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Related Experiment Videos

Parameter convergence and learning curves for neural networks.

T L Fine1, S Mukherjee

  • 1School of Electrical Engineering, ETC 388, Cornell University, Ithaca, NY 14850, USA. tlfine@ee.cornell.edu

Neural Computation
|March 23, 1999
PubMed
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This study rigorously establishes conditions for neural network parameter estimates to converge to generalization error minima. It analyzes the asymptotic distribution of these estimates, providing insights into learning curve convergence rates.

Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Statistical Learning Theory

Background:

  • Neural network training algorithms are widely studied for their asymptotic behavior.
  • Empirical and generalization errors in neural networks often exhibit multiple minima.
  • Previous analyses of parameter estimate convergence have relied on informal calculations.

Purpose of the Study:

  • To rigorously establish conditions for parameter estimates to converge to generalization error minima.
  • To analyze the asymptotic distribution of the distance between parameter estimates and generalization error minima.
  • To derive learning curves and bounds on convergence rates.

Main Methods:

  • Analysis of the asymptotic behavior of parameter estimates in neural networks.

Related Experiment Videos

  • Rigorous mathematical derivations accounting for multiple error minima.
  • Evaluation of the asymptotic distribution of the distance metric.

    • Main Results:

    • Conditions are established for parameter estimates to strongly converge into the set of generalization error minima.
    • Convergence to a specific parameter value is not guaranteed.
    • The asymptotic distribution of the distance to the nearest minimum is evaluated.

    Conclusions:

    • The study provides a rigorous foundation for understanding parameter convergence in neural networks.
    • Results offer insights into the behavior of learning curves and convergence rates.
    • The findings highlight the complexity of asymptotic analysis in the presence of multiple minima.