Learning trivializing flows

TL;DR

This paper proposes a local normalizing flow approach at the correlation length scale to enhance sampling efficiency in lattice gauge theories, demonstrating improved acceptance and autocorrelation times over traditional HMC in 2D phi^4 theory.

Contribution

It introduces a novel local normalizing flow method at the correlation length scale that, when combined with HMC, improves sampling efficiency and reduces autocorrelation times.

Findings

High acceptance rates achieved with combined flow-HMC method

Reduced autocorrelation times compared to standard HMC

Effective scaling demonstrated in 2D phi^4 theory

Abstract

The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of normalizing flows has been shown to lead to bad scaling with the volume. In this talk we propose using local normalizing flows at a scale given by the correlation length. Even if naively these transformations have a small acceptance, when combined with the HMC algorithm lead to algorithms with high acceptance, and also with reduced autocorrelation times compared with HMC. Several scaling tests are performed in the $\phi^{4}$ theory in 2D.