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Hyperbolic Deep Neural Networks: A Survey

arXiv 2101.04562 ↗First posted 12 Jan 2021cs.LG cs.CVcited by 138

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Abstract (arXiv)

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer to the model as hyperbolic deep neural network in this paper. Such a hyperbolic neural architecture potentially leads to drastically compact model withmuch more physical interpretability than its counterpart in Euclidean space. To stimulate future research, this paper presents acoherent and comprehensive review of the literature around the neural components in the construction of hyperbolic deep neuralnetworks, as well as the generalization of the leading deep approaches to the Hyperbolic space. It also presents current applicationsaround various machine learning tasks on several publicly available datasets, together with insightful observations and identifying openquestions and promising future directions.

Key facts. Cited by 138 papers in the map (data through 7 Oct 2026). Builds on 100 of its 215 references that are in the map. First posted on arXiv 12 Jan 2021.

Builds on

100 of 215 references.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 18; 2023: 27; 2024: 24; 2025: 36; 2026: 29.

138 papers.

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  1. 2022Hyperbolic Image Segmentationcited by 101
  2. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  3. 2024Compositional Entailment Learning for Hyperbolic Vision-Language Modelscited by 72
  4. 2023E^2VPT: An Effective and Efficient Approach for Visual Prompt Tuningcited by 70
  5. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 48
  6. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  7. 2022Knowledge Graph Embedding: A Survey from the Perspective of Representation Spacescited by 41
  8. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  9. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 27
  10. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  11. 2023Poincar'e ResNetcited by 24
  12. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 24
38 more
  1. 2022Graph Neural Networks Designed for Different Graph Types: A Surveycited by 21
  2. 2023Hyperbolic Representation Learning: Revisiting and Advancingcited by 21
  3. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  4. 2023Hyperbolic Audio-visual Zero-shot Learningcited by 19
  5. 2024Hardness of Learning Neural Networks under the Manifold Hypothesiscited by 18
  6. 2021Neural Distance Embeddings for Biological Sequencescited by 17
  7. 2022Hyperbolic Uncertainty Aware Semantic Segmentationcited by 17
  8. 2024Lorentzian Residual Neural Networkscited by 17
  9. 2025Hyperbolic Safety-Aware Vision-Language Modelscited by 17
  10. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  11. 2023Hyperbolic Contrastive Learningcited by 15
  12. 2021HyperExpan: Taxonomy Expansion with Hyperbolic Representation Learningcited by 14
  13. 2022kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learningcited by 14
  14. 2023HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Predictioncited by 13
  15. 2024HyperVQ: MLR-based Vector Quantization in Hyperbolic Spacecited by 13
  16. 2021Generalization Error Bound for Hyperbolic Ordinal Embeddingcited by 12
  17. 2022Rethinking Few-Shot Class-Incremental Learning with Open-Set Hypothesis in Hyperbolic Geometrycited by 12
  18. 2023Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Spacecited by 12
  19. 2025HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modulescited by 12
  20. 2023Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstructioncited by 10
  21. 2024Understanding Hyperbolic Metric Learning through Hard Negative Samplingcited by 10
  22. 2025HoPE: Hyperbolic Rotary Positional Encoding for Stable Long-Range Dependency Modeling in Large Language Modelscited by 10
  23. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  24. 2022Hyperbolic Hierarchical Contrastive Hashingcited by 9
  25. 2023Hyperbolic Random Forestscited by 9
  26. 2023Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classificationcited by 8
  27. 2023Federated Learning with Manifold Regularization and Normalized Update Reaggregationcited by 8
  28. 2023Hyperbolic Space with Hierarchical Margin Boosts Fine-Grained Learning from Coarse Labelscited by 8
  29. 2024HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generationcited by 8
  30. 2022Autoencoding Hyperbolic Representation for Adversarial Generationcited by 7
  31. 2022Neural Embedding: Learning the Embedding of the Manifold of Physics Datacited by 7
  32. 2023GPr-Net: Geometric Prototypical Network for Point Cloud Few-Shot Learningcited by 7
  33. 2024A Fashion Item Recommendation Model in Hyperbolic Spacecited by 7
  34. 2025PHyCLIP: ℓ1-Product of Hyperbolic Factors Unifies Hierarchy and Compositionality in Vision-Language Representation Learningcited by 7
  35. 2023HypLL: The Hyperbolic Learning Librarycited by 6
  36. 2025Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Spacecited by 6
  37. 2025Analytical Survey of Learning with Low-Resource Data: From Analysis to Investigationcited by 5
  38. 2025OpenHype: Hyperbolic Embeddings for Hierarchical Open-Vocabulary Radiance Fieldscited by 5

50 most cited of 138 All 138 (JSON)