GRADIENT DESCENT LEARNING IN PERCEPTRONS - A REVIEW OF ITS POSSIBILITIES

We present a streamlined formalism which reduces the calculation of th e generalization error for a perceptron, trained on random examples ge nerated by a teacher perceptron, to a matter of simple algebra. The me thod is valid whenever the student perceptron can be identified as the unique minimum of a specific cost function. The asymptotic generaliza tion error is calculated explicitly for a broad class of cost function s, and a specific cost function is singled out that leads to a general ization error extremely close to the one of the Bayes classifier.