Constructive Approximation of Discontinuous Functions by Neural Networks

  • Authors:

  • B. Llanas;S. Lantarón;F. J. Sáinz

  • Affiliations:

  • Departamento de Matemática Aplicada, E.T.S.I. de Caminos, Universidad Politécnica de Madrid, Madrid, Spain 28040;Departamento de Matemática Aplicada, E.T.S.I. de Caminos, Universidad Politécnica de Madrid, Madrid, Spain 28040;Departamento de Matemática Aplicada, E.T.S.I. de Caminos, Universidad Politécnica de Madrid, Madrid, Spain 28040

  • Venue:
  • Neural Processing Letters
  • Year:
  • 2008

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Abstract

In this paper, we give a constructive proof that a real, piecewise continuous function can be almost uniformly approximated by single hidden-layer feedforward neural networks (SLFNNs). The construction procedure avoids the Gibbs phenomenon. Computer experiments show that the resulting approximant is much more accurate than SLFNNs trained by gradient descent.