Spectral approximation of functions by using three-layered feedforward neural networks

The universal approximation capability exhibited by one-hidden-layer neural network is analyzed in the frequency domain. Hidden neurons are studied in terms of spectral generators and the output neurons as units linearly combining the spectra. The learning phase is described in terms of spectral approximation: it is directed to reduce the distance between the reference function spectrum and the output network´s one. In this paper, we propose a new spectrum-based technique to train 1-N-1 networks which approximate y=f(x) functions, with x,y∈R; and this method also takes into account the robustness of the resulting weight configuration