A new learning method using prior information of neural networks

In this paper, we present a new learning method using prior information for three-layered neural networks. Usually when neural networks are used for identification of systems, all of their weights are trained independently, without considering their interrelation of weight values. Thus the training results are not usually good. The reason for this is that each parameter has its influence on others during the learning. To overcome this problem, first, we give an exact mathematical equation that describes the relation between weight values given by a set of data conveying prior information. Then we present a new learning method that trains a part of the weights and calculates the others by using these exact mathematical equations. In almost all cases, this method keeps prior information given by a mathematical structure exactly during the learning. In addition, a learning method using prior information expressed by inequality is also presented. In any case, the degree of freedom of networks (the number of adjustable weights) is appropriately limited in order to speed up the learning and ensure small errors. Numerical computer simulation results are provided to support the present approaches.