awesome-hypercomplex-neural-networks

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

Contents

• Resources
  • Introductory Papers
  • Introductory Videos
  • Others
• Papers
  • Survey
  • Computer Vision and Graphics
  • Geometry Deep Learning
  • Others

Resources

Introductory Papers

• Introduction to Quaternions (Chinese Version) [Github][Book]

Introductory Videos

• Visualizing Quaternions (4d Numbers) with Stereographic Projection [3blue1brown]

• Quaternions and 3d Rotation, Explained Interactively [3blue1brown]

Others

• Visualizing Quaternions [Website]

• Quaternions in Numpy [Github]

• PyTorch Implementations of Various Quaternion Neural Networks (QNN) [Github]

Papers

Survey

• Quaternion Neural Networks: State-of-the-Art and Research Challenges [2020]

• A Survey of Quaternion Neural Networks [2020]

Computer Vision and Graphics

• Quaternion Convolutional Neural Networks [ECCV 2018][Code]

• A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers [ICCV 2019][Code]

• 3D-Rotation-Equivariant Quaternion Neural Networks [ECCV 2020][Code]

• Quaternion Equivariant Capsule Networks for 3D Point Clouds [ECCV 2020][Code]

• Synchronizing Probability Measures on Rotations via Optimal Transport [CVPR 2020][Code]

• Quaternion product units for deep learning on 3d rotation groups [CVPR 2020][Code]

• PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions [Arxiv 2021][Code]

• Pose-NDF: Modeling Human Pose Manifolds with Neural Distance Fields [ECCV 2022][Code]

• Quaternion Orthogonal Transformer for Facial Expression Recognition in the Wild [ICASSP 2023][Code]

• Generalizing Medical Image Representations via Quaternion Wavelet Networks [Arxiv 2023][Code]

• Quaternion Representation Learning for cross-modal matching [2023]

• Delving into Discrete Normalizing Flows on SO($3$) Manifold for Probabilistic Rotation Modeling [CVPR 2023][Code]

• Fast Quaternion Product Units for Learning Disentangled Representations in SO($3$) [TPAMI 2023][Code]

• Prompt Learning with Quaternion Networks [ICLR 2024 Under Review]

Geometry Deep Learning

• Geometric Algebra Attention Networks for Small Point Clouds [Arxiv 2021][Code]

• Denoising Diffusion Probabilistic Models on SO($3$) for Rotational Alignment [ICLR 2022 Workshop]

• Rigid Body Flows for Sampling Molecular Crystal Structure [ICML 2023][Code]

• E($n$) Equivariant Message Passing Simplicial Networks [ICML 2023]

• Clifford Neural Layers for PDE Modeling [ICLR 2023][Code]

• Geometric Clifford Algebra Networks [ICML 2023][Code]

• Geometric Algebra Transformers [NeurIPS 2023]

• Clifford Group Equivariant Neural Networks [NeurIPS 2023][Code]

• Clifford Group Equivariant Simplicial Message Passing Networks [ICLR 2024 Under Review]

Others

• Quaternion Knowledge Graph Embeddings [NeurIPS 2019] [Code]

• Quaternion Recurrent Neural Networks [ICLR 2019][Code]

• Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks [ACL 2019][Code]

• Quaternion Neural Networks for Multi-channel Distant Speech Recognition [2020][Code]

• Quaternion Graph Neural Networks [ACML 2021] [Code]

• Dual Quaternion Knowledge Graph Embeddings [AAAI 2021][Code]

• Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with $1/n$ Parameters [ICLR 2021 Outstanding][Code]

• Quaternion Generative Adversarial Networks [Arxiv 2021][Code]

• Quaternion Backpropagation [Arxiv 2022]

• Quaternion Ordinal Embedding [IJCA 2022]

• RotateQVS: Representing Temporal Information as Rotations in Quaternion Vector Space for Temporal Knowledge Graph Completion [ACL 2022]

• Learning Hierarchy-Aware Quaternion Knowledge Graph Embeddings with Representing Relations as 3D Rotations [ACL 2022][Code]

• QuatRE: Relation-Aware Quaternions for Knowledge Graph Embeddings [WWW 2022][Code]

• Learning to Rotate: Quaternion Transformer for Complicated Periodical Time Series Forecasting [KDD 2022][Code]

• A Comparison of Quaternion Neural Network Backpropagation A Comparison of Quaternion Neural Network Backpropagation Algorithms [2023]

• From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford’s Geometric Algebra and Convexity [Arxiv 2023]

• TransERR: Translation-based Knowledge Graph Completion via Efficient Relation Rotation [2023][Code]

• Graph Quaternion-Valued Attention Networks for Node Classification [2023]