Density and Approximation by Using Feed Forward Artificial Neural Networks - Naoum, R.S.; Ta wfiq, L.N.M. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
I n this paper ,we ’viii consider the density questions associC;lted with the single hidden layer feed forward model. We proved that a FFNN with one hidden layer can uniformly approximate any continuous function in C(k)(where k is a compact set in R11 ) to any required accuracy. However, if the set of basis function is dense then the ANN’s can has al most one hidden layer. But if the set of basis function non-dense, then we need more hidden layers. Also, we have shown that there exist localized functions and that there is no theoretical lower bound on the degree of a pproximation common to all acti vation functions(contrary to the si tuation in the single hidden layer model).