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Introduction

Recently, hyperbolic spaces have emerged as a promising alternative for processing data with a tree-like structure or power-law distribution, owing to its exponential growth property and tree-likeness prior. Different from the Euclidean space, which expands polynomially, the hyperbolic space grows exponentially which makes it gain natural advantages in abstracting tree-like or scale-free data with hierarchical organizations. In this repository, we categorize papers related to hyperbolic representation learning into different types to facilitate researcher studies and to promote the development of the community. We will keep updating this repository with the latest research developments. We are aware that there will inevitably be some mistakes and oversights, so if you have any questions or suggestions, please feel free to contact us (menglin.yang[@]outlook.com).

1. Latest Update
2. Surveys, Books, Tools and Tutorials
 2.1 Surveys  2.2 Books
 2.3 Tools  2.4 Tutorials
3. Methods and Models
 3.1 Hyperbolic Shallow Model  3.2 Hyperbolic Neural Network
 3.3 Hyperbolic Graph Neural Network  3.4 Hyperbolic Transformer
 3.5 Mixed Curvature Learning  3.6 Semi-Riemannian Learning
 3.7 Hyperbolic Generative Models  3.8 Hyperbolic Operations
 3.9 LLM && Hyperbolic Space  3.10 Analysis
 3.11 Numerical Problems  3.12 Explicitly Tree Embedding
4. Applications
 4.1 Recommender Systems  4.2 Knowledge Graphs
 4.3 Molecular Learning  4.4 Dynamic Graphs
 4.5 Code Representation  4.6 Graph Embedding
 4.7 Word Embedding  4.8 Multi-label Learning
 4.9 Computer Vision  4.10 Natural Language Processing
 4.11 Hyperbolic Metric Learning  4.12 Data-driven Geometry Learning

Hyperbolic Slack Group

Latest Update

🔥 Update Notes (Sept 8, 2024) : add ICML 2024, KDD 2024, WWW 2024, SIGIR 2024, ICDE 2024, CVPR 2024 papers, if I missed your papers, feel free to let me know.

ICML 2024

  1. Hyperbolic Active Learning for Semantic Segmentation under Domain Shift, ICML 2024
    Luca Franco, Paolo Mandica, Konstantinos Kallidromitis, Devin Guillory, Yu-Teng Li, Trevor Darrell, Fabio Galasso

  2. Hyperbolic Geometric Latent Diffusion Model for Graph Generation, ICML 2024
    Xingcheng Fu · Yisen Gao · Yuecen Wei · Qingyun Sun · Hao Peng · Jianxin Li · Xianxian Li

  3. Bringing Motion Taxonomies to Continuous Domains via GPLVM on Hyperbolic manifolds, ICML 2024
    Noémie Jaquier, Leonel Rozo, Miguel González-Duque, Viacheslav Borovitskiy, Tamim Asfour

  4. Hyperbolic Optimizer as a Dynamical System, ICML 2024
    Nico Alvarado, Hans Lobel

KDD 2024

  1. Hypformer: Exploring Efficient Hyperbolic Transformer Fully in Hyperbolic Space, KDD 2024
    Menglin Yang, Harshit Verma, Delvin Ce Zhang, Jiahong Liu, Irwin King, Rex Ying

  2. Predicting Long-term Dynamics of Complex Networks via Identifying Skeleton in Hyperbolic Space, KDD 2024
    Ruikun Li, Huandong Wang, Jinghua Piao, Qingmin Liao, Yong Li

  3. Improving Robustness of Hyperbolic Neural Networks by Lipschitz Analysis, KDD 2024
    Yuekang Li*, Yidan Mao*, Yifei Yang, Dongmian Zou

WWW 2024

  1. An Efficient Automatic Meta-Path Selection for Social Event Detection via Hyperbolic Space, WWW 2024
    Zitai Qiu. Congbo Ma, Jia Wu. Jian Yang

SIGIR 2024

  1. MetaHKG: Meta Hyperbolic Learning for Few-shot Temporal Reasonin, SIGIR 2024
    Ruijie Wang, Yutong Zhang, Jinyang Li, Shengzhong Liu, Dachun Sun, Tianchen Wang, Tianshi Wang, Yizhuo Chen, Denizhan Kara and Tarek Abdelzaher

ICDE 2024

  1. Logical Relation Modeling and Mining in Hyperbolic Space for Recommendation, ICDE 2024
    Yanchao Tan, Hang Lv, Zihao Zhou, Wenzhong Guo, Bo Xiong, Weiming Liu, Chaochao Chen, Shiping Wang, Carl Yang

CVPR 2024

  1. Rethinking Generalizable Face Anti-spoofing via Hierarchical Prototype-guided Distribution Refinement in Hyperbolic Space, CVPR 2024
    Chengyang Hu, Ke-Yue Zhang, Taiping Yao, Shouhong Ding, Lizhuang Ma

  2. Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping, CVPR 2024
    Hyeongjun Kwon, Jinhyun Jang, Jin Kim, Kwonyoung Kim, Kwanghoon Sohn

  3. Hyperbolic Learning with Synthetic Captions for Open-World Detection, CVPR 2024
    Fanjie Kong, Yanbei Chen, Jiarui Cai, Davide Modolo

  4. Hyperbolic Anomaly Detection, CVPR 2024
    Huimin Li, Zhentao Chen, Yunhao Xu, Junlin Hu

  5. Accept the Modality Gap: An Exploration in the Hyperbolic Space, CVPR 2024
    Sameera Ramasinghe Violetta Shevchenko Gil Avraham Ajanthan Thalaiyasingam

