Interactive gradient algorithm for artificial neural networks

According to the thought of "divide and conquer", we divide the neural network into two parts: environment representative model (ERM) and environment generated model (EGM) whose parameter spaces are Riemannian spaces. And we propose the interactive gradient learning algorithm to train the two parts in turn and obtain an attractive result. Then we propose the interactive natural gradient algorithm theoretically which not only reduces the nonlinear degree of Artificial Neural Networks, but also avoids the slow rate of conventional gradient algorithm.