1. An artificial neural network architecture comprising: a plurality of input terminals adapted to receive n input data signals corresponding to an input pattern to be learned by said network; each said input terminal being connected to a set of N arithmetic and storage units, said arithmetic and storage units being capable of producing the first N terms of either an orthogonal polynomial expansion function or an orthogonal expansion function, where the arguments of said terms are from said input data signal and not from the cumulative probability distribution function of said input data signal; a set of N weight multipliers connected on one side to said arithmetic and storage units and on the other to a weight changer and a weight initializer, each said weight multiplier for generating a weight multiplier output signal consisting of products of output signals from each set of said N arithmetic and storage units, said weight changer and said weight initializer; means for adding connected on one side to (n) (N) said weight multipliers and on the other to m output nodes so as to generate activation values at each of said m output nodes by summing N said weight multiplier output signals received from N said weight multipliers and without using said sum as an argument of a nonlinear function; a comparitor and error generator adapted to receive m said activation values from m said output nodes and compare said activation values from predetermined target values initially ascribed to said output nodes to generate m error signals; said weight changer adapted to receive m said error signals from said comparitor and error generator to determine how much a particular signal from said weight changer is to be changed to minimize said error signals, said weight changer thereafter sending an output signal to said weight multiplier during a learning process of the network.