# Complex Gated Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1806.08267 · HTML: https://mlsanity.com/paper/1806.08267/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2018.

## Built on by (most cited first, 17 of 17)

- [Simplifying and Understanding State Space Models with Diagonal Linear RNNs](https://mlsanity.com/paper/2212.00768/) (2022)
- [Language-Driven Interactive Traffic Trajectory Generation](https://mlsanity.com/paper/2405.15388/) (2024)
- [Towards Understanding Theoretical Advantages of Complex-Reaction Networks](https://mlsanity.com/paper/2108.06711/) (2021)
- [3D Human Pose Estimation Using M"obius Graph Convolutional Networks](https://mlsanity.com/paper/2203.10554/) (2022)
- [Quantitative approximation results for complex-valued neural networks](https://mlsanity.com/paper/2102.13092/) (2021)
- [Revisiting Bi-Linear State Transitions in Recurrent Neural Networks](https://mlsanity.com/paper/2505.21749/) (2025)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [Adapting Pre-trained Language Models for Quantum Natural Language Processing](https://mlsanity.com/paper/2302.13812/) (2023)
- [Physics-constrained Attack against Convolution-based Human Motion Prediction](https://mlsanity.com/paper/2306.11990/) (2023)
- [BeatFormer: Efficient motion-robust remote heart rate estimation through unsupervised spectral zoomed attention filters](https://mlsanity.com/paper/2507.14885/) (2025)
- [Fully complex-valued deep learning model for visual perception](https://mlsanity.com/paper/2212.07146/) (2022)
- [The Quantum Shortcut: Complex Phase-State Dynamics Reduce the Optimization Steps of Sequence Models](https://mlsanity.com/paper/2608.14691/) (2026)
- [Neural Networks with Complex-Valued Weights Have No Spurious Local Minima](https://mlsanity.com/paper/2103.07287/) (2021)
- [FallDeF5: A Fall Detection Framework Using 5G-based Deep Gated Recurrent Unit Networks](https://mlsanity.com/paper/2106.15049/) (2021)
- [Acceleration Method for Learning Fine-Layered Optical Neural Networks](https://mlsanity.com/paper/2109.01731/) (2021)
- [BadHMP: Backdoor Attack against Human Motion Prediction](https://mlsanity.com/paper/2409.19638/) (2024)
- [Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space](https://mlsanity.com/paper/2604.05030/) (2026)

## Abstract (arXiv)

Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from complex representations. We present a novel complex gated recurrent cell, which is a hybrid cell combining complex-valued and norm-preserving state transitions with a gating mechanism. The resulting RNN exhibits excellent stability and convergence properties and performs competitively on the synthetic memory and adding task, as well as on the real-world tasks of human motion prediction.