Rapid mixing in positively weighted restricted Boltzmann machines

TL;DR

This paper establishes polylogarithmic mixing time bounds for the alternating-scan sampler in positively weighted restricted Boltzmann machines, extending analysis to ferromagnetic two-spin systems near critical thresholds.

Contribution

It provides new mixing time bounds for the sampler in RBMs, connecting them to ferromagnetic two-spin systems and analyzing behavior near critical thresholds.

Findings

Polylogarithmic mixing times for the sampler in RBMs.

Analysis applies to ferromagnetic two-spin systems.

Bounds hold up to critical thresholds.

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.