# Complex-Valued vs. Real-Valued Neural Networks for Classification Perspectives: An Example on Non-Circular Data

arXiv: https://arxiv.org/abs/2009.08340 · HTML: https://mlsanity.com/paper/2009.08340/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 12 of 12)

- [Expanding Expressivity in Transformer Models with M"obiusAttention](https://mlsanity.com/paper/2409.12175/) (2024)
- [Steinmetz Neural Networks for Complex-Valued Data](https://mlsanity.com/paper/2409.10075/) (2024)
- [CoShNet: A Hybrid Complex Valued Neural Network using Shearlets](https://mlsanity.com/paper/2208.06882/) (2022)
- [Impact of PolSAR pre-processing and balancing methods on complex-valued neural networks segmentation tasks](https://mlsanity.com/paper/2210.17419/) (2022)
- [Attention based Dual-Branch Complex Feature Fusion Network for Hyperspectral Image Classification](https://mlsanity.com/paper/2311.01624/) (2023)
- [Room Transfer Function Reconstruction Using Complex-valued Neural Networks and Irregularly Distributed Microphones](https://mlsanity.com/paper/2402.04866/) (2024)
- [A Complex UNet Approach for Non-Invasive Fetal ECG Extraction Using Single-Channel Dry Textile Electrodes](https://mlsanity.com/paper/2506.22457/) (2025)
- [Shift-Equivariant Complex-Valued Convolutional Neural Networks](https://mlsanity.com/paper/2511.21250/) (2025)
- [Exploring Polarimetric Properties Preservation during Reconstruction of PolSAR images using Complex-valued Convolutional Neural Networks](https://mlsanity.com/paper/2602.07094/) (2026)
- [Toward Complex-Valued Neural Networks for Waveform Generation](https://mlsanity.com/paper/2603.11589/) (2026)
- [PolSAR Image Classification using a Hybrid Complex-Valued Network (HybridCVNet)](https://mlsanity.com/paper/2605.31137/) (2026)
- [Shortcomings and capacities of real-constrained neural networks in complex spaces](https://mlsanity.com/paper/2606.04390/) (2026)

## Abstract (arXiv)

The contributions of this paper are twofold. First, we show the potential interest of Complex-Valued Neural Network (CVNN) on classification tasks for complex-valued datasets. To highlight this assertion, we investigate an example of complex-valued data in which the real and imaginary parts are statistically dependent through the property of non-circularity. In this context, the performance of fully connected feed-forward CVNNs is compared against a real-valued equivalent model. The results show that CVNN performs better for a wide variety of architectures and data structures. CVNN accuracy presents a statistically higher mean and median and lower variance than Real-Valued Neural Network (RVNN). Furthermore, if no regularization technique is used, CVNN exhibits lower overfitting. The second contribution is the release of a Python library (Barrachina 2019) using Tensorflow as back-end that enables the implementation and training of CVNNs in the hopes of motivating further research on this area.