# Hybrid Real- and Complex-valued Neural Network Architecture

arXiv: https://arxiv.org/abs/2504.03497 · HTML: https://mlsanity.com/paper/2504.03497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [LibriTTS: A Corpus Derived from LibriSpeech for Text-to-Speech](https://mlsanity.com/paper/1904.02882/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [AudioMNIST: Exploring Explainable Artificial Intelligence for Audio Analysis on a Simple Benchmark](https://mlsanity.com/paper/1807.03418/) (2018)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [DCCRN+: Channel-wise Subband DCCRN with SNR Estimation for Speech Enhancement](https://mlsanity.com/paper/2106.08672/) (2021)
- [On Loss Functions for Supervised Monaural Time-Domain Speech Enhancement](https://mlsanity.com/paper/1909.01019/) (2019)
- [TEA-PSE 3.0: Tencent-Ethereal-Audio-Lab Personalized Speech Enhancement System For ICASSP 2023 DNS Challenge](https://mlsanity.com/paper/2303.07704/) (2023)
- [Complex-valued Convolutional Neural Networks for Enhanced Radar Signal Denoising and Interference Mitigation](https://mlsanity.com/paper/2105.00929/) (2021)
- [Rethinking complex-valued deep neural networks for monaural speech enhancement](https://mlsanity.com/paper/2301.04320/) (2023)
- [Phase-Aware Deep Speech Enhancement: It's All About The Frame Length](https://mlsanity.com/paper/2203.16222/) (2022)
- [Binaural Speech Enhancement Using Deep Complex Convolutional Transformer Networks](https://mlsanity.com/paper/2403.05393/) (2024)
- [Neural Networks with A La Carte Selection of Activation Functions](https://mlsanity.com/paper/2206.12166/) (2022)
- [A Hybrid Complex-valued Neural Network Framework with Applications to Electroencephalogram (EEG)](https://mlsanity.com/paper/2207.14799/) (2022)
- [Spectral Masking with Explicit Time-Context Windowing for Neural Network-Based Monaural Speech Enhancement](https://mlsanity.com/paper/2408.15582/) (2024)

## Abstract (arXiv)

We propose a hybrid real- and complex-valued neural network (HNN) architecture, designed to combine the computational efficiency of real-valued processing with the ability to effectively handle complex-valued data. We illustrate the limitations of using real-valued neural networks (RVNNs) for inherently complex-valued problems by showing how it learnt to perform complex-valued convolution, but with notable inefficiencies stemming from its real-valued constraints. To create the HNN, we propose to use building blocks containing both real- and complex-valued paths, where information between domains is exchanged through domain conversion functions. We also introduce novel complex-valued activation functions, with higher generalisation and parameterisation efficiency. HNN-specific architecture search techniques are described to navigate the larger solution space. Experiments with the AudioMNIST dataset demonstrate that the HNN reduces cross-entropy loss and consumes less parameters compared to an RVNN for all considered cases. Such results highlight the potential for the use of partially complex-valued processing in neural networks and applications for HNNs in many signal processing domains.