Stochastic normalizing flows as non-equilibrium transformations

TL;DR

This paper explores stochastic normalizing flows as non-equilibrium transformations, connecting deep generative models with out-of-equilibrium simulations to improve sampling efficiency in lattice field theories.

Contribution

It establishes the theoretical equivalence between stochastic normalizing flows and out-of-equilibrium simulations using Jarzynski's equality, and proposes optimization strategies for these models.

Findings

Unified framework for normalizing flows and out-of-equilibrium simulations

Demonstrated improved sampling efficiency in lattice gauge theories

Proposed optimization methods for stochastic normalizing flows

Abstract

Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of stochastic normalizing flows, in which neural-network layers are combined with Monte Carlo updates, is the same that underlies out-of-equilibrium simulations based on Jarzynski's equality, which have been recently deployed to compute free-energy differences in lattice gauge theories. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.