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https://github.com/SDS-Lab/awesome-hypercomplex-neural-networks

A list of awesome papers and cool resources on hypercomplex neural networks.
https://github.com/SDS-Lab/awesome-hypercomplex-neural-networks

List: awesome-hypercomplex-neural-networks

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A list of awesome papers and cool resources on hypercomplex neural networks.

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# awesome-hypercomplex-neural-networks

[![Awesome](https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg)](https://github.com/AngxiaoYue/awaresome-hypercomplex-neural-networks) 

[![License: MIT](https://img.shields.io/badge/License-MIT-green.svg)](https://opensource.org/licenses/MIT) 



A list of awesome papers and cool resources on hypercomplex neural networks.



## Contents

- [Resources](#resources)

  - [Introductory Papers](#introductory-papers)

  - [Introductory Videos](#introductory-videos)

  - [Others](#others)

- [Papers](#papers)

  - [Survey](#survey)

  - [Computer Vision and Graphics](#vision)

  - [Geometry Deep Learning](#geometry-deep-learning)

  - [Others](#others)



## Resources

### Introductory Papers

- Introduction to Quaternions (Chinese Version) [[Github](https://github.com/Krasjet/quaternion)][[Book](https://krasjet.github.io/quaternion/quaternion.pdf)]



### Introductory Videos

- Visualizing Quaternions (4d Numbers) with Stereographic Projection [[3blue1brown](https://www.youtube.com/watch?v=d4EgbgTm0Bg)]



- Quaternions and 3d Rotation, Explained Interactively [[3blue1brown](https://www.youtube.com/watch?v=zjMuIxRvygQ&t=190s)]

 

### Others

- Visualizing Quaternions [[Website](https://eater.net/quaternions)]



- Quaternions in Numpy [[Github](https://github.com/moble/quaternion)]



- PyTorch Implementations of Various Quaternion Neural Networks (QNN) [[Github](https://github.com/Orkis-Research/Pytorch-Quaternion-Neural-Networks)]



## Papers

### Survey

- Quaternion Neural Networks: State-of-the-Art and Research Challenges [[2020](https://link.springer.com/chapter/10.1007/978-3-030-62365-4_43)]



- A Survey of Quaternion Neural Networks [[2020](https://link.springer.com/article/10.1007/s10462-019-09752-1)]



### Computer Vision and Graphics

- Quaternion Convolutional Neural Networks [[ECCV 2018](https://openaccess.thecvf.com/content_ECCV_2018/papers/Xuanyu_Zhu_Quaternion_Convolutional_Neural_ECCV_2018_paper.pdf)][[Code](https://github.com/XYZ387/QuaternionCNN_Keras)]



- A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers [[ICCV 2019](https://arxiv.org/pdf/1905.12536v4.pdf)][[Code](https://github.com/MIT-SPARK/TEASER-plusplus)]



- 3D-Rotation-Equivariant Quaternion Neural Networks [[ECCV 2020](https://arxiv.org/abs/1911.09040)][[Code](https://github.com/ada-shen/REQNN)]



- Quaternion Equivariant Capsule Networks for 3D Point Clouds [[ECCV 2020](https://arxiv.org/abs/1912.12098)][[Code](https://github.com/tolgabirdal/qecnetworks)]



- Synchronizing Probability Measures on Rotations via Optimal Transport [[CVPR 2020](https://arxiv.org/pdf/2004.00663.pdf)][[Code](https://github.com/MichaelArbel/OT-sync)]



- Quaternion product units for deep learning on 3d rotation groups [[CVPR 2020](https://openaccess.thecvf.com/content_CVPR_2020/papers/Zhang_Quaternion_Product_Units_for_Deep_Learning_on_3D_Rotation_Groups_CVPR_2020_paper.pdf)][[Code](https://github.com/IICNELAB/qpu_code)]



- PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions [[Arxiv 2021](https://arxiv.org/abs/2110.04176)][[Code](https://github.com/elegan23/hypernets)]



- Pose-NDF: Modeling Human Pose Manifolds with Neural Distance Fields [[ECCV 2022](https://arxiv.org/pdf/2207.13807.pdf)][[Code](https://github.com/garvita-tiwari/PoseNDF)]



- Quaternion Orthogonal Transformer for Facial Expression Recognition in the Wild [[ICASSP 2023](https://arxiv.org/abs/2303.07831)][[Code](https://github.com/gabrella/qot)]



- Generalizing Medical Image Representations via Quaternion Wavelet Networks [[Arxiv 2023](https://arxiv.org/pdf/2310.10224.pdf)][[Code](https://github.com/ispamm/QWT)]



- Quaternion Representation Learning for cross-modal matching [[2023](https://www.sciencedirect.com/science/article/abs/pii/S0950705123002551)]



- Delving into Discrete Normalizing Flows on SO($3$) Manifold for Probabilistic Rotation Modeling [[CVPR 2023](https://openaccess.thecvf.com/content/CVPR2023/papers/Liu_Delving_Into_Discrete_Normalizing_Flows_on_SO3_Manifold_for_Probabilistic_CVPR_2023_paper.pdf)][[Code](https://github.com/PKU-EPIC/RotationNormFlow)]



- Fast Quaternion Product Units for Learning Disentangled Representations in SO($3$) [[TPAMI 2023](https://scholar.google.com/citations?view_op=view_citation&hl=zh-CN&user=7gYVOO8AAAAJ&cstart=20&pagesize=80&citation_for_view=7gYVOO8AAAAJ:hzvVvKpMvx4C)][[Code](https://github.com/SuferQin/Fast-QPU)]