  6. G^3-LQ: Marrying Hyperbolic Alignment with Explicit Semantic-Geometric Modeling for 3D Visual Grounding, CVPR 2024
    Yuan Wang, Yali Li, Shengjin Wang

Surveys, Books, Tools, Tutorials

Surveys

  1. Hyperbolic Deep Learning in Computer Vision: A Survey, arxiv 2023
    Pascal Mettes, Mina Ghadimi Atigh, Martin Keller-Ressel, Jeffrey Gu, Serena Yeung

  2. Hyperbolic Graph Neural Networks: A Review of Methods and Application, arxiv 2022. GitHub
    Menglin Yang, Min Zhou, Zhihao Li, Jiahong Liu, Lujia Pan, Hui Xiong, Irwin King

  3. Hyperbolic Deep Neural Networks: A Survey, TPAMI 2022. GitHub
    Wei Peng, Tuomas Varanka, Abdelrahman Mostafa, Henglin Shi, Guoying Zhao

  4. Hyperbolic Geometry in Computer Vision: A Survey, arxiv 2023.
    Pengfei Fang, Mehrtash Harandi, Trung Le, Dinh Phung

Books

  1. An Introduction to Geometric Topology, 2022
    Bruno Martelli

  2. Hyperbolic Geometry, 2020.
    Brice Loustau

  3. Manifolds and Differential Geometry, 2009.
    Jeffrey M. Lee

  4. Introduction to Hyperbolic Geometry, 1995.
    A Ramsay, RD Richtmyer

Tools

  1. Geoopt: Riemannian Adaptive Optimization Methods ICLR 2019
    Max Kochurov and Rasul Karimov and Serge Kozlukov

  2. Curvature Learning Framework
    Alibaba

  3. GraphZoo: A Development Toolkit for Graph Neural Networks with Hyperbolic Geometries WWW 2022
    Anoushka Vyas, Nurendra Choudhary, Mehrdad Khatir, Chandan K. Reddy

  4. HypLL: The Hyperbolic Learning Library, GitHub
    Max van Spengler, Philipp Wirth, Pascal Mettes

Tutorials

  1. Hyperbolic Deep Learning for Computer Vision
    Pascal Mettes, Max van Spengler, Yunhui Guo, Stella Yu

  2. Hyperbolic networks: Theory, Architecture and Applications
    Nurendra Choudhary, Nikhil Rao, Karthik Subbian, Srinivasan H. Sengamedu, Chandan Reddy

  3. Hyperbolic Graph Neural Networks: A Tutorial on Methods and Applications, KDD 2023
    Min Zhou, Menglin Yang, Bo Xiong, Hui Xiong, Irwin King

  4. Hyperbolic Representation Learning for Computer Vision. Tutorial 2022
    Pascal Mettes, Mina Ghadimi Atigh, Martin Keller-Ressel, Jeffrey Gu, Serena Yeung@ECCV2022
    https://hyperbolic-representation-learning.readthedocs.io/en/latest/

  5. Hyperbolic Graph Representation Learning. Tutorial 2022
    Min Zhou, Menglin Yang, Lujia Pan, Irwin King @ ECML-PKDD 2022

  6. Hyperbolic Neural Network. Tutorial 2022
    Nurendra Choudhary, Nikhil Rao, Karthik Subbian, Srinivasan Sengamedu, Chandan Reddy @ KDD 2022

  7. Hyperbolic Hyperbolic embeddings in machine learning and deep learning. Tutorial 2020
    Octavian Ganea 2020.

Methods and Models

Hyperbolic Shallow Model

  1. Poincaré Embeddings for Learning Hierarchical Representations, NeurIPS 2017
    Maximilian Nickel, Douwe Kiela

  2. Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry, ICML 2018
    Maximilian Nickel, Douwe Kiela

  3. Representation Tradeoffs for Hyperbolic Embeddings, ICML 2018
    Frederic Sala, Christopher De Sa, Albert Gu, Christopher Re´

  4. Hyperbolic Entailment Cones for Learning Hierarchical Embeddings, ICML 2018
    Octavian-Eugen Ganea, Gary Bécigneul, Thomas Hofmann

  5. Lorentzian Distance Learning for Hyperbolic Representations, ICML 2019
    Marc T. Law, Renjie Liao, Jake Snell, Richard S. Zemel

  6. Hyperbolic Disk Embeddings for Directed Acyclic Graphs, ICML 2019
    Ryota Suzuki, Ryusuke Takahama, Shun Onoda

  7. The Dark Side of the Hyperbolic Moon, ICLR 2024
    Tao Yu, Toni J.B. Liu, Albert Tseng, Christopher De Sa

  8. Tempered Calculus for ML: Application to Hyperbolic Model Embedding, arxiv 2024
    Richard Nock, Ehsan Amid, Frank Nielsen, Alexander Soen, Manfred K. Warmuth

Hyperbolic Neural Network

  1. Hyperbolic Neural Networks, NeurIPS 2018
    Octavian-Eugen Ganea, Gary Bécigneul, Thomas Hofmann

  2. Hyperbolic Attention Networks, ICLR 2019
    Caglar Gulcehre, Misha Denil, Mateusz Malinowski, Ali Razavi, Razvan Pascanu, Karl Moritz Hermann, Peter Battaglia, Victor Bapst, David Raposo, Adam Santoro, Nando de Freitas

