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The Dynamics of Matrix Momentum

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Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)


We analyse the matrix momentum algorithm, which provides an efficient approximation to on-line Newton’s method, by extending a recent statistical mechanics framework to include second order algorithms. We study the efficacy of this method when the Hessian is available and also consider a practical implementation which uses a single example estimate of the Hessian. The method is shown to provide excellent asymptotic performance, although the single example implementation is sensitive to the choice of training parameters. We conjecture that matrix momentum could provide efficient matrix inversion for other second order algorithms.


  • Gradient Descent
  • Hide Node
  • Generalization Error
  • Asymptotic Performance
  • Order Algorithm

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  • DOI: 10.1007/978-1-4471-1599-1_24
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© 1998 Springer-Verlag London

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Rattray, M., Saad, D. (1998). The Dynamics of Matrix Momentum. In: Niklasson, L., Bodén, M., Ziemke, T. (eds) ICANN 98. ICANN 1998. Perspectives in Neural Computing. Springer, London.

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  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-76263-8

  • Online ISBN: 978-1-4471-1599-1

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