mlsanityData to 14 Oct 2026

Poincar'e Embeddings for Learning Hierarchical Representations

arXiv 1705.08039 ↗First posted 22 May 2017cs.AI cs.LG stat.MLcited by 684

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Abstract (arXiv)

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Key facts. Cited by 684 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 May 2017.

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Citing papers per year: 2021: 96; 2022: 100; 2023: 77; 2024: 93; 2025: 132; 2026: 186.

684 papers.

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  1. 2024The Geometry of Categorical and Hierarchical Concepts in Large Language Modelscited by 159
  2. 2021Hyperbolic Deep Neural Networks: A Surveycited by 139
  3. 2023Hyperbolic Image-Text Representationscited by 136
  4. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 111
  5. 2021Fully Hyperbolic Neural Networkscited by 108
  6. 2022Hyperbolic Image Segmentationcited by 102
  7. 2022Deep Hierarchical Semantic Segmentationcited by 84
  8. 2021ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphscited by 78
  9. 2024Compositional Entailment Learning for Hyperbolic Vision-Language Modelscited by 74
  10. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 73
  11. 2021Lorentzian Graph Convolutional Networkscited by 68
  12. 2021Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Spacecited by 67
38 more
  1. 2022The Limits of Word Level Differential Privacycited by 63
  2. 2022Hyperbolic Contrastive Learning for Visual Representations beyond Objectscited by 61
  3. 2022Plug & Play Attacks: Towards Robust and Flexible Model Inversion Attackscited by 60
  4. 2022Rickrolling the Artist: Injecting Backdoors into Text Encoders for Text-to-Image Synthesiscited by 59
  5. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 57
  6. 2021A Hyperbolic-to-Hyperbolic Graph Convolutional Networkcited by 53
  7. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
  8. 2021Probing BERT in Hyperbolic Spacescited by 50
  9. 2021Learning the Predictability of the Futurecited by 49
  10. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  11. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 47
  12. 2024Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Spacecited by 43
  13. 2021von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learningcited by 42
  14. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  15. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 41
  16. 2022Knowledge Graph Embedding: A Survey from the Perspective of Representation Spacescited by 41
  17. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  18. 2021Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervisioncited by 39
  19. 2021Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Conescited by 38
  20. 2021Link Prediction with Persistent Homology: An Interactive Viewcited by 37
  21. 2024LLMs are Good Action Recognizerscited by 37
  22. 2021Modeling Fine-Grained Entity Types with Box Embeddingscited by 36
  23. 2021Select, Substitute, Search: A New Benchmark for Knowledge-Augmented Visual Question Answeringcited by 33
  24. 2021A Self-supervised Mixed-curvature Graph Neural Networkcited by 33
  25. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  26. 2022Contextual Semantic Embeddings for Ontology Subsumption Predictioncited by 31
  27. 2021Pseudo-Riemannian Graph Convolutional Networkscited by 30
  28. 2022Proton: Probing Schema Linking Information from Pre-trained Language Models for Text-to-SQL Parsingcited by 30
  29. 2021CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Datacited by 28
  30. 2024Language Models as Hierarchy Encoderscited by 28
  31. 2024Beyond Single Concept Vector: Modeling Concept Subspace in LLMs with Gaussian Distributioncited by 27
  32. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 27
  33. 2022Learning Hierarchy Aware Features for Reducing Mistake Severitycited by 26
  34. 2022HIER: Metric Learning Beyond Class Labels via Hierarchical Regularizationcited by 26
  35. 2025HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Expertscited by 26
  36. 2021ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Networkcited by 25
  37. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  38. 2023Poincar'e ResNetcited by 25

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