  3. Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders, NeurIPS 2019
    Emile Mathieu, Charline Le Lan, Chris J. Maddison, Ryota Tomioka, Yee Whye Teh

  4. Hyperbolic Neural Network++, ICLR 2021
    Ryohei Shimizu, Yusuke Mukuta, Tatsuya Harada

  5. Fully Hyperbolic Neural Networks, ACL 2022
    Weize Chen, Xu Han, Yankai Lin, Hexu Zhao, Zhiyuan Liu, Peng Li, Maosong Sun, Jie Zhou

  6. Poincaré ResNet, arxiv 2023
    Max van Spengler, Erwin Berkhout, Pascal Mettes

  7. Riemannian Residual Neural Networks, arxiv 2023
    Isay Katsman, Eric Ming Chen, Sidhanth Holalkere, Anna Asch, Aaron Lou, Ser-Nam Lim, Christopher De Sa

  8. Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Design, CVPR 2022
    Xiran Fan, Chun-Hao Yang, Baba C. Vemuri

  9. Fully Hyperbolic Convolutional Neural Networks for Computer Vision, ICLR 2024
    Ahmad Bdeir, Kristian Schwethelm, Niels Landwehr

  10. Hypformer: Exploring Efficient Hyperbolic Transformer Fully in Hyperbolic Space, KDD 2024
    Menglin Yang, Harshit Verma, Delvin Ce Zhang, Jiahong Liu, Irwin King, Rex Ying

Hyperbolic Graph Neural Network

  1. Hyperbolic Graph Convolutional Neural Networks, NeurIPS 2019
    Ines Chami*, Rex Ying*, Christopher Ré, Jure Leskovec

  2. Hyperbolic Graph Neural Network, NeurIPS 2019
    Qi Liu, Maximilian Nickel, Douwe Kiela

  3. Lorentzian Graph Convolutional Networks, WWW 2021
    Yiding Zhang, Xiao Wang, Chuan Shi, Nian Liu, Guojie Song

  4. A Hyperbolic-to-Hyperbolic Graph Convolutional Network, CVPR 2021
    Jindou Dai, Yuwei Wu, Zhi Gao, Yunde Jia

  5. Hyperbolic Graph Attention Network, Transcations on Big Data 2021
    Yiding Zhang, Xiao Wang, Xunqiang Jiang, Chuan Shi, Yanfang Ye

  6. Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders, CVPR 2021
    Jiwoong Park, Junho Cho, Hyung Jin Chang, Jin Young Choi

  7. $\kappa$HGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning, KDD 2023
    Menglin Yang, Min Zhou, Lujia Pan, Irwin King

  8. Residual Hyperbolic Graph Convolution Networks, AAAI 2024
    Yangkai Xue, Jindou Dai, Zhipeng Lu, Yuwei Wu, Yunde Jia

  9. Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach, NeurIPS 2023
    Nurendra Choudhary, Nikhil Rao, Chandan K. Reddy

Hyperbolic Transformer

  1. Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space, KDD 2024
    Menglin Yang, Harshit Verma, Delvin Ce Zhang, Jiahong Liu, Irwin King, Rex Ying

  2. Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning, arxiv 2023
    Sungjun Cho, Seunghyuk Cho, Sungwoo Park, Hankook Lee, Honglak Lee, Moontae Lee

  3. Fully Hyperbolic Neural Networks, ACL 2022
    Weize Chen, Xu Han, Yankai Lin, Hexu Zhao, Zhiyuan Liu, Peng Li, Maosong Sun, Jie Zhou

  4. Hyperbolic Attention Networks, ICLR 2019
    Caglar Gulcehre, Misha Denil, Mateusz Malinowski, Ali Razavi, Razvan Pascanu, Karl Moritz Hermann, Peter Battaglia, Victor Bapst, David Raposo, Adam Santoro, Nando de Freitas

  5. Hyperbolic Neural Network++, ICLR 2021
    Ryohei Shimizu, Yusuke Mukuta, Tatsuya Harada

Theoretical Foundations

  1. Representation Tradeoffs for Hyperbolic Embeddings, ICML 2018
    Christopher De Sa, Albert Gu, Christopher Ré, Frederic Sala

  2. Generalization Error Bound for Hyperbolic Ordinal Embedding, ICML 2021
    Atsushi Suzuki, Atsushi Nitanda, Jing Wang, Linchuan Xu, Marc Cavazza, Kenji Yamanishi

  3. Generalization Bounds for Graph Embedding Using Negative Sampling: Linear vs Hyperbolic, NeurIPS 2021
    Atsushi Suzuki, Atsushi Nitanda, jing wang, Linchuan Xu, Kenji Yamanishi, Marc Cavazza

Analysis

  1. The Numerical Stability of Hyperbolic Representation Learning, ICML 2023
    Gal Mishne, Zhengchao Wan, Yusu Wang, Sheng Yang

  2. Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coin WACV
    Gabriel Moreira, Manuel Marques, João Paulo Costeira, Alexander Hauptmann

  3. Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems KDD 2021
    Sixiao Zhang, Hongxu Chen, Xiao Ming, Lizhen Cui, Hongzhi Yin, Guandong Xu

  4. Improving Robustness of Hyperbolic Neural Networks by Lipschitz Analysis, KDD 2024
    Yuekang Li, Yidan Mao, Yifei Yang, Dongmian Zou

  5. Hyperbolicity Measures “Democracy” in Real-World Networks, Phys. Rev. E 2015 Michele Borassi, Alessandro Chessa, and Guido Caldarelli

