An optimal Q-state neural network using mutual information

Abstract Starting from the mutual information we present a method in order to find a Hamiltonian for a fully connected neural network model with an arbitrary, finite number of neuron states, Q . For small initial correlations between the neurons and the patterns it leads to optimal retrieval performance. For binary neurons, Q =2, and biased patterns we recover the Hopfield model. For three-state neurons, Q =3, we find back the recently introduced Blume–Emery–Griffiths network Hamiltonian. We derive its phase diagram and compare it with those of related three-state models. We find that the retrieval region is the largest.