mlsanityData to 7 Oct 2026

Representation Tradeoffs for Hyperbolic Embeddings

arXiv 1804.03329 ↗First posted 10 Apr 2018cs.LG stat.MLcited by 204

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Abstract (arXiv)

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Key facts. Cited by 204 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Apr 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 39; 2022: 35; 2023: 29; 2024: 29; 2025: 36; 2026: 36.

204 papers.

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  1. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  2. 2022Hyperbolic Image Segmentationcited by 101
  3. 2022Deep Hierarchical Semantic Segmentationcited by 84
  4. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  5. 2021Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Spacecited by 67
  6. 2021Lorentzian Graph Convolutional Networkscited by 66
  7. 2022Hyperbolic Contrastive Learning for Visual Representations beyond Objectscited by 58
  8. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 56
  9. 2021A Hyperbolic-to-Hyperbolic Graph Convolutional Networkcited by 53
  10. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  11. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  12. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
38 more
  1. 2022Knowledge Graph Embedding: A Survey from the Perspective of Representation Spacescited by 41
  2. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 40
  3. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  4. 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
  5. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  6. 2021Marius: Learning Massive Graph Embeddings on a Single Machinecited by 29
  7. 2021Universalizing Weak Supervisioncited by 27
  8. 2022HIER: Metric Learning Beyond Class Labels via Hierarchical Regularizationcited by 26
  9. 2022HICF: Hyperbolic Informative Collaborative Filteringcited by 24
  10. 2023Poincar'e ResNetcited by 24
  11. 2021Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approachcited by 23
  12. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
  13. 2022Latent Graph Inference using Product Manifoldscited by 23
  14. 2023Hyperbolic Representation Learning: Revisiting and Advancingcited by 21
  15. 2023Graph-level Representation Learning with Joint-Embedding Predictive Architecturescited by 21
  16. 2023UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Predictioncited by 20
  17. 2024Hyperbolic Geometric Latent Diffusion Model for Graph Generationcited by 20
  18. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  19. 2022Contrastive Multi-view Hyperbolic Hierarchical Clusteringcited by 19
  20. 2022Skin Lesion Recognition with Class-Hierarchy Regularized Hyperbolic Embeddingscited by 19
  21. 2023Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learningcited by 18
  22. 2023Hyperbolic Active Learning for Semantic Segmentation under Domain Shiftcited by 18
  23. 2025Hyperbolic Safety-Aware Vision-Language Modelscited by 17
  24. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  25. 2024Learning Structured Representations with Hyperbolic Embeddingscited by 16
  26. 2021Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoderscited by 15
  27. 2022HyperMiner: Topic Taxonomy Mining with Hyperbolic Embeddingcited by 15
  28. 2023Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learningcited by 15
  29. 2025Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometriescited by 15
  30. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  31. 2022Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysiscited by 14
  32. 2022kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learningcited by 14
  33. 2021Extracting Event Temporal Relations via Hyperbolic Geometrycited by 13
  34. 2023HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Predictioncited by 13
  35. 2021Knowledge-Enhanced Top-K Recommendation in Poincar'e Ballcited by 12
  36. 2021Generalization Error Bound for Hyperbolic Ordinal Embeddingcited by 12
  37. 2023Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Spacecited by 12
  38. 2021Linear Classifiers in Product Space Formscited by 11

50 most cited of 204 All 204 (JSON)