Partitions of unity improve neural function approximators

Neural function approximators with localized receptive fields are sometimes riddled with disturbing interpolation artifacts. A general principle is proposed to remove these defects. Such approximators should be designed as partitions of unity within their domains. This principle explains earlier empirical results, and its effectiveness is demonstrated by the removal of spurious interpolation artifacts of a radial basis functions (RBF) network. Using well-known partitions of unity, further improvements can be easily obtained. This is demonstrated by converting the piecewise constant functions of standard cerebellar model articulation controller (CMAC) nets into arbitrary smooth functions (C^∞-CMACs)