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arXiv · 2302.08286

Theory and Implementation of Complex-Valued Neural Networks

Jose Agustin Barrachina·Chengfang Ren·Gilles Vieillard·Christele Morisseau·Jean-Philippe Ovarlez
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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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Jose Agustin Barrachina, Chengfang Ren, Gilles Vieillard, Christele Morisseau, Jean-Philippe Ovarlez. 2023-02-16. Theory and Implementation of Complex-Valued Neural Networks. https://arxiv.org/abs/2302.08286

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