Deformation Theory of Boltzmann Distributions

10/25/2022

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by   Bálint Máté, et al.

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Consider a one-parameter family of Boltzmann distributions p_t(x) = 1Z_te^-S_t(x). In this paper we study the problem of sampling from p_t_0 by first sampling from p_t_1 and then applying a transformation Ψ_t_1^t_0 to the samples so that to they follow p_t_0. We derive an equation relating Ψ and the corresponding family of unnormalized log-likelihoods S_t. We demonstrate the utility of this idea on the ϕ^4 lattice field theory by extending its defining action S_0 to a family of actions S_t and finding a τ such that normalizing flows perform better at learning the Boltzmann distribution p_τ than at learning p_0.