Numerical Problems

  1. The Numerical Stability of Hyperbolic Representation Learning, ICML 2023

  2. Representation Tradeoffs for Hyperbolic Embeddings, ICML 2018
    Frederic Sala, Christopher De Sa, Albert Gu, Christopher Re´

Explicitly Tree Embedding

  1. Fast Hyperboloid Decision Tree Algorithms, ICLR 2024

  2. Fitting trees to $\ell_1$-hyperbolic distances, NeurIPS 2023
    Joon-Hyeok Yim, Anna Gilbert

Mixed Curvature Learning

  1. Learning mixed-curvature representations in product spaces, ICLR 2019
    Albert Gu, Frederic Sala, Beliz Gunel, Christopher Ré

  2. Mixed-curvature variational autoencoders, ICLR 2020
    Skopek, Ondrej, Octavian-Eugen Ganea, and Gary Bécigneul

  3. Constant Curvature Graph Convolutional Networks, ICML 2020
    Gregor Bachmann, Gary Bécigneul, Octavian-Eugen Ganea

  4. Mixed-curvature multi-relational graph neural network for knowledge graph completion, WWW 2021
    Wang, Shen, Xiaokai Wei, Cicero Nogueira Nogueira dos Santos, Zhiguo Wang, Ramesh Nallapati, Andrew Arnold, Bing Xiang, Philip S. Yu, and Isabel F. Cruz.

  5. A Self-supervised Mixed-curvature Graph Neural Network, AAAI 2022
    Li Sun, Zhongbao Zhang, Junda Ye, Hao Peng, Jiawei Zhang, Sen Su, Philip S. Yu

  6. Enhancing Hyperbolic Graph Embeddings via Contrastive Learning, NeurIPS 2021 SSL Workshop
    Jiahong Liu, Menglin Yang, Min Zhou, Shanshan Feng, Philippe Fournier-Viger

  7. Geometry Interaction Learning, NeurIPS 2020
    Shichao Zhu, Shirui Pan, Chuan Zhou, Jia Wu, Yanan Cao, Bin Wang

  8. FMGNN: Fused Manifold Graph Neural Network, TKDD 2023
    Cheng Deng, Fan Xu, Jiaxing Ding, Luoyi Fu, Weinan Zhang, Xinbing Wang

  9. Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning, arxiv 2023
    Sungjun Cho, Seunghyuk Cho, Sungwoo Park, Hankook Lee, Honglak Lee, Moontae Lee

  10. Matrix Manifold Neural Networks++, ICLR 2024

Semi-Riemannian Learning

  1. Directed Graph Embeddings in Pseudo-Riemannian Manifolds, ICML 2021
    Aaron Sim, Maciej Wiatrak, Angus Brayne, Páidí Creed, Saee Paliwal

  2. Semi-Riemannian Graph Convolutional Networks, NeurIPS 2022
    Bo Xiong, Shichao Zhu, Nico Potyka, Shirui Pan, Chuan Zhou, Steffen Staab

  3. Ultrahyperbolic Neural Networks, NeurIPS 2021
    Marc T Law

  4. Ultrahyperbolic Representation Learning, NeurIPS 2020
    Marc T. Law, Jos Stam

Hyperbolic Generative Models

  1. Latent Variable Modelling with Hyperbolic Normalizing Flows, ICML 2020
    Avishek Joey Bose, Ariella Smofsky, Renjie Liao, Prakash Panangaden, William L. Hamilton

  2. Hyperbolic Graph Diffusion Model, AAAI 2024
    Lingfeng Wen, Xuan Tang, Mingjie Ouyang, Xiangxiang Shen, Jian Yang, Daxin Zhu, Mingsong Chen, Xian Wei

  3. Hyperbolic VAE via Latent Gaussian Distributions, NeurIPS 2023
    Seunghyuk Cho, Juyong Lee, Dongwoo Kim

  4. Lorentzian fully hyperbolic generative adversarial network, arxiv 2022
    Eric Qu, Dongmian Zou

  5. Hyperbolic VAE via Latent Gaussian Distributions, NeurIPS 2023
    Seunghyuk Cho, Juyong Lee, Dongwoo Kim

  6. Hyperbolic Geometric Latent Diffusion Model for Graph Generation, ICML 2024
    Xingcheng Fu, Yisen Gao, Yuecen Wei, Qingyun Sun, Hao Peng, Jianxin Li, Xianxian Li

Hyperbolic Operations

  1. Mean Computation and BatchNorm
    Differentiating through the Fréchet Mean, ICML 2020
    Aaron Lou, Isay Katsman, Qingxuan Jiang, Serge Belongie, Ser-Nam Lim, Christopher De Sa

  2. Sampling
    Wrapped Distributions on homogeneous Riemannian manifolds, 2022
    Fernando Galaz-Garcia, Marios Papamichalis, Kathryn Turnbull, Simon Lunagomez, Edoardo Airoldi

  3. MixUp and Data Augmentation
    HYPMIX: Hyperbolic Interpolative Data Augmentation, EMNLP 2021
    Ramit Sawhney, Megh Thakkar, Shivam Agarwal, Di Jin, Diyi Yang, Lucie Flek

  4. PCA
    HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections, ICML 2021
    Ines Chami*, Albert Gu*, Dat Nguyen, Christopher Ré*

  5. TSNE
    Accelerating hyperbolic t-SNE, arxiv 2024
    Martin Skrodzki, Hunter van Geffen, Nicolas F. Chaves-de-Plaza, Thomas Höllt, Elmar Eisemann, Klaus Hildebrandt

