mlsanityData to 7 Oct 2026

Theory and Implementation of Complex-Valued Neural Networks

arXiv 2302.08286 ↗First posted 16 Feb 2023stat.ML cs.LGcited by 11

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 10 of its 61 references that are in the map. First posted on arXiv 16 Feb 2023.

Builds on

10 of 61 references.

References · 10

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  2. 2015Unitary Evolution Recurrent Neural Networkscited by 291
  3. 2017Deep Complex Networkscited by 215
  4. 2021A Survey of Complex-Valued Neural Networkscited by 61
  5. 2017Better than Real: Complex-valued Neural Nets for MRI Fingerprintingcited by 30
  6. 2016On Complex Valued Convolutional Neural Networkscited by 26
  7. 2018Complex-valued Neural Networks with Non-parametric Activation Functionscited by 19
  8. 2018Evaluation of Complex-Valued Neural Networks on Real-Valued Classification Taskscited by 9
  9. 2019Pixel-Wise PolSAR Image Classification via a Novel Complex-Valued Deep Fully Convolutional Networkcited by 6
  10. 2017On the Computation of Complex-valued Gradients with Application to Statistically Optimum Beamformingcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 2; 2026: 3.

11 papers.

  1. 2024Cauchy activation function and XNetcited by 4
  2. 2024CoNO: Complex Neural Operator for Continous Dynamical Physical Systemscited by 3
  3. 2023Complex-Valued Neural Networks for Data-Driven Signal Processing and Signal Understandingcited by 2
  4. 2025The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limitcited by 2
  5. 2023Complex-valued Neural Networks -- Theory and Analysiscited by 1
  6. 2023Emerging Approaches for THz Array Imaging: A Tutorial Review and Software Toolcited by 0
  7. 2024Neural Controlled Differential Equations with Quantum Hidden Evolutionscited by 0
  8. 2025A Complex UNet Approach for Non-Invasive Fetal ECG Extraction Using Single-Channel Dry Textile Electrodescited by 0
  9. 2026Exploring Polarimetric Properties Preservation during Reconstruction of PolSAR images using Complex-valued Convolutional Neural Networkscited by 0
  10. 2026Batch Normalization for Neural Networks on Complex Domainscited by 0
  11. 2026Entanglement is Half the Story: Post-Selection vs. Partial Tracescited by 0