The research on the relation of self-learning ratio and the convergence speed in BP networks

The relation of self-learning ratio and the convergence speed in BP network is proposed in this paper. In theory, only when the self-learning ratio μ→0, the real gradient descent can be got, and the computation will converge to a certain local minimum point. But, a too small μ will cause a slow convergence speed and a too large μ may cause divergence. On the base of mathematical analysis and some computer simulations, the relation formula is given out as follows: n=ln[ε/|W(0)-W*|]/ln(1-μa) where n is the amount of iterative, μ is self-learning ratio, w(0) is the original weight and w* is the best weight, ε is the precision requirement, a is the slope of gradient imitative straight line. It is also proposed for a method to determine a better self-learning ratio