A neural network with multi-neurons

Abstract

This paper proposes a neural network, which is formed by groups of neurons with nonlinear interactions. It is assumed that interactions are much stronger for neurons inside the group then for ones outside. Because a strong (and nonlinear) interaction is a natural description of a group, in terms of collective variables, it is convenient to think of such a neuron group as one ‘multi-neuron’ whose state is described by the set of numbers. For some reasonable approximations this model can be formulated in terms of statistical physics and has an exact analytical solution. This neural network is capable of discerning correlated patterns. Its memory does not have the spurious states. The network possesses cognitive ability and certain elements of ‘interest’. The model is simple enough to serve as a starting point for investigation of a more complicated neural system.