From statistical mechanics to neural networks and back

The neural-network models, which have attracted so much attention in the physics community, consist of a large assembly of two-state elements, highly interconnected by ferromagnetic and antiferromagnetic interactions. Methods of statistical mechanics have been applied to these models, bringing new discoveries and surprises to neural-network science. At the same time, neural-network models have posed new problems and incentives to statistical mechanics. One of the basic problems is that of learning, which in the context of these models, means a choice of the interactions for which the network dynamics leads to specific attractors. The main emphasis in this paper is on the essential developments and results on this problem, derived from methods of statistical mechanics.