Optimization in cascaded Boltzmann machines with a temperature gradient: an alternative to simulated annealing

Abstract

Boltzmann machines can be series-coupled with one-way retinotopic connections to produce good (suboptimal) solutions to classic optimization problems. Each isothermal Bokzmann machine in the series has a lower temperature than the one which drives it through excitatory spanning links. This scheme is an alternative to the usual simulated annealing approach in which a single network is cooled over the course of time. The simplest case features two identical subnets, one at a positive temperature and the other at zero temperature. Its performance in solving n-to-n assignment probems is compared to that obtained by simulated annealing with a geometric cooling schedule.