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A general weight matrix formulation using optimal control.

O Farotimi1, A Dembo, T Kailath

  • 1Inf. Syst. Lab., Stanford Univ., CA.

IEEE Transactions on Neural Networks
|January 1, 1991
PubMed
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Optimal control theory provides general forms for neural network weights by encoding tasks in a performance index. This approach unifies various weight rules, offering a new perspective on neural network learning and applications.

Area of Science:

  • Computational Neuroscience
  • Machine Learning
  • Control Theory

Background:

  • Neural network weight determination is crucial for learning and application.
  • Existing methods like outer product rule and recurrent back-propagation have limitations.
  • Optimal control theory offers a powerful framework for dynamic system optimization.

Purpose of the Study:

  • To derive general forms for neural network weights using optimal control theory.
  • To demonstrate how different performance index structures lead to various weight update rules.
  • To compare the proposed method with existing techniques.

Main Methods:

  • Application of classical optimal control theory to neural network weight derivation.
  • Formulation of the learning or application task within a generalized performance index.

Related Experiment Videos

  • Comparative analysis against outer product rule, spectral methods, and recurrent back-propagation.

    • Main Results:

    • General forms for neural network weights derived from optimal control principles.
    • Demonstration that common weight rules emerge as special cases of the general framework.
    • Simulation results validating the derived weight rules and their performance.

    Conclusions:

    • Optimal control theory provides a unified and generalizable framework for deriving neural network weight update rules.
    • The proposed method offers a systematic way to develop and understand various learning algorithms.
    • This approach has the potential to advance the design and application of neural networks.