Study of generalization of fractal neural network

Abstract

By the definition of fractal, the BP network is proved to be a fractal whose fractal dimension ranges from 2.5 to 5. The relationship between generalization and learning rate of the BP network and the relationship between generalization and fractal dimension of weights are researched in this paper. The results present that the generalization of BP network becomes better with the increasing of the learning rate and the generalizations of the constant learning rate and the variable learning rate are almost identical if the initial learning rate is greater. On the basis of these results, the maximum iteration time of BP network training can be predicted to raise the efficiency of the BP network learning and decrease the useless iteration times. In addition, the results also show that the best generalization appears in the fractal dimension range from 3 to 4.