Concaving Space Algorithm for Neural Network

The global optimum solution, convergence rate are much more concerned for neural network training process. The efficient use of information resources works noticeably in the design of training methods. In this paper, not only gradient information but also Hessian matrix resource is applied for improving the learning efficiency and stability of neural network The necessary and sufficient condition of semi-positive definite Hessian matrix is gained .So the connecting weight matrix W can be revised within concave domains. Hence, the stable distribution of weights can be reached. The algorithm guides the training process to developing towards optimum goal. Compared with standard gradient method, the oscillating divergent phenomenon is avoided. The convergence of the algorithm is accelerated.