Theory and Implementation of Complex-Valued Neural Networks
Machine Learning
2023-02-17 v1 Machine Learning
Abstract
This work explains in detail the theory behind Complex-Valued Neural Network (CVNN), including Wirtinger calculus, complex backpropagation, and basic modules such as complex layers, complex activation functions, or complex weight initialization. We also show the impact of not adapting the weight initialization correctly to the complex domain. This work presents a strong focus on the implementation of such modules on Python using cvnn toolbox. We also perform simulations on real-valued data, casting to the complex domain by means of the Hilbert Transform, and verifying the potential interest of CVNN even for non-complex data.
Keywords
Cite
@article{arxiv.2302.08286,
title = {Theory and Implementation of Complex-Valued Neural Networks},
author = {Jose Agustin Barrachina and Chengfang Ren and Gilles Vieillard and Christele Morisseau and Jean-Philippe Ovarlez},
journal= {arXiv preprint arXiv:2302.08286},
year = {2023}
}
Comments
42 pages, 18 figures