FUNCTION EMULATION USING RADIAL BASIS FUNCTION NETWORKS

While learning an unknown input-output task, humans first strive to un derstand the qualitative structure of the function. Accuracy of perfor mance is then improved with practice. In contrast, existing neural net work function approximators do not have an explicit means for abstract ing the qualitative structure of a target function. To fill this gap, we introduce the concept of function emulation, according to which the central goal of training is to ''emulate'' the qualitative structure of the target function. The framework of catastrophe or singularity th eory is used to characterize the qualitative structure of a smooth fun ction, which is organized by the critical points of the function. The proposed scheme of function emulation uses the radial basis function n etwork to realize a modular architecture wherein each module emulates the target function in the neighborhood of a critical point. The netwo rk size required to emulate the target in the neighborhood of a critic al point is shown to be related to a certain complexity measure of the critical point. For a large class of smooth functions, the present sc heme produces a graph-like abstraction of the target, thereby providin g a qualitative representation of a quantitative input-output relation . (C) 1997 Elsevier Science Ltd.