Abstract

An optical Boltzmann machine is a highly parallel computing module for inverting matrix equations expressed g = Af. A Monte Carlo procedure is used, being more efficient with large matrices and because the transform matrix A often has no true inverse. Since the operation is not determinstic, the resultant data $\widehat{f}$ will only be an estimate if the data f, although confidence that it is the best possible estimate of f can be made very high. An energy function E of the estimate $\widehat{f}$ is defined with minimum at the best estimate; then the starting estimate is iteratively perturbed by adding or subtracting grains such that the running estimate generally decreases E. Brief excursions of increasing E are initially accepted to prevent the estimate from settling into a local minimum, but these excursions are gradually prohibited to let f settle in the best estimate. Highly parallel optical systems can be used to very quickly calculate the energy of an estimate and to decide if excursions to higher energy should be accepted. A few of the possible architectures will be described, capable of processing speeds of 10⁶–10⁷ grains/s with only moderate advantage of the parallelism available being taken.

© 1985 Optical Society of America