ABSTRACT
The simplest version of the networks, or "neural networks," as they are somewhat improperly called, is the one proposed by J. Hopfield in 1982. The Hopfield network is but a very approximate model of the cognitive function of the brain. Its greatest value is that it goes from the cellular level, modeled by the automata, to the cognitive level of the brain, modeled by the collective dynamical properties of the network. This chapter develops some calculations based on a very simple method. It describes a change of variables which will simplify the derivations. Of course, there is no reason for the fixed points which are reached to be identical—they depend on the initial configuration. Similarly, the energies obtained are not identical. Three methods can be used to predict the behavior of threshold neural networks constructed with the Hebb rule and to explain the results of the simulations.
