# Quaternion Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1903.00658 · HTML: https://mlsanity.com/paper/1903.00658/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2019.

## Built on by (most cited first, 30 of 48)

- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (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)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Underwater Image Restoration Through a Prior Guided Hybrid Sense Approach and Extensive Benchmark Analysis](https://mlsanity.com/paper/2501.02701/) (2025)
- [Speech Emotion Recognition Using Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/2111.00404/) (2021)
- [ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation](https://mlsanity.com/paper/2502.14637/) (2025)
- [Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2305.07283/) (2023)
- [HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations](https://mlsanity.com/paper/2108.05774/) (2021)
- [A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation](https://mlsanity.com/paper/2103.14799/) (2021)
- [Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss](https://mlsanity.com/paper/2202.02063/) (2022)
- [Color Equivariant Convolutional Networks](https://mlsanity.com/paper/2310.19368/) (2023)
- [Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Network](https://mlsanity.com/paper/2303.10722/) (2023)
- [Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling](https://mlsanity.com/paper/2104.01716/) (2021)
- [Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebra](https://mlsanity.com/paper/2302.01191/) (2023)
- [RingCNN: Exploiting Algebraically-Sparse Ring Tensors for Energy-Efficient CNN-Based Computational Imaging](https://mlsanity.com/paper/2104.09056/) (2021)
- [Two-view Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2112.09231/) (2021)
- [Pneumonia Detection in Chest X-Ray Images : Handling Class Imbalance](https://mlsanity.com/paper/2301.08479/) (2023)
- [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)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Learning Characteristics of Reverse Quaternion Neural Network](https://mlsanity.com/paper/2411.05816/) (2024)
- [Feature Entanglement-based Quantum Multimodal Fusion Neural Network](https://mlsanity.com/paper/2601.07856/) (2026)
- [Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosis](https://mlsanity.com/paper/2112.06685/) (2021)
- [Enhancing ResNet Image Classification Performance by using Parameterized Hypercomplex Multiplication](https://mlsanity.com/paper/2301.04623/) (2023)
- [Neural Networks at a Fraction with Pruned Quaternions](https://mlsanity.com/paper/2308.06780/) (2023)
- [Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterion](https://mlsanity.com/paper/2402.14227/) (2024)
- [An Intrinsic Vector Heat Network](https://mlsanity.com/paper/2406.09648/) (2024)
- [Quaternion Generative Adversarial Neural Networks and Applications to Color Image Inpainting](https://mlsanity.com/paper/2406.11567/) (2024)

## Abstract (arXiv)

Neural networks in the real domain have been studied for a long time and achieved promising results in many vision tasks for recent years. However, the extensions of the neural network models in other number fields and their potential applications are not fully-investigated yet. Focusing on color images, which can be naturally represented as quaternion matrices, we propose a quaternion convolutional neural network (QCNN) model to obtain more representative features. In particular, we redesign the basic modules like convolution layer and fully-connected layer in the quaternion domain, which can be used to establish fully-quaternion convolutional neural networks. Moreover, these modules are compatible with almost all deep learning techniques and can be plugged into traditional CNNs easily. We test our QCNN models in both color image classification and denoising tasks. Experimental results show that they outperform the real-valued CNNs with same structures.