LEAPS: A discrete neural sampler via locally equivariant networks

Understand

We propose "LEAPS", an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC).

• LEAPS can be seen as a continuous-time formulation of annealed importance sampling and sequential Monte Carlo methods, extended so that the variance of the importance weights is offset by the inclusion of the CTMC.
• To derive these importance weights, we introduce a set of Radon-Nikodym derivatives of CTMCs over their path measures.
• Because the computation of these weights is intractable with standard neural network parameterizations of rate matrices, we devise a new compact representation for rate matrices via what we call "locally equivariant" functions.