The construction and approximation for feedforword neural networks with fixed weights

There have been various studies on approximation ability of feedforward neural networks. More existing studies are only concerned with the density on how a continuous function can be approximated by the networks. However, the results concerning the error of approximation of neural networks, in applications, are of particular interest to engineers. The results reported in the literature have “slow approximation rates” (of the order of 1/√n, where n is the number of nodes in the hid-den layer of neural networks). Here we show by a constructive method that for any f ∊ C [a, b], the function can be approximated by a neural network with one hidden layer, and the order of approximation is 1/nα for the target function f ∊ LipM (α), 0 < ≤ 1. This approach naturally yields the design of the hidden layer and some Jackson-type estimations.