APPROXIMATIONS OF FUNCTIONS BY A MULTILAYER PERCEPTRON - A NEW APPROACH

We provide a radically elementary proof of the universal approximation property of the one-hidden layer perceptron based on the Taylor expan sion and the Vandermonde determinant. It works for both L-q and unifor m approximation on compact sets. This approach naturally yields some b ounds for the design of the hidden layer and convergence results (incl uding some rates) for the derivatives. A partial answer to Hornik's co njecture on the universality of the bias is proposed. An extension to vector valued functions is also carried out. (C) 1997 Elsevier Science Ltd.