Generalization in a multi-state neural network
David Domínguez, W. K. Theumann · Journal of Physics A Mathematical and General · 1996
The generalization ability of an extremely dilute feedback neural network with multi-state 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 . 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 .