Sampling from Energy distributions with Target Concrete Score Identity
This method addresses sampling challenges in discrete domains like statistical physics, but appears incremental as it builds on existing CTMC and score-based approaches.
The paper tackles the problem of sampling from unnormalized densities on discrete state spaces by introducing the Target Concrete Score Identity Sampler (TCSIS), which learns reverse dynamics of a Continuous-Time Markov Chain without needing samples from the target distribution or partition function computations, and demonstrates its effectiveness on statistical physics problems.
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.