Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks - Huisheng Zhang; Dongpo Xu; Zhiping Wang (Discrete Dynamics in Nature and Society)
The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings.