Theory and Implementation of Complex-Valued Neural Networks

Jose Agustin Barrachina, Chengfang Ren, Gilles Vieillard, Christele Morisseau, Jean-Philippe Ovarlez

2/16/2023

stat.MLcs.LG

No official code found. Best implementation: NEGU93/cvnn (197 stars, MIT, TensorFlow, last commit 2026-04-23). 1 more below.

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.

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Code Implementations(2)

NEGU93/cvnnCommunity100%

TensorFlowMIT

Library to help implement a complex-valued neural network (cvnn) using tensorflow as back-end

19737Shell, PythonSep 16, 20206 months agoMIT

complex-networkscomplex-neural-networkscomplex-numbersdeep-learningmachine+4 more

JesperDramsch/keras-complexCommunity100%

TensorFlow

Keras-Tensorflow implementation of complex-valued convolutional neural networks

13245PythonFeb 5, 20191 years agoNOASSERTION

cnncomplexcomplex-numbersconvolutional-neural-networksdeep-learning+4 more

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Cite this paper

@article{barrachina2023theory,
  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},
  year   = {2023},
  eprint = {2302.08286},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2302.08286v1}
}

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