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ABSTRACT

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF). GRBF networks are not only equivalent to generalized splines, but are also closely related to several pattern recognition methods and neural network algorithms. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.