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Approximation properties of a multilayered feedforward artificial neural network


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).

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  • Neural networks
  • uniform approximation
  • multivariate splines
  • analytic functions
  • modulus of smoothness

Subject classification

  • (AMS) 41A15
  • 41A63