LLM and Hyperbolic Space

  1. Language Models as Hierarchy Encoders, arxiv 2024
    Yuan He, Zhangdie Yuan, Jiaoyan Chen, Ian Horrocks

  2. HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generation, arxiv 2024
    Zhiying Leng, Tolga Birdal, Xiaohui Liang, Federico Tombari

  3. LLMs are Good Action Recognizers, arxiv 2024
    Haoxuan Qu, Yujun Cai, Jun Liu

Applications

Recommender Systems

  1. HICF: Hyperbolic Informative Collaborative Filtering, KDD 2022
    Menglin Yang, Zhihao Li, Min Zhou, Jiahong Liu, Irwin King

  2. HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization, WWW 2022
    Menglin Yang, Min Zhou, Jiahong Liu, Defu Lian, Irwin King

  3. HGCF: Hyperbolic Graph Convolution Networks for Collaborative Filtering, WWW 2021
    Jianing Sun,Zhaoyue Cheng,Saba Zuberi,Felipe Perez,Maksims Volkovs

  4. HAKG: Hierarchy-Aware Knowledge Gated Network for Recommendation, SIGIR 2022
    Yuntao Du, Xinjun Zhu, Lu Chen, Baihua Zheng, and Yunjun Gao

  5. Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation, WSDM 2022
    Yankai Chen, Menglin Yang, Yingxue Zhang, Mengchen Zhao, Ziqiao Meng, Jianye Hao, Irwin King

  6. Geometric Inductive Matrix Completion: A Hyperbolic Approach with Unified Message Passing, WSDM 2022
    Chengkun Zhang , Hongxu Chen , Sixiao Zhang , Guandong Xu , Junbin Gao

  7. Hypersorec: Exploiting hyperbolic user and item representations with multiple aspects for social-aware recommendation, TOIS 2021
    Hao Wang, Defu Lian, Hanghang Tong, Qi Liu, Zhenya Huang and Enhong Chen

  8. Knowledge Based Hyperbolic Propagation, SIGIR short paper 2021
    Chang-You Tai, Chien-Kun Huang, Liang-Ying Huang, Lun-Wei Ku

  9. HSR: hyperbolic social recommender, Information Sciences 2022
    Anchen Li, Bo Yang

  10. Enhancing Hierarchy-Aware Graph Networks with Deep Dual Clustering for Session-based Recommendation, WWW 2023
    Jiajie Su, Chaochao Chen, Weiming Liu, Fei Wu, Xiaolin Zheng, Haoming Lyu

  11. HCGR: Hyperbolic Contrastive Graph Representation Learning for Session-based Recommendation, arxiv 2021
    Naicheng Guo, Xiaolei Liu, Shaoshuai Li, Qiongxu Ma, Yunan Zhao, Bing Han, Lin Zheng, Kaixin Gao, Xiaobo Guo

  12. Hyperbolic Hypergraphs for Sequential Recommendation, CIKM 2021
    Yicong Li, Hongxu Chen, Xiangguo Sun, Zhenchao Sun, Lin Li, Lizhen Cui, Philip S. Yu, Guandong Xu

  13. HGCC: Enhancing Hyperbolic Graph Convolution Networks on Heterogeneous Collaborative Graph for Recommendation, arxiv 2022
    Lu Zhang, Ning Wu

  14. Lorentz Equivariant Model for Knowledge-Enhanced Collaborative Filtering, arxiv 2023
    Bosong Huang, Weihao Yu, Ruzhong Xie, Jing Xiao, Jin Huang

  15. Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems KDD 2021
    Sixiao Zhang, Hongxu Chen, Xiao Ming, Lizhen Cui, Hongzhi Yin, Guandong Xu

  16. HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems, WSDM 2020
    Lucas Vinh Tran, Yi Tay, Shuai Zhang, Gao Cong, Xiaoli Li

  17. Learning Feature Interactions with Lorentzian Factorization Machine, AAAI 2020
    Canran Xu, Ming Wu

  18. Scalable Hyperbolic Recommender Systems, WSDM 2020
    Benjamin Paul Chamberlain, Stephen R. Hardwick, David R. Wardrope, Fabon Dzogang, Fabio Daolio, Saúl Vargas

  19. A hyperbolic metric embedding approach for next-poi recommendation, SIGIR 2020
    Shanshan Feng , Lucas Vinh Tran , Gao Cong , Lisi Chen , Jing Li , Fan Li

  20. Node2LV: Squared Lorentzian Representations for Node Proximity， ICDE 2021
    Shanshan Feng, Lisi Chen, Kaiqi Zhao, Wei Wei, Fan Li, Shuo Shang

  21. Hyperbolic Neural Collaborative Recommender, TKDE 2022
    Anchen Li; Bo Yang; Huan Huo; Hongxu Chen; Guandong Xu; Zhen Wang

  22. Enhancing Recommendation with Automated Tag Taxonomy Construction in Hyperbolic Space, ICDE 2022
    Yanchao Tan; Carl Yang; Xiangyu Wei; Chaochao Chen; Longfei Li; Xiaolin Zheng

  23. Hyperbolic Personalized Tag Recommendation, DASFAA 2022
    Weibin Zhao, Aoran Zhang, Lin Shang, Yonghong Yu, Li Zhang, Can Wang, Jiajun Chen & Hongzhi Yin

Knowledge Graphs

  1. Low-Dimensional Hyperbolic Knowledge Graph Embeddings, ACL 2019
    Ines Chami, Adva Wolf, Da-Cheng Juan, Frederic Sala, Sujith Ravi, Christopher Ré

