mlsanityData to 14 Oct 2026

A Hyperbolic-to-Hyperbolic Graph Convolutional Network

arXiv 2104.06942 ↗First posted 14 Apr 2021cs.LGcited by 53

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Abstract (arXiv)

Hyperbolic graph convolutional networks (GCNs) demonstrate powerful representation ability to model graphs with hierarchical structure. Existing hyperbolic GCNs resort to tangent spaces to realize graph convolution on hyperbolic manifolds, which is inferior because tangent space is only a local approximation of a manifold. In this paper, we propose a hyperbolic-to-hyperbolic graph convolutional network (H2H-GCN) that directly works on hyperbolic manifolds. Specifically, we developed a manifold-preserving graph convolution that consists of a hyperbolic feature transformation and a hyperbolic neighborhood aggregation. The hyperbolic feature transformation works as linear transformation on hyperbolic manifolds. It ensures the transformed node representations still lie on the hyperbolic manifold by imposing the orthogonal constraint on the transformation sub-matrix. The hyperbolic neighborhood aggregation updates each node representation via the Einstein midpoint. The H2H-GCN avoids the distortion caused by tangent space approximations and keeps the global hyperbolic structure. Extensive experiments show that the H2H-GCN achieves substantial improvements on the link prediction, node classification, and graph classification tasks.

Key facts. Cited by 53 papers in the map (data through 14 Oct 2026). Builds on 27 of its 52 references that are in the map. First posted on arXiv 14 Apr 2021.

Builds on

27 of 52 references.

References · 27

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2018How Powerful are Graph Neural Networks?cited by 4,393
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  7. 2019Simplifying Graph Convolutional Networkscited by 1,477
  8. 2018Deep Graph Infomaxcited by 1,106
  9. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  10. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  11. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 787
  12. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
15 more
  1. 2018Hyperbolic Neural Networkscited by 402
  2. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  3. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 310
  4. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  5. 2019Hyperbolic Graph Neural Networkscited by 244
  6. 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
  7. 2019Hyperbolic Image Embeddingscited by 221
  8. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 206
  9. 2019Multi-relational Poincar'e Graph Embeddingscited by 126
  10. 2019Hyperbolic Graph Attention Networkcited by 70
  11. 2020From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clusteringcited by 65
  12. 2020Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embeddingcited by 36
  13. 2020Knowledge Association with Hyperbolic Knowledge Graph Embeddingscited by 31
  14. 2020Robust Large-Margin Learning in Hyperbolic Spacecited by 21
  15. 2016Cross Euclidean-to-Riemannian Metric Learning with Application to Face Recognition from Videocited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 7; 2023: 10; 2024: 20; 2025: 8; 2026: 4.

53 papers.

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  1. 2022Hyperbolic Image Segmentationcited by 102
  2. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 73
  3. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  4. 2021Pseudo-Riemannian Graph Convolutional Networkscited by 30
  5. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 27
  6. 2023Poincar'e ResNetcited by 25
  7. 2024Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learningcited by 23
  8. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  9. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 16
  10. 2024SA-GDA: Spectral Augmentation for Graph Domain Adaptationcited by 16
  11. 2024Learning Structured Representations with Hyperbolic Embeddingscited by 16
  12. 2022Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysiscited by 15
38 more
  1. 2023Contrastive Graph Clustering in Curvature Spacescited by 15
  2. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  3. 2023HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Predictioncited by 14
  4. 2024Matrix Manifold Neural Networks++cited by 13
  5. 2022Public Wisdom Matters! Discourse-Aware Hyperbolic Fourier Co-Attention for Social-Text Classificationcited by 11
  6. 2021D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learningcited by 8
  7. 2022Autoencoding Hyperbolic Representation for Adversarial Generationcited by 7
  8. 2023Hyperbolic Graph Diffusion Modelcited by 7
  9. 2024A Fashion Item Recommendation Model in Hyperbolic Spacecited by 7
  10. 2024Klein Model for Hyperbolic Neural Networkscited by 5
  11. 2025Continual Hyperbolic Learning of Instances and Classescited by 5
  12. 2026Hyperbolic Busemann Neural Networkscited by 5
  13. 2023DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networkscited by 4
  14. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  15. 2025Curvature Learning for Generalization of Hyperbolic Neural Networkscited by 4
  16. 2022Supervised Contrastive Learning with Structure Inference for Graph Classificationcited by 3
  17. 2024Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spacescited by 3
  18. 2024Three Revisits to Node-Level Graph Anomaly Detection: Outliers, Message Passing and Hyperbolic Neural Networkscited by 3
  19. 2024Hyperbolic Metric Learning for Visual Outlier Detectioncited by 3
  20. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  21. 2022Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spacescited by 2
  22. 2023FMGNN: Fused Manifold Graph Neural Networkcited by 2
  23. 2023Hyperbolic Convolution via Kernel Point Aggregationcited by 2
  24. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  25. 2024Residual Hyperbolic Graph Convolution Networkscited by 2
  26. 2024Hgformer: Hyperbolic Graph Transformer for Recommendationcited by 2
  27. 2025HyperbolicRAG: Enhancing Retrieval-Augmented Generation with Hyperbolic Representationscited by 2
  28. 2021Unit Ball Model for Embedding Hierarchical Structures in the Complex Hyperbolic Spacecited by 1
  29. 2023FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completioncited by 1
  30. 2024Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphscited by 1
  31. 2024Hyperbolic Knowledge Transfer in Cross-Domain Recommendation Systemcited by 1
  32. 2025Hyperbolic Cycle Alignment for Infrared-Visible Image Fusioncited by 1
  33. 2025HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detectioncited by 1
  34. 2023HLoOP -- Hyperbolic 2-space Local Outlier Probabilitiescited by 0
  35. 2024Core Knowledge Learning Framework for Graph Adaptation and Scalability Learningcited by 0
  36. 2024Seg-HGNN: Unsupervised and Light-Weight Image Segmentation with Hyperbolic Graph Neural Networkscited by 0
  37. 2025A Set-to-Set Distance Measure in Hyperbolic Spacecited by 0
  38. 2025Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detectioncited by 0

50 most cited of 53 All 53 (JSON)