mlsanityData to 7 Oct 2026

Hyperbolic Neural Networks

arXiv 1805.09112 ↗First posted 23 May 2018cs.LG stat.MLcited by 393

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Abstract (arXiv)

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural network layers. This makes it hard to use hyperbolic embeddings in downstream tasks. Here, we bridge this gap in a principled manner by combining the formalism of M"obius gyrovector spaces with the Riemannian geometry of the Poincar'e model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks such as gated recurrent units. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

Key facts. Cited by 393 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 May 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 53; 2022: 52; 2023: 55; 2024: 65; 2025: 73; 2026: 95.

393 papers.

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  1. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  2. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 109
  3. 2021Fully Hyperbolic Neural Networkscited by 107
  4. 2022Hyperbolic Image Segmentationcited by 101
  5. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  6. 2024Compositional Entailment Learning for Hyperbolic Vision-Language Modelscited by 72
  7. 2023E^2VPT: An Effective and Efficient Approach for Visual Prompt Tuningcited by 70
  8. 2021Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Spacecited by 67
  9. 2021Lorentzian Graph Convolutional Networkscited by 66
  10. 2022Hyperbolic Contrastive Learning for Visual Representations beyond Objectscited by 58
  11. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 56
  12. 2021A Hyperbolic-to-Hyperbolic Graph Convolutional Networkcited by 53
38 more
  1. 2021Probing BERT in Hyperbolic Spacescited by 50
  2. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 49
  3. 2021Learning the Predictability of the Futurecited by 48
  4. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  5. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 48
  6. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  7. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  8. 2021von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learningcited by 42
  9. 2023HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representationscited by 42
  10. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  11. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 40
  12. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  13. 2021Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervisioncited by 39
  14. 2022Mask and Reason: Pre-Training Knowledge Graph Transformers for Complex Logical Queriescited by 39
  15. 2024Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Spacecited by 39
  16. 2021Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Conescited by 38
  17. 2024LLMs are Good Action Recognizerscited by 36
  18. 2022HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularizationcited by 34
  19. 2025RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometrycited by 32
  20. 2021Pseudo-Riemannian Graph Convolutional Networkscited by 30
  21. 2022Proton: Probing Schema Linking Information from Pre-trained Language Models for Text-to-SQL Parsingcited by 30
  22. 2022A Survey of Mix-based Data Augmentation: Taxonomy, Methods, Applications, and Explainabilitycited by 30
  23. 2021CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Datacited by 28
  24. 2024Language Models as Hierarchy Encoderscited by 26
  25. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  26. 2021Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systemscited by 24
  27. 2021ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Networkcited by 24
  28. 2022A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learningcited by 24
  29. 2023Poincar'e ResNetcited by 24
  30. 2023HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusioncited by 24
  31. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 24
  32. 2023Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classificationcited by 23
  33. 2024Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learningcited by 23
  34. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  35. 2022The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generationcited by 22
  36. 2025HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Expertscited by 22
  37. 2021BScNets: Block Simplicial Complex Neural Networkscited by 21
  38. 2023Hyperbolic Representation Learning: Revisiting and Advancingcited by 21

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