Learning by parallel Boltzmann machines

A parallel implementation of the Boltzmann machine in which each unit is updated independently of, but simultaneously with, the other units is studied. A transparent representation of the transition matrix and of the equilibrium distribution emphasizes the role, for the stochastic parallel evolution of the dynamical features of the underlying synchronous deterministic Hopfield model. As a consequence of this fact, the parallel Boltzmann machine explores an energy landscape quite different from the one of the sequential model. It is shown that it is, nevertheless, possible to derive, for the parallel model, a realistic learning rule having the same feature of locality as the well-known learning rule for the sequential Boltzmann machine proposed by D. Ackley et al. (1985)