mlsanityData to 7 Oct 2026

Deep Quaternion Networks

arXiv 1712.04604 ↗First posted 13 Dec 2017cs.NE cs.CVcited by 48

Not on the map. Why?

Abstract (arXiv)

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parameters

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Dec 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 8; 2023: 10; 2024: 8; 2025: 8; 2026: 1.

48 papers.

Sort:

By area:

  1. 2021Compacter: Efficient Low-Rank Hypercomplex Adapter Layerscited by 458
  2. 2022The Unsurprising Effectiveness of Pre-Trained Vision Models for Controlcited by 155
  3. 2022Clifford Neural Layers for PDE Modelingcited by 91
  4. 2021Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with 1/n Parameterscited by 66
  5. 2021PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutionscited by 26
  6. 2021Quaternion Generative Adversarial Networkscited by 17
  7. 2023Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentationcited by 10
  8. 2021Convolutional Filtering and Neural Networks with Non Commutative Algebrascited by 8
  9. 2022Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Losscited by 8
  10. 2022Dual Quaternion Ambisonics Array for Six-Degree-of-Freedom Acoustic Representationcited by 8
  11. 2022Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networkscited by 8
  12. 2021Parameterized Hypercomplex Graph Neural Networks for Graph Classificationcited by 7
36 more
  1. 2022Learning Speech Emotion Representations in the Quaternion Domaincited by 7
  2. 2022Multi-View Hypercomplex Learning for Breast Cancer Screeningcited by 7
  3. 2023Color Equivariant Convolutional Networkscited by 7
  4. 2023Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Networkcited by 6
  5. 2021Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modellingcited by 4
  6. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  7. 2023Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networkscited by 4
  8. 2021RingCNN: Exploiting Algebraically-Sparse Ring Tensors for Energy-Efficient CNN-Based Computational Imagingcited by 3
  9. 2021Two-view Graph Neural Networks for Knowledge Graph Completioncited by 3
  10. 2023Quaternion Convolutional Neural Networks: Current Advances and Future Directionscited by 3
  11. 2024Time Series Compression using Quaternion Valued Neural Networks and Quaternion Backpropagationcited by 3
  12. 2021Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosiscited by 1
  13. 2023Enhancing ResNet Image Classification Performance by using Parameterized Hypercomplex Multiplicationcited by 1
  14. 2023Neural Networks at a Fraction with Pruned Quaternionscited by 1
  15. 2024Quaternion recurrent neural network with real-time recurrent learning and maximum correntropy criterioncited by 1
  16. 2024Improving Quaternion Neural Networks with Quaternionic Activation Functionscited by 1
  17. 2024Fully tensorial approach to hypercomplex-valued neural networkscited by 1
  18. 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Datasetcited by 1
  19. 2025Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detectioncited by 1
  20. 2025LiteFusion: Taming 3D Object Detectors from Vision-Based to Multi-Modal with Minimal Adaptationcited by 1
  21. 2021Neural Networks with Complex-Valued Weights Have No Spurious Local Minimacited by 0
  22. 2021Improving Axial-Attention Network Classification via Cross-Channel Weight Sharingcited by 0
  23. 2021Quaternion-Based Graph Convolution Network for Recommendationcited by 0
  24. 2022Quaternion Backpropagationcited by 0
  25. 2023Deep Axial Hypercomplex Networkscited by 0
  26. 2023Quaternion Orthogonal Transformer for Facial Expression Recognition in the Wildcited by 0
  27. 2024Multi-scale Quaternion CNN and BiGRU with Cross Self-attention Feature Fusion for Fault Diagnosis of Bearingcited by 0
  28. 2024KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorchcited by 0
  29. 2024Metric Learning for Clifford Group Equivariant Neural Networkscited by 0
  30. 2024An Effective, Robust and Fairness-aware Hate Speech Detection Frameworkcited by 0
  31. 2025Graph Neural Networks at a Fractioncited by 0
  32. 2025Compressing Quaternion Convolutional Neural Networks for Audio Classificationcited by 0
  33. 2025Interaction as Interference: A Quantum-Inspired Aggregation Approachcited by 0
  34. 2025Beyond Real Weights: Hypercomplex Representations for Stable Quantizationcited by 0
  35. 2025Training-Free Color-Aware Adversarial Diffusion Sanitization for Diffusion Stegomalware Defense at Security Gatewayscited by 0
  36. 2026QC-GAN: A Parameter-Efficient Quaternion Conformer GAN for High-Fidelity Speech Enhancementcited by 0