A general class of neural networks

Striving to derive minimal network architectures for neural networks has been at the center of attention for several years now. To this date numerous algorithms have been proposed to automatically construct networks. Unfortunately, these algorithms lack a fundamental theoretical analysis of their capabilities and only empirical evaluations on a few selected benchmark problems exist. In this work we describe a general class of 2-layer networks with 2 hidden units capable of representing a large set of problems. The cardinality of this class grows exponentially with regard to the inputs N. Furthermore, we outline a simple algorithm that allows us to determine, if any function (problem) is a member of this class. The class considered in this paper includes the benchmark problems parity and symmetry