# Complex-valued neural networks for machine learning on non-stationary physical data

arXiv: https://arxiv.org/abs/1905.12321 · HTML: https://mlsanity.com/paper/1905.12321/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 7 of 7)

- [Machine Learning for the Detection and Identification of Internet of Things (IoT) Devices: A Survey](https://mlsanity.com/paper/2101.10181/) (2021)
- [Machine Learning in Nuclear Physics](https://mlsanity.com/paper/2112.02309/) (2021)
- [The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limit](https://mlsanity.com/paper/2507.05303/) (2025)
- [Holographic Transformers for Complex-Valued Signal Processing: Integrating Phase Interference into Self-Attention](https://mlsanity.com/paper/2509.19331/) (2025)
- [Adaptive Latent Space Tuning for Non-Stationary Distributions](https://mlsanity.com/paper/2105.03584/) (2021)
- [Multi-Weight Respecification of Scan-specific Learning for Parallel Imaging](https://mlsanity.com/paper/2204.01979/) (2022)
- [Phase-Aware Wavelet-Based-Scattering Encoder-Decoder for Dense Predictions](https://mlsanity.com/paper/2605.24621/) (2026)

## Abstract (arXiv)

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks.