Constructive approximations for neural networks by sigmoidal functions

A constructive algorithm for uniformly approximating real continuous mappings by linear combinations of bounded sigmoidal functions is given. G. Cybenko (1989) has demonstrated the existence of uniform approximations to any continuous f provided that σ is continuous; the proof is nonconstructive, relying on the Hahn-Branch theorem and the dual characterization of C(Iⁿ ). Cybenko´s result is extended to include any bounded sigmoidal (even nonmeasurable ones). The approximating functions are explicitly constructed. The number of terms in the linear combination is minimal for first-order terms