Coupled Neural Networks

Abstract

Multilayered feed-forward networks (perceptrons) are special cases of the general McCulloch-Pitts neural network with arbitrarily interconnected neurons. On the other hand, any general “recurrent” neural network can be considered to be represente by a feed-forward perceptron, albeit one with possibly very many layers. The reason for this strange equivalence is that the temporal evolution (3.5) of an arbitrary network constructed from binary neurons is necessarily periodic. This statement follows immediately from the observation that the N neurons can only assume 2^N configurations altogether, and hence some state of the network must reoccur after at most 2^N steps. Since only the present state of the network enters on the right-hand side of the evolution law (14.1), the subsequent evolution proceeds strictly periodically from that moment on. If one considers the neural network at a certain moment t = n as the nth layer of a perceptron (with all layers identical!), the temporal-evolution law can be viewed as the law governing the flow of information from one layer to the next. It is then sufficient to take into account only a finite number of such layers, just as many as there are time steps leading up to the first repetition of a network configuration.