Sampling Decisions: Exact Path-Space Correction, Prior Cancellation and Local-Boltzmann Guidance

תקציר מקורי באנגליתarXiv:2503.14549v3 Announce Type: replace-cross Abstract: How can a cheap but biased sequential, finite-horizon sampler over a discrete space be corrected so that its terminal output follows a prescribed Gibbs distribution? We formulate Sampling Decisions as a path-space relative-entropy projection on a growing autoregressive state graph. The unique prior-relative minimizer is a Doob transform governed by a linear backward recursion. A route-resolved formulation then yields a finite-particle algorithm based on conditional self-normalized importance sampling, and we prove convergence of its transition kernels and terminal law as the path budget grows. For binary graphical models, we prove an exact cancellation theorem: all fixed singleton-product priors disappear from the population correct