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,, and the average generalization ability G, as a function of the size m of the training set. Learning curves G, vs rn 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.
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