Convergence rates for a class of neural networks with logarithmic function

The aim of this paper is to estimate the approximation error which results from the method of feedforward neural networks (FNNs) with logarithmic sigmoidal function s(x) = (1 + e^-x)^-1. By means of an extending function approach, a class of FNNs with single hidden layer and the active function s(x) is constructed to approximate the continuous function defined on a compact interval. By using the modulus of continuity of function as metric, the rate of convergence of the FNNs is estimated. Also, a numerical examples for illustrating the theoretical results is given.