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Universal Approximation Using Radial-Basis-Function Networks.

J Park1, I W Sandberg1

  • 1Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, Texas 78712 USA.

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Summary
This summary is machine-generated.

Radial-basis-function (RBF) networks with one hidden layer can approximate any function. A specific class of RBF networks with consistent smoothing factors demonstrates universal approximation capabilities.

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Neural Networks

Background:

  • Recent research explores feedforward networks for approximating arbitrary functionals.
  • Studies have investigated networks with non-sigmoid hidden-layer nonlinearities, inspired by successful applications.

Purpose of the Study:

  • To investigate the universal approximation capabilities of radial-basis-function (RBF) networks.
  • To analyze RBF networks with a single hidden layer and consistent smoothing factors.

Main Methods:

  • Theoretical analysis of radial-basis-function (RBF) networks.
  • Focus on RBF networks with identical smoothing factors in each kernel node.

Main Results:

  • It is proven that RBF networks with one hidden layer possess universal approximation capabilities.
  • A specific class of RBF networks, characterized by a uniform smoothing factor, is shown to be sufficiently broad for universal approximation.

Conclusions:

  • Radial-basis-function (RBF) networks are powerful tools for function approximation.
  • The findings support the use of RBF networks with consistent smoothing factors in various applications.