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Related Experiment Videos

Analysis of Tikhonov regularization for function approximation by neural networks.

Martin Burger1, Andreas Neubauer

  • 1Institut für Industriemathematik, Johannes Kepler Universität, A-4040, Linz, Austria

Neural Networks : the Official Journal of the International Neural Network Society
|February 11, 2003
PubMed
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This study analyzes Tikhonov regularization for neural network function approximation. It demonstrates stable convergence for output smoothing and weight decay methods, crucial for accurate data approximation.

Area of Science:

  • Machine Learning
  • Numerical Analysis
  • Neural Networks

Background:

  • Function approximation is a core problem in machine learning.
  • Tikhonov regularization is a standard technique for solving ill-posed inverse problems.
  • Feed-forward neural networks are widely used for complex function approximation tasks.

Purpose of the Study:

  • To analyze the convergence and stability of Tikhonov regularization for function approximation using feed-forward neural networks.
  • To investigate regularization by output smoothing, weight decay, and their combination.
  • To establish theoretical guarantees for approximation accuracy and convergence rates.

Main Methods:

  • Analysis of Tikhonov regularization with output smoothing and weight decay.

Related Experiment Videos

  • Convergence analysis in Sobolev and L(2)-norms.
  • Derivation of convergence rates based on noise level and network size.
  • Application to perceptrons and translation networks.

    • Main Results:

    • Stable approximations are achieved as noise tends to zero.
    • Convergence to the approximated function in a desired Sobolev space is demonstrated.
    • Convergence rates are established under additional smoothness assumptions.
    • Theoretical results are applicable to perceptrons and translation networks.

    Conclusions:

    • Tikhonov regularization, particularly with output smoothing and weight decay, provides stable and accurate function approximation with neural networks.
    • The choice of regularization parameter and network size is critical for achieving desired convergence and rates.
    • The findings have practical implications for designing effective neural network models for approximation tasks.