Awesome Hyperbolic Graph Neural Network Papers: Methods and Applications (Keep update)

Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks https://github.com/marlin-codes/HGNNs , unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. For reader convenience, we also list the non-HGNN research. If there are some typos or you have any question, just feel free to contact us ([email protected], [email protected]).

Hyperbolic Manifolds

!!! New added (update on July 19)

HICF: Hyperbolic Informative Collaborative Filtering, KDD 2022

HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering KDD 2022

Wrapped Distributions on homogeneous Riemannian manifolds for hyperbolic sampling

Contrastive Multi-view Hyperbolic Hierarchical Clustering for clustering, IJCAI 2022

Hyperbolic Relevance Matching for Neural Keyphrase Extraction for key phrases matching

Cross-lingual Word Embeddings in Hyperbolic Space for word embedding

Geometry Interaction Knowledge Graph Embeddings for KG, AAAI 2022

1. Survey and Book

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

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

Hyperbolic Geometry, Arxiv 2020 TextBook.
Brice Loustau

2. Hyperbolic Models

2.1 Hyperbolic Shallow Model

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

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

2.2 Hyperbolic Neural Network (HNN)

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

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

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

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

2.3 Hyperbolic Graph Neural Network (HGNN)

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

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

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

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

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

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

2.4 Mixed/Multiple Curvature Space NN/GNN

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

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

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

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

2.5 UnltraHyperblic/Semi-Riemannian NN/GNN

Ultrahyperbolic Neural Networks, NeurIPS 2021
Marc T Law

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

Semi-Riemannian Graph Convolutional Networks, arxiv 2021
Bo Xiong, Shichao Zhu, Nico Potyka, Shirui Pan, Chuan Zhou, Steffen Staab

4. Applications

4.1 Hyperbolic Models for Recommender System (RS)

4.1.1 Hyperbolic GNN for RS

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

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

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

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

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

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

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

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

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

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

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

4.1.2 Hyperbolic Shallow/NN models for RS

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

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

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

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

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

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

4.2 Hyperbolic Moldes for Knowledge Graph (KG)

4.2.1 Hyperbolic GNN for KG

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

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

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

4.2.2 Hyperbolic Shallow/NN models for KG

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

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

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

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

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

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

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

4.3 Hyperbolic models for Molecular

4.3.1 Hyperbolic GNN for Molecular

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

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

4.3.2 Hyperbolic Shallow/NN models for Molecular

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

4.4 Hyperbolic Models for Dynamic Graph

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

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

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

4.5 Hyperbolic Models for Code Representation

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

Note: The following research works not limited to HGNNs but higly related to hyperbolic geometry.

5 Hyperbolic Embeddings

5.1 Hyperbolic Geometry for Heterogeneous Network Embedding

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

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

5.2 Hyperbolic Geometry for Directed Graph Embedding

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

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

5.3 Hyperbolic Geometry for Signed Graph Embedding

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

5.4 Hyperbolic Geometry for Attributed Graph Embedding

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

5.5 Hyperbolic Geometry for Word Embedding

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

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

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

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

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

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

Hyperbolic Multiplex Network Embedding with Maps of Random Walk
Peiyuan Sun

5.6 Hyperbolic Geometry for Multi-label Classification

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

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

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

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

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

6 Hyperbolic Baisc Operations

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

7 Hyperbolic Geometry for Computer Vision

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

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

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

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

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

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

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

8 Hyperbolic Geometry for Natural Language Process

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

9 Hyperbolic Metric Learning

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

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

Tools

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

https://github.com/AnoushkaVyas/GraphZoo

TBA

sampling Wrapped Distributions on homogeneous Riemannian manifolds

data argumentation HYPMIX: Hyperbolic Interpolative Data Augmentation

HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections, ICML 2021 http://proceedings.mlr.press/v139/chami21a/chami21a.pdf

Ines Chami* Albert Gu* Dat Nguyen* Christopher Re´

ANTHEM: Attentive Hyperbolic Entity Model for Product Search, WSDM 2022 https://dl.acm.org/doi/10.1145/3488560.3498456

Nurendra Choudhary , Nikhil Rao , Sumeet Katariya , Karthik Subbian , Chandan K. Reddy