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.

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