Density and Approximation by Using Feed Forward Artificial Neural Networks

In this paper , we will consider the density questions associated with the single hjdden layer feed forward model. We proved that a FFNN with one hidden layci can uniformly approximate any continuous function in C(k) (where k is a compact set in R ^n) to any requited accuracy; However, if the set of basis fi.mction is dense then the ANN s can has almost one hidden layer. But if the set of basis function non-dense, then we need more hidden layers. 1lso, we have shown that there exist localized functions and that there is no theoretical lower bound on the degree of approximation common to all activation functions( contrary to the s ituation in the single hidden layer model).