Density and approximation by using feed forward artificial neural networks

Abstract EN

in this is paper ,we consider the density questions associated with the single hidden layer feed forward model.

We proved that a FFNN with one hidden layer can uniformly approximate any continuous fonction in C(k)(where k is a compact set in Rn ) to any required accuracy.

However, if the set of basis function is dense then the ANN'S can has almost one hidden layer.

But ؛!'the set of basis function non-dense.

then we need more hidden layers.

Also, W'e have shown that there exist localized functions and that there is no theoretical lower bound on the degree of approximation common to all activation fanctions(contrary to the situation in the single hidden layer model).