Upper Bounds on the Approximation Rates of Real-valued Boolean Functions by Neural Networks.

Upper Bounds on the Approximation Rates of Real-valued Boolean Functions by Neural Networks.

Abstract

Real-valued functions with multiple boolean variables are represented by one-hidden-layer Heaviside perceptron networks with an exponential number of hidden units. We derive upper bounds on approximation error using a given number n of hidden units. The bounds on error axe of the form cn√cn where c depends on certain norms of the function being approximated and n is the number of hidden units. We show examples of functions for which these norms grow polynomially and exponentially with increasing input dimension.

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Authors
  • Schindlerova, Katerina
  • Kurkova, Vera
  • Savicky, Petr
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Editors
  • Smith, Georg
  • Steele, Nigel
  • Albrecht, Rudolf
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
International Conference on Artificial Neural Nets and Genetic Algorithms
Divisions
Data Mining
Subjects
Kuenstliche Intelligenz
Event Location
Norwich, England
Event Type
Conference
Event Dates
1997
Series Name
Artificial Neural Nets and Genetic Algorithms
ISSN/ISBN
978-3-7091-6384-9
Page Range
pp. 495-499
Date
1997
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