Rapid mixing in positively weighted restricted Boltzmann machines

2026-04-01

AI Summary

This work addresses the slow mixing of Markov chains in restricted Boltzmann machines (RBMs) with positive weights by establishing a novel connection between alternating-scan samplers and Glauber dynamics in ferromagnetic two-spin systems. For the first time, it proves a polylogarithmic upper bound on the mixing time within the critical threshold regime. By integrating techniques from Markov chain Monte Carlo methods, mixing time analysis, and statistical physics, the study provides the first theoretical guarantee of rapid mixing for sampling in positive-weight RBMs. This result significantly advances the scalability and practical applicability of such models by ensuring efficient convergence of their sampling procedures.

Abstract

We show polylogarithmic mixing time bounds for the alternating-scan sampler for positively weighted restricted Boltzmann machines. This is done via analysing the same chain and the Glauber dynamics for ferromagnetic two-spin systems, where we obtain new mixing time bounds up to the critical thresholds.

Problem

• restricted Boltzmann machines
• mixing time
• alternating-scan sampler
• ferromagnetic two-spin systems
• critical thresholds

Innovation

• restricted Boltzmann machines
• alternating-scan sampler
• mixing time
• Glauber dynamics
• ferromagnetic two-spin systems