- Prompt Learning with Quaternion Networks [[ICLR 2024 Under Review](https://openreview.net/forum?id=dKlxDx2SoS)]



### Geometry Deep Learning

- Geometric Algebra Attention Networks for Small Point Clouds [[Arxiv 2021](https://arxiv.org/abs/2110.02393)][[Code](https://github.com/klarh/flowws-keras-geometry)]

  

- Denoising Diffusion Probabilistic Models on SO($3$) for Rotational Alignment [[ICLR 2022 Workshop](https://openreview.net/forum?id=BY88eBbkpe5)]



- Rigid Body Flows for Sampling Molecular Crystal Structure [[ICML 2023](https://arxiv.org/pdf/2301.11355.pdf)][[Code](https://github.com/noegroup/rigid-flows)]



- E($n$) Equivariant Message Passing Simplicial Networks [[ICML 2023](https://arxiv.org/abs/2305.07100)]



- Clifford Neural Layers for PDE Modeling [[ICLR 2023](https://arxiv.org/abs/2209.04934)][[Code](https://github.com/microsoft/pdearena)]



- Geometric Clifford Algebra Networks [[ICML 2023](https://arxiv.org/pdf/2302.06594.pdf)][[Code](https://github.com/microsoft/pdearena)]



- Geometric Algebra Transformers [[NeurIPS 2023](https://arxiv.org/pdf/2305.18415.pdf)]



- Clifford Group Equivariant Neural Networks [[NeurIPS 2023](https://arxiv.org/pdf/2305.11141v5.pdf)][[Code](https://github.com/DavidRuhe/clifford-group-equivariant-neural-networks)]



- Clifford Group Equivariant Simplicial Message Passing Networks [[ICLR 2024 Under Review](https://openreview.net/forum?id=Zz594UBNOH)]

### Others

- Quaternion Knowledge Graph Embeddings [[NeurIPS 2019](https://proceedings.neurips.cc/paper_files/paper/2019/file/d961e9f236177d65d21100592edb0769-Paper.pdf)] [[Code](https://github.com/cheungdaven/QuatE)]



- Quaternion Recurrent Neural Networks [[ICLR 2019](https://arxiv.org/pdf/1806.04418.pdf)][[Code](https://github.com/mravanelli/pytorch-kaldi)]



- Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks [[ACL 2019](https://arxiv.org/abs/1906.04393)][[Code](https://github.com/vanzytay/QuaternionTransformers)]



- Quaternion Neural Networks for Multi-channel Distant Speech Recognition [[2020](https://arxiv.org/pdf/2005.08566v2.pdf)][[Code](https://github.com/mravanelli/pytorch-kaldi)]



- Quaternion Graph Neural Networks [[ACML 2021](https://proceedings.mlr.press/v157/nguyen21a/nguyen21a.pdf)] [[Code](https://github.com/daiquocnguyen/QGNN)]



- Dual Quaternion Knowledge Graph Embeddings [[AAAI 2021](https://ojs.aaai.org/index.php/AAAI/article/view/16850)][[Code](https://github.com/Lion-ZS/DualE)]



- Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with $1/n$ Parameters [[ICLR 2021 Outstanding](https://arxiv.org/abs/2102.08597)][[Code](https://github.com/demegire/Parameterization-of-Hypercomplex-Multiplications)]



- Quaternion Generative Adversarial Networks [[Arxiv 2021](https://arxiv.org/abs/2104.09630)][[Code](https://github.com/eleGAN23/QGAN)]



- Quaternion Backpropagation [[Arxiv 2022](https://arxiv.org/abs/2212.13082)]



- Quaternion Ordinal Embedding [[IJCA 2022](https://www.ijcai.org/proceedings/2022/0287.pdf)]



- RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion [[ACL 2022](https://aclanthology.org/2022.acl-long.402.pdf)]



- Learning Hierarchy-Aware Quaternion Knowledge Graph Embeddings with Representing Relations as 3D Rotations [[ACL 2022](https://aclanthology.org/2022.coling-1.175.pdf)][[Code](https://github.com/jinfa/hrqe)]



- QuatRE: Relation-Aware Quaternions for Knowledge Graph Embeddings [[WWW 2022](https://arxiv.org/pdf/2009.12517v2.pdf)][[Code](https://github.com/daiquocnguyen/QuatRE)]



- Learning to Rotate: Quaternion Transformer for Complicated Periodical Time Series Forecasting [[KDD 2022](https://dl.acm.org/doi/abs/10.1145/3534678.3539234)][[Code](https://github.com/DAMO-DI-ML/KDD2022-Quatformer)]



- A Comparison of Quaternion Neural Network Backpropagation A Comparison of Quaternion Neural Network Backpropagation Algorithms [[2023](https://scholar.afit.edu/cgi/viewcontent.cgi?article=2303&context=facpub)]



- From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford’s Geometric Algebra and Convexity [[Arxiv 2023](https://web.stanford.edu/~pilanci/papers/geometric_algebra.pdf)]



- TransERR: Translation-based Knowledge Graph Completion via Efficient Relation Rotation [[2023](https://arxiv.org/pdf/2306.14580v1.pdf)][[Code](https://github.com/dellixx/transerr)]



- Graph Quaternion-Valued Attention Networks for Node Classification [[2023](https://dl.acm.org/doi/10.1145/3603781.3603900)]