Multilayer Feedforward Networks with Non-Polynomial Activation Functions Can Approximate Any Function

Abstract

Several researchers characterized the activation functions under which multilayer feedforwardnetworks can act as universal approximators. We show that all the characterizationsthat were reported thus far in the literature ark special cases of the following general result:a standard multilayer feedforward network can approximate any continuous functionto any degree of accuracy if and only if the network's activation functions are not polynomial.We also emphasize the important role of the threshold, asserting that without it thelast theorem doesn't hold.

Keywords: Multilayer feedforward networks, Activation functions, role of threshold, Universal approximation capabilities, LP(μ) approximation