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Related Experiment Videos

Dynamical and complexity results for high order neural networks

E Goles1, M Matamala

  • 1Universidad de Chile, Facultad de Ciencias Físicas y Matématicas, Departamento de Ingeniería Matéatica, Santiago.

International Journal of Neural Systems
|September 1, 1994
PubMed
Summary

We studied neural network dynamics with polynomial arguments. Only symmetric sequential iteration converges to fixed points; others exhibit complex behaviors like non-bounded cycles.

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Area of Science:

  • Computational Neuroscience
  • Dynamical Systems Theory
  • Artificial Neural Networks

Background:

  • Neural networks with polynomial arguments exhibit complex dynamics.
  • Understanding iteration modes is crucial for predicting network behavior.

Purpose of the Study:

  • Investigate the dynamical behavior of block-sequential iterations in polynomial neural networks.
  • Identify conditions for convergence to fixed points.
  • Characterize complex dynamics in non-convergent iterations.

Main Methods:

  • Analysis of block-sequential iteration schemes for neural networks.
  • Application of symmetric hypotheses to study convergence.
  • Examination of high-order memory iteration schemes.

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Main Results:

  • Under symmetric conditions, only sequential iteration converges to fixed points.
  • Other iteration modes display complex dynamics, including non-bounded cycles.
  • A high-order memory iteration scheme with an energy functional shows bounded memory step cycles.

Conclusions:

  • The choice of iteration mode significantly impacts neural network dynamics.
  • Symmetric sequential iteration offers predictable convergence.
  • Non-symmetric iterations present challenges due to complex, unbounded behaviors.