mlsanityData to 7 Oct 2026

Quaternion Convolutional Neural Networks

arXiv 1903.00658 ↗First posted 2 Mar 2019cs.CVcited by 48

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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.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Mar 2019.

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Citing papers per year: 2021: 10; 2022: 2; 2023: 11; 2024: 11; 2025: 7; 2026: 7.

48 papers.

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  1. 2021Compacter: Efficient Low-Rank Hypercomplex Adapter Layerscited by 458
  2. 2022Clifford Neural Layers for PDE Modelingcited by 91
  3. 2021Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameterscited by 66
  4. 2023Clifford Group Equivariant Neural Networkscited by 54
  5. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  6. 2025Underwater Image Restoration Through a Prior Guided Hybrid Sense Approach and Extensive Benchmark Analysiscited by 16
  7. 2021Speech Emotion Recognition Using Quaternion Convolutional Neural Networkscited by 11
  8. 2023Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentationcited by 10
  9. 2025ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generationcited by 10
  10. 2021HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrationscited by 9
  11. 2021A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluationcited by 8
  12. 2022Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Losscited by 8
36 more
  1. 2023Color Equivariant Convolutional Networkscited by 7
  2. 2023Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Networkcited by 6
  3. 2021Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modellingcited by 4
  4. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  5. 2021RingCNN: Exploiting Algebraically-Sparse Ring Tensors for Energy-Efficient CNN-Based Computational Imagingcited by 3
  6. 2021Two-view Graph Neural Networks for Knowledge Graph Completioncited by 3
  7. 2023Pneumonia Detection in Chest X-Ray Images : Handling Class Imbalancecited by 3
  8. 2023Quaternion Convolutional Neural Networks: Current Advances and Future Directionscited by 3
  9. 2024Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagationcited by 3
  10. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  11. 2024Learning Characteristics of Reverse Quaternion Neural Networkcited by 2
  12. 2026Feature Entanglement-based Quantum Multimodal Fusion Neural Networkcited by 2
  13. 2021Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosiscited by 1
  14. 2023Enhancing ResNet Image Classification Performance by using Parameterized Hypercomplex Multiplicationcited by 1
  15. 2023Neural Networks at a Fraction with Pruned Quaternionscited by 1
  16. 2024Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterioncited by 1
  17. 2024An Intrinsic Vector Heat Networkcited by 1
  18. 2024Quaternion Generative Adversarial Neural Networks and Applications to Color Image Inpaintingcited by 1
  19. 2024Improving Quaternion Neural Networks with Quaternionic Activation Functionscited by 1
  20. 2024Fully tensorial approach to hypercomplex-valued neural networkscited by 1
  21. 2024HyReaL: Clustering Attributed Graph via Hyper-Complex Space Representation Learningcited by 1
  22. 2025Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detectioncited by 1
  23. 2026Learning Physiology-Informed Vocal Spectrotemporal Representations for Speech Emotion Recognitioncited by 1
  24. 2026Quaternion Self-Attention with Shared Scorescited by 1
  25. 2021Quaternion-Based Graph Convolution Network for Recommendationcited by 0
  26. 2023On the Matrix Form of the Quaternion Fourier Transform and Quaternion Convolutioncited by 0
  27. 2023Syntax-Aware Complex-Valued Neural Machine Translationcited by 0
  28. 2024Order Theory in the Context of Machine Learningcited by 0
  29. 2025FoGE: Fock Space inspired encoding for graph promptingcited by 0
  30. 2025Compressing Quaternion Convolutional Neural Networks for Audio Classificationcited by 0
  31. 2025A-QCF-Net: An Adaptive Quaternion Cross-Fusion Network for Multimodal Liver Tumor Segmentation from Unpaired Datasetscited by 0
  32. 2025Training-Free Color-Aware Adversarial Diffusion Sanitization for Diffusion Stegomalware Defense at Security Gatewayscited by 0
  33. 2026EdgeLDR: Quaternion Low-Displacement Rank Neural Networks for Edge-Efficient Deep Learningcited by 0
  34. 2026UHD Low-Light Image Enhancement via Real-Time Enhancement Methods with Clifford Information Fusioncited by 0
  35. 2026Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learningcited by 0
  36. 2026QC-GAN: A Parameter-Efficient Quaternion Conformer GAN for High-Fidelity Speech Enhancementcited by 0