Exhaustive Learning

Exhaustive exploration of an ensemble of networks is used to model learning and generalization in layered neural networks. A simple Boolean learning problem involving networks with binary weights is numerically solved to obtain the entropy S_m and the average generalization ability G_m as a function of the size _m of the training set. Learning curves G_m vs m are shown to depend solely on the distribution of generalization abilities over the ensemble of networks. Such distribution is determined prior to learning, and provides a novel theoretical tool for the prediction of network performance on a specific task.