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On the optimality of neural-network approximation using incremental algorithms.

R Meir1, V E Maiorov

  • 1Department of Electrical Engineering, Technion, Haifa 32000, Israel.

IEEE Transactions on Neural Networks
|February 6, 2008
PubMed
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This study develops incremental neural network algorithms for function approximation. It establishes error bounds and convergence rates for various norms, offering practical algorithms and insights into network weight properties.

Area of Science:

  • Computational mathematics
  • Machine learning theory
  • Neural network approximation

Background:

  • Neural networks are powerful tools for function approximation.
  • Understanding approximation error bounds and convergence rates is crucial for algorithm development.
  • Previous work focused on specific norms (e.g., L2), limiting broader applicability.

Purpose of the Study:

  • To study function approximation by neural networks using incremental algorithms.
  • To compute upper bounds on approximation error for a general class of functions.
  • To extend existing results to various Lq norms and provide explicit algorithms.

Main Methods:

  • Analysis of function approximation error using Lq norms (1 ≤ q ≤ ∞).
  • Development of incremental algorithms for neural network function approximation.

Related Experiment Videos

  • Derivation of upper bounds on approximation error and convergence rates.

    • Main Results:

    • Established upper bounds on approximation error for functions with L2 smoothness properties.
    • Demonstrated near-optimal convergence rates for q ≤ 2, outperforming linear approximation.
    • Showcased that positive hidden-to-output weights do not limit generality and provided explicit bounds.

    Conclusions:

    • The study provides a theoretical framework and practical algorithms for neural network function approximation.
    • Results offer improved approximation error rates across different Lq norms.
    • Findings confirm the efficiency of positive hidden-to-output weights in neural networks.