Some notes on perceptron learning
Marco Budinich · Journal of Physics A Mathematical and General · 1993
The author extends the geometrical approach to the perceptron and shows that, given n examples, learning is of maximal difficulty when the number of inputs d is such that n=5d. He then presents a new perceptron algorithm that takes advantage of the peculiarities of the cost function. In his tests it is more than two times faster than the standard algorithm. More importantly it does not have fixed parameters, like the usual learning constant eta , but it adapts them to the cost function. He shows that there exist an optimal choice for beta , the steepness of the transfer function. He presents also a brief systematic study of the parameters eta and beta of the standard perceptron algorithm.