### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of the 8th International Conference on Artificial Neural Networks |

Editors | Lars F. Niklasson, Mikael B. Boden, Tom Ziemke |

Publisher | Springer |

Pages | 183-188 |

Number of pages | 6 |

Volume | 1 |

ISBN (Print) | 3540762639 |

DOIs | |

Publication status | Published - 1 Sep 1998 |

### Bibliographical note

The original publication is available at www.springerlink.com### Keywords

- matrix momentum
- statistical mechanics
- asymptotic performance
- matrix inversion
- Hessian

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## Cite this

Rattray, M., & Saad, D. (1998). The dynamics of matrix momentum. In L. F. Niklasson, M. B. Boden, & T. Ziemke (Eds.),

*Proceedings of the 8th International Conference on Artificial Neural Networks*(Vol. 1, pp. 183-188). Springer. https://doi.org/10.1007/978-1-4471-1599-1_24