Stochastic normalizing flows as non-equilibrium transformations

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.

Comments: 1+28 pages, 8 figures; v2: 1+29 pages, 8 figures, added references, discussion in section 4 improved; v3: 1+31 pages, 9 figures, added references, discussion in section 4 expanded, matches published version