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Related Experiment Videos

Constructive function-approximation by three-layer artificial neural networks.

Shin Suzuki1

  • 1Information Science Research Laboratory, NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi-Shi, Kanagawa Pref., Japan

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
Summary
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This study proves constructive theorems for three-layer artificial neural networks. These networks can approximate Lebesgue-integrable and continuous functions with explicit error estimations.

Area of Science:

  • Artificial Intelligence
  • Computational Mathematics

Background:

  • Artificial neural networks (ANNs) are powerful tools for function approximation.
  • Understanding the theoretical capabilities of ANNs is crucial for their practical application.

Purpose of the Study:

  • To establish constructive theorems for three-layer ANNs with different activation functions.
  • To demonstrate the ability of these networks to approximate specific function spaces.
  • To provide explicit methods for network construction and error estimation.

Main Methods:

  • Proving constructive theorems for three-layer ANNs.
  • Utilizing trigonometric, piecewise linear, and sigmoidal hidden-layer units.
  • Focusing on the approximation of 2π-periodic pth-order Lebesgue-integrable functions (Lp(2π)) and continuous functions (C(2π)).

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Main Results:

  • Explicit equational representations for approximating networks.
  • Specifications for the number of hidden-layer units.
  • Formulations for approximation-error estimations.
  • Demonstrated applicability to non-periodic functions.

Conclusions:

  • Theorems provide practical and calculable methods for function approximation using ANNs.
  • The results offer explicit error bounds for the approximations.
  • The findings facilitate the application of ANNs to a broader range of mathematical problems.