# Quaternion Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1806.04418 · HTML: https://mlsanity.com/paper/1806.04418/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 30 of 41)

- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [SpeechBrain: A General-Purpose Speech Toolkit](https://mlsanity.com/paper/2106.04624/) (2021)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameters](https://mlsanity.com/paper/2102.08597/) (2021)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)
- [Quaternion Generative Adversarial Networks](https://mlsanity.com/paper/2104.09630/) (2021)
- [Domain Prompt Learning with Quaternion Networks](https://mlsanity.com/paper/2312.08878/) (2023)
- [Parameter Efficient Fine-tuning via Cross Block Orchestration for Segment Anything Model](https://mlsanity.com/paper/2311.17112/) (2023)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Parameterized Hypercomplex Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2103.16584/) (2021)
- [Multi-View Hypercomplex Learning for Breast Cancer Screening](https://mlsanity.com/paper/2204.05798/) (2022)
- [Attention-Map Augmentation for Hypercomplex Breast Cancer Classification](https://mlsanity.com/paper/2310.07633/) (2023)
- [Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling](https://mlsanity.com/paper/2104.01716/) (2021)
- [Hypercomplex Image-to-Image Translation](https://mlsanity.com/paper/2205.02087/) (2022)
- [Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs](https://mlsanity.com/paper/2312.17361/) (2023)
- [Latent Knowledge-Guided Video Diffusion for Scientific Phenomena Generation from a Single Initial Frame](https://mlsanity.com/paper/2411.11343/) (2024)
- [Two-view Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2112.09231/) (2021)
- [Quaternion Convolutional Neural Networks: Current Advances and Future Directions](https://mlsanity.com/paper/2307.08663/) (2023)
- [Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagation](https://mlsanity.com/paper/2403.11722/) (2024)
- [Promoting AI Equity in Science: Generalized Domain Prompt Learning for Accessible VLM Research](https://mlsanity.com/paper/2405.08668/) (2024)
- [SSPA: Split-and-Synthesize Prompting with Gated Alignments for Multi-Label Image Recognition](https://mlsanity.com/paper/2407.20920/) (2024)
- [Neural Networks at a Fraction with Pruned Quaternions](https://mlsanity.com/paper/2308.06780/) (2023)
- [Vision-Informed Flow Image Super-Resolution with Quaternion Spatial Modeling and Dynamic Flow Convolution](https://mlsanity.com/paper/2401.15913/) (2024)
- [Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterion](https://mlsanity.com/paper/2402.14227/) (2024)
- [Quaternion Generative Adversarial Neural Networks and Applications to Color Image Inpainting](https://mlsanity.com/paper/2406.11567/) (2024)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [HyReaL: Clustering Attributed Graph via Hyper-Complex Space Representation Learning](https://mlsanity.com/paper/2411.14727/) (2024)
- [Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detection](https://mlsanity.com/paper/2509.05512/) (2025)
- [LiteFusion: Taming 3D Object Detectors from Vision-Based to Multi-Modal with Minimal Adaptation](https://mlsanity.com/paper/2512.20217/) (2025)

## Abstract (arXiv)

Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due to their capability to learn short and long-term dependencies between the basic elements of a sequence. Nonetheless, popular tasks such as speech or images recognition, involve multi-dimensional input features that are characterized by strong internal dependencies between the dimensions of the input vector. We propose a novel quaternion recurrent neural network (QRNN), alongside with a quaternion long-short term memory neural network (QLSTM), that take into account both the external relations and these internal structural dependencies with the quaternion algebra. Similarly to capsules, quaternions allow the QRNN to code internal dependencies by composing and processing multidimensional features as single entities, while the recurrent operation reveals correlations between the elements composing the sequence. We show that both QRNN and QLSTM achieve better performances than RNN and LSTM in a realistic application of automatic speech recognition. Finally, we show that QRNN and QLSTM reduce by a maximum factor of 3.3x the number of free parameters needed, compared to real-valued RNNs and LSTMs to reach better results, leading to a more compact representation of the relevant information.