Three-layer feedforward structures smoothly approximating polynomial functions

Abstract

This paper considers a structure of three-layer feedforward networks that approximate polynomial functions. The feedforward network has some system parameters such as the coupling coefficients and the biases. The structure of the feedforward network is determined by the system parameters. For any polynomial function, a simple calculation method of the parameters is proposed when the three-layer feedforward network sufficiently approximates the polynomial function. Moreover, it is shown that the obtained feedforward network smoothly approximates the polynomial function. © 2010 Springer-Verlag Berlin Heidelberg.