  2. Multi-relational Poincaré Graph Embeddings, NeurIPS 2019
    Ivana Balažević, Carl Allen, Timothy Hospedales

  3. Knowledge Association with Hyperbolic Knowledge Graph Embeddings, EMNLP 2020
    Zequn Sun, Muhao Chen, Wei Hu, Chengming Wang, Jian Dai, Wei Zhang

  4. Knowledge Graph Representation via Hierarchical Hyperbolic Neural Graph Embedding, IEEE Big Data
    Shen Wang, Xiaokai Wei, Cicero Nogueira Dos Santos, Zhiguo Wang, Ramesh Nallapati, Andrew Arnold, Philip S. Yu

  5. Mixed-Curvature Multi-relational Graph Neural Network for Knowledge Graph Completion, WWW 2021
    Shen Wang , Xiaokai Wei , Cicero Nogueira Nogueira dos Santos , Zhiguo Wang , Ramesh Nallapati , Andrew Arnold , Bing Xiang , Philip S. Yu , Isabel F. Cruz

  6. Geometry Interaction Knowledge Graph Embeddings for KG embedding, AAAI 2022
    Zongsheng Cao, Qianqian Xu, Zhiyong Yang, Xiaochun Cao, Qingming Huang

  7. Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones， NeurIPS 2021
    Yushi Bai, Rex Ying, Hongyu Ren, Jure Leskovec

  8. Hyperbolic Temporal Knowledge Graph Embeddings with Relational and Time Curvatures, ACL 2021
    Sebastien Montella, Lina Rojas-Barahona, Johannes Heinecke

  9. Self-supervised hyperboloid representations from logical queries over knowledge graphs, WWW 2021
    Nurendra Choudhary, Nikhil Rao, Sumeet Katariya, Karthik Subbian, Chandan K. Reddy

  10. HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion, arxiv
    Prodromos Kolyvakis, Alexandros Kalousis, Dimitris Kiritsis

  11. Hyperbolic Hierarchy-Aware Knowledge Graph Embedding for Link Prediction. EMNLP findings 2021
    Zhe Pan, Peng Wang

  12. FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion,arxiv 2023
    Wentao Shi, Junkang Wu, Xuezhi Cao, Jiawei Chen, Wenqiang Lei, Wei Wu, Xiangnan He

  13. Mixed Geometry Message and Trainable Convolutional Attention Network for Knowledge Graph Completion, AAAI 2024
    Bin Shang, Yinliang Zhao, Jun Liu, Di Wang

Molecular Learning

  1. Semi-supervised hierarchical drug embedding inhyperbolic space, J. Chem. Inf. Model 2020
    Ke Yu*, Shyam Visweswaran*, and Kayhan Batmanghelich

  2. HiG2Vec: hierarchical representations of Gene Ontology and genes in the Poincaré ball, Bioinformatics, 2021
    Jaesik Kim, Dokyoon Kim, Kyung-Ah Sohn

  3. Hyperbolic relational graph convolution networks plus: a simple but highly efficient QSAR-modeling method, Briefings in Bioinformatics 2021
    Zhenxing Wu, Dejun Jiang, Chang-Yu Hsieh, Guangyong Chen, Ben Liao, Dongsheng Cao, Tingjun Hou

  4. Contrastive Poincaré Maps for single-cell data analysis, ICLR workshop 2024
    Nithya Bhasker, Hattie Chung, Louis Boucherie, Vladislav Kim, Stefanie Speidel, Melanie Weber

  5. Hyperbolic Graph Diffusion Model, AAAI 2024
    Lingfeng Wen, Xuan Tang, Mingjie Ouyang, Xiangxiang Shen, Jian Yang, Daxin Zhu, Mingsong Chen, Xian Wei

  6. Hyperbolic Geometric Latent Diffusion Model for Graph Generation, ICML 2024
    Xingcheng Fu, Yisen Gao, Yuecen Wei, Qingyun Sun, Hao Peng, Jianxin Li, Xianxian Li

  7. Deep generative model embedding of single-cell RNA-Seq profiles on hyperspheres and hyperbolic spaces, Natur Communications 2021
    Jiarui Ding, Aviv Regev

Dynamic Graphs

  1. Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space, KDD 2021
    Menglin Yang, Min Zhou, Marcus Kalander, Zengfeng Huang, Irwin King

  2. Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs, AAAI 2021
    Li Sun, Zhongbao Zhang, Jiawei Zhang, Feiyang Wang, Hao Peng, Sen Su, Philip S. Yu

  3. Exploring the Scale-Free Nature of Stock Markets: Hyperbolic Graph Learning for Algorithmic Trading, WWW 2021
    Ramit Sawhney, Shivam Agarwal, Arnav Wadhwa , Rajiv Shah

Code Representation

  1. Hyperbolic Representations of Source Code AAAI 2022
    Raiyan Khan, Thanh V. Nguyen, Sengamedu H. Srinivasan

Graph Embeddings

  1. SINCERE: Sequential Interaction Networks representation learning on Co-Evolving RiEmannian manifolds, WWW 2023
    Junda Ye, Zhongbao Zhang, Li Sun, Yang Yan, Feiyang Wang, Fuxin Ren

  2. Hyperbolic Heterogeneous Information Network Embedding, AAAI 2020
    Xiao Wang, Yiding Zhang, Chuan Shi

  3. Embedding Heterogeneous Information Network in Hyperbolic Spaces, TKDD 2022
    Yiding Zhang, Xiao Wang, Nian Liu, Chuan Shi

