The capability of feedforward neural networks with Omega -shaped activation functions

Abstract

The capability of the multilayer feedforward layered neural network with Omega -shaped activation functions is studied. The authors prove that a three layer neural network with any continuous Omega -shaped activation function can approximate any continuous function in the multidimensional real space. Further theoretical extensions to the generalized Omega -shaped function are also explored. One example of this kind of neural network is the Hermite network.<>