Approximating functions by neural networks: A constructive solution in the uniform norm

Mark Meltser, Moshe Shoham, Larry M. Manevitz

Research output: Contribution to journalArticlepeer-review

Abstract

A method for constructively approximating functions in the uniform (i.e., maximal error) norm by successive changes in the weights and number of neurons in a neural network is developed. This is a realization of the approximation results of Cybenko, Hecht-Nielsen, Hornik, Stinchcombe, White, Callant, Funahashi, Leshno et al., and others. The constructive approximation in the uniform norm is more appropriate for a number of examples, such as robotic arm motion, and stands in contrast with more standard methods, such as back-propagation, which approximate only in the average error norm.

Original languageEnglish
Pages (from-to)965-978
Number of pages14
JournalNeural Networks
Volume9
Issue number6
DOIs
StatePublished - Aug 1996

Keywords

  • approximating functions
  • artificial neural networks
  • constructive approximation
  • dynamic neural network architecture
  • feed-forward
  • uniform norm

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence

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