  4. Hyperbolic Disk Embeddings for Directed Acyclic Graphs，ICML 2019
    Ryota Suzuki, Ryusuke Takahama, Shun Onoda

  5. A hyperbolic Embedding Model for Directed Networks
    Zongning Wu, Zengru Di, Ying Fan (this paper includes many errors)

  6. Hyperbolic Node Embedding for Signed Networks, Neurcomputing 2021
    Wenzhuo Song, Hongxu Chen, Xueyan Liu, Hongzhe Jiang, Shengsheng Wang

  7. HEAT: Hyperbolic Embedding of Attributed Networks, IDEAL 2020
    David McDonald, Shan He

  8. Hyperbolic Multiplex Network Embedding with Maps of Random Walk
    Peiyuan Sun

Word Embeddings

  1. Poincare Glove: Hyperbolic Word Embeddings, ICLR 2019
    Alexandru Tifrea and Gary Becigneul and Octavian-Eugen Gane

  2. Skip-gram word embeddings in hyperbolic space, ACL 2018
    Matthias Leimeister, Benjamin J. Wilson

  3. Embedding text in hyperbolic spaces, ACL 2018
    Bhuwan Dhingra, Christopher J. Shallue, Mohammad Norouzi, Andrew M. Dai, George E. Dahl

  4. Hyperbolic entailment cones for learning hierarchical embeddings, ICML 2018
    Octavian-Eugen Ganea, Gary Bécigneul, Thomas Hofmann

  5. Low-rank approximations of hyperbolic embeddings
    Pratik Jawanpuria, Mayank Meghwanshi, Bamdev Mishra

  6. Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings
    Matt Le, Stephen Roller, Laetitia Papaxanthos, Douwe Kiela, Maximilian Nickel

Multi-label Learning

  1. Hyperbolic interaction model for hierarchical multi-label classification, AAAI 2021
    Boli Chen, Xin Huang, Lin Xiao, Zixin Cai, Liping Jing

  2. Hyperbolic Capsule Networks for Multi-Label Classification, ACL 2020
    Boli Chen, Xin Huang, Lin Xiao, Liping Jing

  3. Joint Learning of Hyperbolic Label Embeddings for Hierarchical Multi-label Classification, EACL 2021
    Soumya Chatterjee, Ayush Maheshwari, Ganesh Ramakrishnan, Saketha Nath Jagaralpudi

  4. Hyperbolic Embeddings for Hierarchical Multi-label Classification, 2020
    Tomaž StepišnikEmail, Dragi Kocev

  5. A Fully Hyperbolic Neural Model for Hierarchical Multi-Class Classification, EMNLP findings
    Federico López, Michael Strube

  6. Hyperbolic Relevance Matching for Neural Keyphrase Extraction for key phrases matching, Naacl 2022
    Mingyang Song, Yi Feng, Liping Jing

  7. Cross-lingual Word Embeddings in Hyperbolic Space for word embedding, arxiv 2022 Chandni Saxena, Mudit Chaudhary, Helen Meng

  8. Hyperbolic Space with Hierarchical Margin Boosts Fine-Grained Learning from Coarse Labels, NeurIPS, 2023
    Shu-Lin Xu, Yifan Sun, Faen Zhang, Anqi Xu, Xiu-Shen Wei, Yi Yang

Computer Vision

  1. Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping Hyeongjun Kwon, Jinhyun Jang, Jin Kim, Kwonyoung Kim, Kwanghoon Sohn

  2. HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generation, arxiv 2024
    Zhiying Leng, Tolga Birdal, Xiaohui Liang, Federico Tombari

  3. Hyperbolic Image Embedding, CVPR 2020
    Valentin Khrulkov, Leyla Mirvakhabova, Evgeniya Ustinova, Ivan Oseledets, Victor Lempitsky

  4. Hyperbolic Image Segmentation, CVPR 2022
    Mina GhadimiAtigh, Julian Schoep, Erman Acar, Nanne van Noord, Pascal Mettes

  5. Hyperbolic Vision Transformers: Combining Improvements in Metric Learning,CVPR 2022
    Aleksandr Ermolov, Leyla Mirvakhabova, Valentin Khrulkov, Nicu Sebe, Ivan Oseledets

  6. Hyperbolic Image-Text Representations, ICML 2023
    Karan Desai, Maximilian Nickel, Tanmay Rajpurohit, Justin Johnson, Ramakrishna Vedantam

  7. Hyperbolic Busemann Learning with Ideal Prototypes, NeurIPS 2021 Mina Ghadimi Atigh, Martin Keller-Ressel, Pascal Mettes

  8. Rethinking the compositionality of point clouds through regularization in the hyperbolic space (NeurIPS 2022)
    Antonio Montanaro, Diego Valsesia, Enrico Magli

  9. HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusion, CVPR 2023
    Sijie Wang, Qiyu Kang, Rui She, Wei Wang, Kai Zhao, Yang Song, Wee Peng Tay

  10. Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers, CVPR 2022
    Yunhui Guo, Xudong Wang, Yubei Chen, Stella X. Yu

  11. Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations NeurIPS 2021
    Joy Hsu, Jeffrey Gu, Gong-Her Wu, Wah Chiu, Serena Yeung

  12. Learning Hyperbolic Representations of Topological Features ICLR 2021
    Panagiotis Kyriakis, Iordanis Fostiropoulos, Paul Bogdan

