Using full parallel Boltzmann Machines for Optimization
Johannes Faassen
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.