The modeling of a neural net as a best input-output map approximation in a generalized Fock space

In filter design theory, one derives the filter structure by requiring that the frequency response of the filter match, in some optimal way, a desired frequency response. A similar philosophy is adopted to derive the architecture of a neural net, except that in this case, because of the nonlinear nature of the neural net, the frequency response can no longer be used as a design criterion. Instead, it is required that the net N, whose structure is to be determined, match a set of exemplary input-output pairs while minimizing the maximum error in some appropriate space. The latter criterion guarantees the robustness of the net