New learning method using prior information of neural networks

In this paper, we present a new learning method using prior information for three-layer neural networks. Usually when neural networks are used for identification of systems, all of their weights are trained independently, without considering their inter-relation of weights 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 exact mathematical equation that describes the relation between weight values given a set of data conveying prior information. Then we present a new learning method that trains the part of the weights and calculates the others by using these exact mathematical equations. This method often keeps a priori given mathematical structure exactly during the learning, in other words, training is done so that the network follows predetermined trajectory. Numerical computer simulation results are provided to support the present approaches.