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Theory and Implementation of Complex-Valued Neural Networks

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arxiv 2302.08286 v1 pith:N73WDFS2 submitted 2023-02-16 stat.ML cs.LG

Jose Agustin Barrachina , Chengfang Ren , Gilles Vieillard , Christele Morisseau , Jean-Philippe Ovarlez This is my paper · ORCID
classification stat.MLcs.LG
keywords complexcvnncomplex-valueddatadomainimplementationinitializationmodules
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation

    cs.LG 2025-09 unverdicted novelty 7.0 of 10

    Robust Filter Attention models self-attention as consistency-based state estimation under a linear SDE for token trajectories, matching standard attention complexity while showing lower perplexity and better zero-shot...

  2. A Complex UNet Approach for Non-Invasive Fetal ECG Extraction Using Single-Channel Dry Textile Electrodes

    eess.SP 2025-06 reject novelty 5.0 of 10

    A Complex U-Net trained on synthetic dry-electrode abdominal signals extracts single-channel fetal ECG with lower reported distortion than several baselines, though real-world validation is only qualitative.

  3. Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs

    physics.flu-dyn 2026-07 conditional novelty 4.0 of 10

    Split complex-valued PINNs achieve lower benchmark errors than real-valued PINNs, but the comparison is confounded by doubled parameters and unresolved internal error inconsistencies.

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