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Related Experiment Videos

XOR has no local minima: A case study in neural network error surface analysis.

Leonard G. C. Hamey1

  • 1Department of Computing, Macquarie University, Sydney, Australia

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
Summary

This study introduces a new method to analyze local minima in feedforward neural networks. The analysis proves no local minima exist for the XOR problem, aiding in the development of better training algorithms.

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Neural Networks

Background:

  • Local minima in feedforward neural networks pose challenges for training algorithms.
  • The XOR problem is a classic benchmark often cited for exhibiting local minima.

Purpose of the Study:

  • To present a novel methodology for analyzing local minima in feedforward neural networks.
  • To investigate the presence of local minima in the XOR problem using the new analysis method.

Main Methods:

  • Developing a methodology based on analyzing trajectories through weight space.
  • Applying the methodology to the XOR problem to identify potential escapes from local minima.

Main Results:

  • The analysis demonstrated the absence of local minima for the XOR problem.

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  • Significant aspects of the error surface structure were revealed.

    • Conclusions:

    • The study contributes to understanding local minima in neural networks.
    • Findings can inform the development of training algorithms that avoid local minima entrapment.