An Analytical Framework for Local Feedforward Networks 1

Although feedforward neural networks are well suited to function approximation, in some applications networks experience problems when learning a desired function. One problem is interference which occurs when learning in one area of the input space causes unlearning in another area. Networks that are less susceptible to interference are referred to as spatially local networks. To understand these properties, a theoretical framework, consisting of a measure of interference and a measure of network localization, is developed that incorporates not only the network weights and architecture but also the learning algorithm. Using this framework to analyze sigmoidal multi-layer perceptron (MLP) networks that employ the back-prop learning algorithm, we address a familiar misconception that sigmoidal networks are inherently non-local by demonstrating that given a suuciently large number of adjustable parameters, sigmoidal MLPs can be made arbitrarily local while retaining the ability to represent any continuous function on a compact domain.