Part of Advances in Neural Information Processing Systems 6 (NIPS 1993)

*H. Schwarze, J. Hertz*

The problem of learning from examples in multilayer networks is studied within the framework of statistical mechanics. Using the replica formalism we calculate the average generalization error of a fully connected committee machine in the limit of a large number of hidden units. If the number of training examples is proportional to the number of inputs in the network, the generalization error as a function of the training set size approaches a finite value. If the number of training examples is proportional to the number of weights in the network we find first-order phase transitions with a discontinuous drop in the generalization error for both binary and continuous weights.

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