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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Neural networks for localized approximation


Authors: C. K. Chui, Xin Li and H. N. Mhaskar
Journal: Math. Comp. 63 (1994), 607-623
MSC: Primary 65D15; Secondary 41A15, 41A30, 92B20
MathSciNet review: 1240656
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1240656-2
PII: S 0025-5718(1994)1240656-2
Keywords: Neural networks, sigmoidal functions, spline functions, wavelets
Article copyright: © Copyright 1994 American Mathematical Society