We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can be achieved. We also discuss the problem of approximation of a compact subset of a Euclidean space with such networks with a classical sigmoidal response function.
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Dedicated to Dr. C.A. Micchelli on the occasion of his fiftieth birthday, December 1992
Research supported in part by AFOSR Grant No. 226 113 and by the AvH Foundation.
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Mhaskar, H.N. Approximation properties of a multilayered feedforward artificial neural network. Adv Comput Math 1, 61–80 (1993). https://doi.org/10.1007/BF02070821
- Neural networks
- uniform approximation
- multivariate splines
- analytic functions
- modulus of smoothness
- (AMS) 41A15