This project will investigate a variety of approaches, to improve the ability of artificial neural networks (ANN) to learn classifications or general mathematical functions. It will investigate alternative functional forms for ANNs, building on the PI's prior work with radial basic functions and B-splines. It will investigate methods for adapting learning rates, based on ideas about stochastic gradient learning theory. It will investigate alternative error functions, beyond the usual square error function, designed to yield better generalization power. Such alterative error function, designed to yield better generalization power. Such alternative error functions may also be used in determining the topology of an ANN.