Sampling from Energy distributions with Target Concrete Score Identity

TL;DR

The paper presents TCSIS, a novel sampling method for unnormalized densities on discrete spaces that estimates ratios of probabilities using a neural network and a new score identity, demonstrated on physics problems.

Contribution

Introduction of the Target Concrete Score Identity and two algorithms for efficient sampling without partition function computation.

Findings

Effective sampling demonstrated on statistical physics problems.

Neural network approximation of the concrete score works well.

Two algorithms, Self-Normalized and Unbiased TCSIS, outperform existing methods.

Abstract

We introduce the Target Concrete Score Identity Sampler (TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a Continuous-Time Markov Chain (CTMC). Our approach builds on a forward in time CTMC with a uniform noising kernel and relies on the proposed Target Concrete Score Identity, which relates the concrete score, the ratio of marginal probabilities of two states, to a ratio of expectations of Boltzmann factors under the forward uniform diffusion kernel. This formulation enables Monte Carlo estimation of the concrete score without requiring samples from the target distribution or computation of the partition function. We approximate the concrete score with a neural network and propose two algorithms: Self-Normalized TCSIS and Unbiased TCSIS. Finally, we demonstrate the effectiveness of TCSIS on problems from statistical physics.