Generalization in a multi-state neural network

The generalization ability of an extremely dilute feedback neural network with multistate neurons is studied by means of a deterministic noiseless parallel dynamics. The overlap with any one of a macroscopic number of binary, full activity, concepts is determined when the network is trained with examples of variable activity according to a Hebbian learning algorithm that favours stable symmetric mixture states. Explicit results about the phase diagram and the generalization error are obtained for a network with three-state neurons which remain inactive below a threshold θ . It is shown that the generalization ability can be considerably enhanced either by training the network with low-activity examples or by means of a moderate increase in θ .