Uniform approximation capabilities of sum-of-product and sigma-pi-sigma neural networks

Abstract

Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNN with its activation function in C(R) is dense in C(K) for any compact double struck K sign ∈ ℝN, if and only if the activation function is not a polynomial. It is also shown that if the activation function of an SPSNN is in C(R), then the functions generated by the SPSNN are dense in C(K) if and only if the activation function is not a constant. © Springer-Verlag Berlin Heidelberg 2007.