The Hopfield Model with Multi-Level Neurons

Abstract

The Hopfield neural network model for associative memory is generalized. The generalization replaces two state neurons by neurons taking a richer set of values. Two classes of neuron input output relations are developed guaranteeing convergence to stable states. The first is a class of continuous relations and the second is a class of allowed quantization rules for the neurons. The information capacity for networks from the second class is found to be of order N3 bits for a network with N neurons. A generalization of the sum of outer products learning rule is developed and investigated as well.