was extended and used as a mechanism of providing uncorrelated proposals in a Monte Carlo simulation in Ref.[8].