Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks

Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks

The batch split-complex backpropagation BSCBP algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. ...

Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks

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 z...

Convergence of Split-Complex Backpropagation Algorithm with Momentum∗

This paper investigates a split-complex backpropagation algorithm with momentum (SCBPM) for complex-valued neural networks. Some convergence results for SCBPM are proved under relaxed conditions compared with existing results. The monotonicity of the error function during the training iteration process is also guaranteed. Two numerical examples are given to support the theoretical findings.

Complex-Valued Neural Networks

The usual real-valued artificial neural networks have been applied to various fields such as telecommunications, robotics, bioinformatics, image processing and speech recognition, in which complex numbers (two dimensions) are often used with the Fourier transformation. This indicates the usefulness of complex-valued neural networks whose input and output signals and parameters such as weights a...

Complex-Valued Neural Networks