  13. Curvature Generation in Curved Spaces for Few-Shot Learning, ICCV 2021
    Zhi* Gao, Yuwei Wu*, Yunde Jia, Mehrtash Harandi

  14. Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervision, CVPR 2021
    Zhenzhen Weng, Mehmet Giray Ogut, Shai Limonchik, Serena Yeung

  15. Searching for Actions on the Hyperbole, CVPR 2020
    Teng Long, Pascal Mettes, Heng Tao Shen, Cees Snoek

  16. Mix Dimension in Poincaré Geometry for 3D Skeleton-based Action Recognition, ACM MM 2020
    Wei Peng, Jingang Shi, Zhaoqiang Xia, Guoying Zhao

  17. Meta Hyperbolic Networks for Zero-Shot Learning, Neurocomputing
    Yan Xu, Lifu Mu, ZhongJi, Xiyao Liu, JungongHan

  18. Poincaré ResNet, arxiv 2023
    Max van Spengler, Erwin Berkhout, Pascal Mettes

Robot Design

  1. Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design, arxiv 2023
    Heng Dong, Junyu Zhang, Chongjie Zhang

Natural Language Processing

  1. HISum: Hyperbolic Interaction Model for Extractive Multi-Document Summarization, WWW 2023
    Mingyang Song, Yi Feng, Liping Jing

  2. Public Wisdom Matters! Discourse-Aware Hyperbolic Fourier Co-Attention for Social-Text Classification, NeurIPS 2022 Oral (Spotlight)
    K Grover, SM Angara, M Akhtar, T Chakraborty

  3. Probing BERT in Hyperbolic Spaces. ICLR 2021
    Boli Chen, Yao Fu, Guangwei Xu, Pengjun Xie, Chuanqi Tan, Mosha Chen, Liping Jing

  4. Medical Triage Chatbot Diagnosis Improvement via Multi-relational Hyperbolic Graph Neural Network. SIGIR short paper 2021
    Zheng Liu , Xiaohan Li , Zeyu You , Tao Yang , Wei Fan , Philip Yu

  5. ANTHEM: Attentive Hyperbolic Entity Model for Product Search. WSDM 2022
    Nurendra Choudhary , Nikhil Rao , Sumeet Katariya , Karthik Subbian , Chandan K. Reddy

  6. Leveraging Hierarchical Representations for Preserving Privacy and Utility in Text, ICDM 2019 Oluwaseyi Feyisetan, Tom Diethe, Thomas Drake

  7. Hyperbolic Representation Learning for Fast and Efficient Neural Question Answering, WSDM 2018 Yi Tay, Luu Anh Tuan, Siu Cheung Hui

Hyperbolic Metric Learning

  1. Contrastive Multi-view Hyperbolic Hierarchical Clustering for clustering, IJCAI 2022
    Fangfei Lin, Bing Bai, Kun Bai, Yazhou Ren, Peng Zhao, Zenglin Xu

  2. Hyperbolic Busemann Learning with Ideal Prototypes, NeurIPS 2021
    Mina Ghadimi Atigh, Martin Keller-Ressel, Pascal Mettes

  3. Unsupervised Hyperbolic Metric Learning, CVPR 2021
    Jiexi Yan, Lei Luo, Cheng Deng, Heng Huang

  4. Hyperbolic Contrastive Learning, arxiv
    Yun Yue, Fangzhou Lin, Kazunori D Yamada, Ziming Zhang

  5. A Quadtree for Hyperbolic Space, arxiv 2023
    Sándor Kisfaludi-Bak, Geert van Wordragen

  6. Alignment and Outer Shell Isotropy for Hyperbolic Graph Contrastive Learning, arxiv 2023
    Yifei Zhang, Hao Zhu, Jiahong Liu, Piotr Koniusz, Irwin King

Data-driven Geometry Learning

  1. Dimensionality Selection for Hyperbolic Embeddings using Decomposed Normalized Maximum Likelihood Code-Length, arxiv 2023
    Ryo Yuki, Yuichi Ike, Kenji Yamanishi

  2. CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data for embedding visualization, CVPR 2022
    Yunhui Guo, Haoran Guo, Stella Yu

  3. Wrapped Distributions on homogeneous Riemannian manifolds for hyperbolic sampling, arxiv 2022
    Fernando Galaz-Garcia, Marios Papamichalis, Kathryn Turnbull, Simon Lunagomez, Edoardo Airoldi

  4. HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering for clustering, KDD 2022
    Eli Chien, Puoya Tabaghi, Olgica Milenkovic

  5. Hyperbolic Feature Augmentation via Distribution Estimation and Infinite Sampling on Manifolds NeurIPS 2022
    Zhi Gao, Yuwei Wu, Yunde Jia, Mehrtash Harandi

  6. Exploring Data Geometry for Continual Learning CVPR 2023
    Zhi Gao, Chen Xu, Feng Li, Yunde Jia, Mehrtash Harandi, Yuwei Wu

  7. Curvature-Adaptive Meta-Learning for Fast Adaptation to Manifold Data, TPAMI
    Zhi Gao, Yuwei Wu, Mehrtash Harandi, and Yunde Jia

Citation

To cite this repository:

@misc{hyperbolic-repo,
  author = {Menglin Yang, Min Zhou},
  title = {{Hyperbolic Representation and Deep Learning: A Comprehensive Collection}},
  howpublished = {\url{https://github.com/marlin-codes/Awesome-Hyperbolic-Representation-and-Deep-Learning}},
  year = 2024,
  month = September
}