On the inverse of Hopfield-type dynamical neural networks

Abstract

A technique is given for finding the system inverse to an Hopfield class of continuous time dynamical artificial neural networks, that is, for finding the system which yields the equivalence class of inputs which lead to a given output. This is accomplished by applying the theory of inverse semistate linear systems to the linear part and directly inverting the activation functions. An example is given for a two-input two-output degree two (two neuron) system. The results could be of use in finding the set of patterns which fall into different classes of a neural network dynamic pattern classifier.