# Phase-Aware Deep Learning with Complex-Valued CNNs for Audio Signal Applications

arXiv: https://arxiv.org/abs/2510.09926 · HTML: https://mlsanity.com/paper/2510.09926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [CNN Architectures for Large-Scale Audio Classification](https://mlsanity.com/paper/1609.09430/) (2016)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Phase-aware Speech Enhancement with Deep Complex U-Net](https://mlsanity.com/paper/1903.03107/) (2019)
- [Better than Real: Complex-valued Neural Nets for MRI Fingerprinting](https://mlsanity.com/paper/1707.00070/) (2017)
- [On Complex Valued Convolutional Neural Networks](https://mlsanity.com/paper/1602.09046/) (2016)
- [Enhanced Radar Imaging Using a Complex-valued Convolutional Neural Network](https://mlsanity.com/paper/1712.10096/) (2017)
- [Sound Event Detection Using Spatial Features and Convolutional Recurrent Neural Network](https://mlsanity.com/paper/1706.02291/) (2017)
- [Complex Fully Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1807.03343/) (2018)
- [Evaluation of Complex-Valued Neural Networks on Real-Valued Classification Tasks](https://mlsanity.com/paper/1811.12351/) (2018)
- [Characterizing Types of Convolution in Deep Convolutional Recurrent Neural Networks for Robust Speech Emotion Recognition](https://mlsanity.com/paper/1706.02901/) (2017)

## Abstract (arXiv)

This study explores the design and application of Complex-Valued Convolutional Neural Networks (CVCNNs) in audio signal processing, with a focus on preserving and utilizing phase information often neglected in real-valued networks. We begin by presenting the foundational theoretical concepts of CVCNNs, including complex convolutions, pooling layers, Wirtinger-based differentiation, and various complex-valued activation functions. These are complemented by critical adaptations of training techniques, including complex batch normalization and weight initialization schemes, to ensure stability in training dynamics. Empirical evaluations are conducted across three stages. First, CVCNNs are benchmarked on standard image datasets, where they demonstrate competitive performance with real-valued CNNs, even under synthetic complex perturbations. Although our focus is audio signal processing, we first evaluate CVCNNs on image datasets to establish baseline performance and validate training stability before applying them to audio tasks. In the second experiment, we focus on audio classification using Mel-Frequency Cepstral Coefficients (MFCCs). CVCNNs trained on real-valued MFCCs slightly outperform real CNNs, while preserving phase in input workflows highlights challenges in exploiting phase without architectural modifications. Finally, a third experiment introduces GNNs to model phase information via edge weighting, where the inclusion of phase yields measurable gains in both binary and multi-class genre classification. These results underscore the expressive capacity of complex-valued architectures and confirm phase as a meaningful and exploitable feature in audio processing applications. While current methods show promise, especially with activations like cardioid, future advances in phase-aware design will be essential to leverage the potential of complex representations in neural networks.