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

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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
  • Hlavackova-Schindler, 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 and Machine Learning
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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