Piecewise linear approximation applied to nonlinear function of a neural network

Abstract

An efficient piecewise linear approximation of a nonlinear function (PLAN) is proposed. This uses a simple digital gate design to perform a direct transformation from X to Y, where X is the input and Y is the approximated sigmoidal output. This PLAN is then used within the outputs of an artificial neural network to perform the nonlinear approximation. The comparison of this technique with two other sigmoidal approximation techniques for digital circuits is presented and the results show that the fast and compact digital circuit proposed produces the closest approximation to the sigmoid function. The hardware implementation of PLAN has been verified by a VHDL simulation with Mentor Graphics running under the UNIX operating system.