Generalization Ability of Hopfield Neural Network
with Spin-S Ising Neurons

Abstract

We investigate a fully connected Hopfield neural network with spin-S (S ≥ 1) Ising neurons, including S=∞, when binary patterns are embedded by the Hebbian learning rule. We analyze the energy function of the neural network using the replica method. We investigate a generalization ability of the neural network within the replica symmetric (RS) solutions. We clarify that the generalization ability of the neural network with a larger value of S is enhanced when the finite number of concepts are extracted from the presented examples.