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).