On learning a function of perceptrons

This paper concerns the generalization accuracy when training a classifier that is a fixed Boolean function of the outputs of a number of perceptrons. The analysis involves the ´margins´ achieved by the constituent perceptrons on the training data. A special case is that in which the fixed Boolean function is the majority function (where we have a ´committee of perceptrons´). Recent work of Auer et al. studied the computational properties of such networks (where they were called ´parallel perceptrons´), proposed an incremental learning algorithm for them. The results given here provide further motivation for the use of this learning rule.