- Published: 20 June 2017
authors: Charles K. Chui, Xin Li, Hrushikesh N. Mhaskar
journal: Mathematics of Computation
publication year: 1994
links: jstor
abstract: We prove that feedforward artificial neural networks with a single hidden layer and an ideal sigmoidal response function cannot provide localized approximation in a Euclidean space of dimension higher than one. We also show that networks with two hidden layers can be designed to provide localized approximation. Since wavelet bases are most effective for local approximation, we give a discussion of the implementation of spline wavelets using multilayered networks where the response function is a sigmoidal function of order at least two.