### Abstract

Original language | English |
---|---|

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 |

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### Bibliographical note

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

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

### Cite this

*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

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

**The dynamics of matrix momentum.** / Rattray, Magnus; Saad, David.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - The dynamics of matrix momentum

AU - Rattray, Magnus

AU - Saad, David

N1 - The original publication is available at www.springerlink.com

PY - 1998/9/1

Y1 - 1998/9/1

N2 - 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.

AB - 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.

KW - matrix momentum

KW - statistical mechanics

KW - asymptotic performance

KW - matrix inversion

KW - Hessian

UR - https://link.springer.com/chapter/10.1007/978-1-4471-1599-1_24

U2 - 10.1007/978-1-4471-1599-1_24

DO - 10.1007/978-1-4471-1599-1_24

M3 - Chapter

SN - 3540762639

VL - 1

SP - 183

EP - 188

BT - Proceedings of the 8th International Conference on Artificial Neural Networks

A2 - Niklasson, Lars F.

A2 - Boden, Mikael B.

A2 - Ziemke, Tom

PB - Springer

ER -