Perceptrons with Polynomial Post-Processing

We introduce tensor product neural networks, composed of a layer of univariate neurons followed by U net of polynomial post-processing. We look at the general approximation problem by these networks observing in particular their relationship to the StoneWeierstrass theorem for uniform function algebras. The implementation of the post-processing as a two-layer network with logarithmic and exponential neurons leads to potentially important ‘generalised’ product networks, which however require a complex approximation theory of Miintz-Szasz-Ehrenpreis type. A back-propagation algorithm for product networks is presented and used in three computational experiments. In particular, approximation by a sigmoid product network is compared to that of a single layer radial basis network, and a multiple layer sigmoid network.