Convergence analysis of fully complex backpropagation algorithm based on Wirtinger calculus
Related Experiment Video
Updated: Apr 30, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
Published on: June 21, 2022
Huisheng Zhang1, Xiaodong Liu2, Dongpo Xu3
1Department of Mathematics, Dalian Maritime University, Dalian, 116026 People's Republic of China ; Research Center of Information and Control, Dalian University of Technology, Dalian, 116024 People's Republic of China.
Abstract:
This paper considers the fully complex backpropagation algorithm (FCBPA) for training the fully complex-valued neural networks. We prove both the weak convergence and strong convergence of FCBPA under mild conditions. The decreasing monotonicity of the error functions during the training process is also obtained. The derivation and analysis of the algorithm are under the framework of Wirtinger calculus, which greatly reduces the description complexity. The theoretical results are substantiated by a simulation example.
Related Concept Videos
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Convolution Properties II
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Vector Representation of Complex Numbers
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
Convolution: Math, Graphics, and Discrete Signals
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Fundamental Theorem of Calculus II
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

