### Abstract

The back-propagation algorithm has been applied to many fields, and has shown large capability of neural networks. Many people use the back-propagation algorithm together with a momentum term to accelerate its convergence. However, in spite of the importance for theoretical studies, theoretical background of a momentum term has been unknown so far. First, this paper explains clearly the theoretical origin of a momentum term in the back-propagation algorithm for both a batch mode learning and a pattern-by-pattern learning. We will prove that the back-propagation algorithm having a momentum term can be derived through the following two assumptions: 1) The cost function is E^{n} = n/Σ/μ α^{n-μ} E_{μ}, where E_{μ} is the summation of squared error at the output layer at the μth learning time and a is the momentum coefficient. 2) The latest weights are assumed in calculating the cost function E^{n}. Next, we derive a simple relationship between momentum, learning rate, and learning speed and then further discussion is made with computer simulation.

Original language | English |
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Pages (from-to) | 1080-1086 |

Number of pages | 7 |

Journal | IEICE Transactions on Information and Systems |

Volume | E78-D |

Issue number | 8 |

Publication status | Published - 1995 Aug 1 |

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

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## Cite this

*IEICE Transactions on Information and Systems*,

*E78-D*(8), 1080-1086.