Using full parallel Boltzmann Machines for Optimization

It is well known that synchronously full parallel Boltzmann machines do not converge to the minima of the quadratic energy but to a so called pseudo energy. So far the pseudo energy was treated as a defect disturbing the convergence of these Boltzmann machines. Various simulations suggest that convergence can be ensured if one reduces the degree of parallelism. Another approach that we follow in this paper is to map the problem onto the pseudo energy i.e. we directly exploit the dynamics of the full parallel Boltzmann machine. First we prove that minimizing the pseudo energy is NP-hard and derive a simple mapping scheme that allows us to reduce an arbitrary quadratic 0-1-problem to the minimization of the pseudo energy. After that we present some simulation results showing the potential of this approach and compare it to the results obtained by Aarts, Korst, and Zwietering 1, 12].