Square unit augmented, radially extended, multilayer perceptrons

Consider a multilayer perceptron (MLP) with d inputs, a single hidden sigmo idal layer and a linear output. By adding an additional d inputs to the net work with values set to the square of the first d inputs, properties remini scent of higher-order neural networks and radial basis function networks (R BFN) are added to the architecture with little added expense in terms of we ight requirements. Of particular interest, this architecture has the abilit y to form localized features in a d-dimensional space with a single hidden node but can also span large volumes of the input space; thus, the architec ture has the localized properties of an RBFN but does not suffer as badly f rom the curse of dimensionality. I refer to a network of this type as a SQu are Unit Augmented, Radially Extended, MultiLayer Perceptron (SQUARE-MLP or SMLP).