Approximation of sigmoid function and the derivative for hardware implementation of artificial neurons

Abstract

A piecewise linear recursive approximation scheme is applied to the computation of the sigmoid function and its derivative in artificial neurons with learning capability. The scheme provides high approximation accuracy with very low memory requirements. The recursive nature of this method allows for the control of the rate accuracy/computation-delay just by modifying one parameter with no impact on the occupied area. The error analysis shows an accuracy comparable to or better than other reported piecewise linear approximation schemes. No multiplier is needed for a digital implementation of the sigmoid generator and only one memory word is required to store the parameter that optimises the approximation.