Scaling and Generalization in Neural Networks: A Case Study

Part of Advances in Neural Information Processing Systems 1 (NIPS 1988)

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Subutai Ahmad, Gerald Tesauro


The issues of scaling and generalization have emerged as key issues in current studies of supervised learning from examples in neural networks. Questions such as how many training patterns and training cycles are needed for a problem of a given size and difficulty, how to represent the inllUh and how to choose useful training exemplars, are of considerable theoretical and practical importance. Several intuitive rules of thumb have been obtained from empirical studies, but as yet there are few rig(cid:173) orous results. In this paper we summarize a study Qf generalization in the simplest possible case-perceptron networks learning linearly separa(cid:173) ble functions. The task chosen was the majority function (i.e. return a 1 if a majority of the input units are on), a predicate with a num(cid:173) ber of useful properties. We find that many aspects of.generalization in multilayer networks learning large, difficult tasks are reproduced in this simple domain, in which concrete numerical results and even some analytic understanding can be achieved.