An efficient mapping of Boltzmann machine computations onto distributed-memory multiprocessors

Abstract

In this paper, an efficient mapping scheme of Boltzmann Machine computations onto a distributed-memory multiprocessor, which exploits the synchronous spatial parallelism, is presented. In this scheme, the neurons in the Boltzmann Machine are partitioned into p disjoint sets, and each set is mapped on a processor of a p-processor system. A parallel convergence and learning algorithms of Boltzmann Machine, necessary communication pattern among the processors, and their time complexities when neurons are partitioned and mapped onto a distributed-memory multiprocessor are investigated. An expected p-processor speed-up of the parallelizing scheme over a single processor is also analyzed theoretically. It can be used as a basis in determining the most cost-effective or optimal number of processors with respect to the communication capabilities and interconnection topologies of given distributed-memory multiprocessor.