A new nonlinear functional analytic framework for modeling artificial neural networks

A framework is presented for modeling the input-output map f ˆ: R^N→R^M of artificial neural networks used in pattern classification. Assuming only that fˆ belongs to an appropriate space F (called a neural space) of nonlinear analytic maps, its structure is obtained by requiring that fˆ match a set of exemplary input-output pairs while minimizing a maximum error in an uncertainty ball in F . This criterion guarantees robustness of the solution. The optimal model fˆ thus obtained consists of a two-layer feedforward net, the first layer being the same as the matching score layer of the Hamming net, and the second layer being a new layer (absent in the Hamming net) possessing synaptic weights which result from the described optimization procedure