A Simple Weight Decay Can Improve Generalization

Part of Advances in Neural Information Processing Systems 4 (NIPS 1991)

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Anders Krogh, John Hertz


It has been observed in numerical simulations that a weight decay can im(cid:173) prove generalization in a feed-forward neural network. This paper explains why. It is proven that a weight decay has two effects in a linear network. First, it suppresses any irrelevant components of the weight vector by choosing the smallest vector that solves the learning problem. Second, if the size is chosen right, a weight decay can suppress some of the effects of static noise on the targets, which improves generalization quite a lot. It is then shown how to extend these results to networks with hidden layers and non-linear units. Finally the theory is confirmed by some numerical simulations using the data from NetTalk.