Analysis of Momentum Term in Back-Propagation

概要

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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=Σ^^n__μα^<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.
社団法人電子情報通信学会の論文
1995-08-25