On the bound of the approximation capacity of multi-layer neural network

The authors deal with the approximation capacity of a multilayer neural network (MLNN) and present a strict mathematical expression for the bound of the approximation ability of a single input-output MLNN with hidden units of sigmoid activation functions. The influence of the number of hidden units, connections, and the threshold on the approximation accuracy is also discussed. The relationship between the order of the polynomial and the number of MLNN hidden units used to approximate the polynomial is given