Some notes on perceptron learning

We extend the geometkcal approach to the Perceptron and show that. given n examples, learning is of maximal difficulty when the number of inputs dis such that n = 5d. We then present a nea' Perceptron algorithm that takes advantage of the peculiarities of the cost function. In our tests it is more than two times faster that the standard algorithm. More importantly it does not have k e d parameters, like the usual learning constant q, but it adapts them to the cost function. We show that there exist an optimal choice forg, the steepness of the transfer function. We present also a brief systematic study of the parameters and b of the standard Perceptron algorithm.