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Approximating Functions by Neural Networks: A Constructive Solution in the Uniform Norm.

Larry M. Manevitz1, Moshe Shoham, Mark Meltser

  • 1University of Haifa, Haifa, Israel

Neural Networks : the Official Journal of the International Neural Network Society
|August 1, 1996
PubMed
Summary

This study introduces a novel neural network method for function approximation using maximal error, outperforming standard average error methods like back-propagation for applications such as robotic arm motion.

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Area of Science:

  • Computational neuroscience
  • Artificial intelligence
  • Machine learning

Background:

  • Traditional neural network training often relies on average error norms, which may not be optimal for all applications.
  • Existing approximation theories provide a foundation for developing new neural network methodologies.
  • Specific applications, like robotic arm control, demand precise error bounds.

Purpose of the Study:

  • To develop a constructive method for function approximation in neural networks using the uniform norm (maximal error).
  • To demonstrate the advantages of uniform norm approximation over average error norms for specific real-world problems.
  • To provide a practical realization of established theoretical results in neural network approximation.

Main Methods:

  • A novel constructive approximation algorithm is developed for neural networks.

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  • The method involves iterative adjustments to network weights and the number of neurons.
  • The approximation is performed in the uniform (maximal error) norm.

    • Main Results:

    • The developed method successfully approximates functions in the uniform norm.
    • This approach offers a more suitable approximation for tasks like robotic arm motion compared to average error methods.
    • The technique validates and implements theoretical findings from prominent researchers in the field.

    Conclusions:

    • Constructive approximation in the uniform norm is a viable and often superior alternative to average error methods for neural networks.
    • The proposed method has practical implications for control systems and other applications requiring precise error guarantees.
    • This work bridges theoretical approximation results with practical neural network implementation.