Capacity of diluted multi-state neural networks

The optimal storage capacity is studied for diluted networks with multi-state neurons and continuous respectively discrete couplings, within the replica-symmetric Gardner approach. The Gardner-Derrida line, the de Almeida-Thouless line and the zero-entropy line are compared and the validity of the replica-symmetric approximation is discussed in detail. The distribution of the synaptic couplings is determined. The results are analysed in terms of the number of states of the neuron, the distribution of the stored patterns, the amount of dilution and the number of discrete values for the couplings.