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Changing Network Weights by Lie Groups

  • David W. Pearson

Abstract

In this paper we investigate how stability properties of a continuous recursive neural network within neighbourhoods of certain equilibrium points can be changed whilst keeping the equilibrium points fixed. This can be achieved, under certain conditions, by the use of Lie group transformations operating on the synaptic weight matrix.

Keywords

Vector Field Equilibrium Point Isotropy Group Group Transformation Unstable Equilibrium 
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References

  1. [1]
    Brockett, R.W.: SIAM J. Control, Vol. 10. No. 2, 265, (1972).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Golub, G.H. and Van Loan, C.F.: Matrix Computatons, London, North Oxford Academic, 1986.Google Scholar

Copyright information

© Springer-Verlag/Wien 1995

Authors and Affiliations

  • David W. Pearson
    • 1
  1. 1.Laboratoire de Génie Informatique et d’Ingénierie de ProductionEMA-EERIENîmesFrance

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