mlsanityData to 7 Oct 2026

Fully Hyperbolic Neural Networks

arXiv 2105.14686 ↗First posted 31 May 2021cs.CL cs.LGcited by 107

Not on the map. Why?

Abstract (arXiv)

Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at the origin of the hyperbolic space. This hybrid method greatly limits the modeling ability of networks. In this paper, we propose a fully hyperbolic framework to build hyperbolic networks based on the Lorentz model by adapting the Lorentz transformations (including boost and rotation) to formalize essential operations of neural networks. Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the capabilities of existing hyperbolic networks. The experimental results on four NLP tasks show that our method has better performance for building both shallow and deep networks. Our code will be released to facilitate follow-up research.

Key facts. Cited by 107 papers in the map (data through 7 Oct 2026). Builds on 36 of its 71 references that are in the map. First posted on arXiv 31 May 2021.

Builds on

36 of 71 references.

References · 36

  1. 2017Attention Is All You Needcited by 59,932
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Graph Attention Networkscited by 8,854
  4. 2017Inductive Representation Learning on Large Graphscited by 6,284
  5. 2014Embedding Entities and Relations for Learning and Inference in Knowledge Basescited by 929
  6. 2019RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Spacecited by 893
  7. 2017Convolutional 2D Knowledge Graph Embeddingscited by 729
  8. 2020Stanza: A Python Natural Language Processing Toolkit for Many Human Languagescited by 719
  9. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  10. 2017Convolutional Sequence to Sequence Learningcited by 550
  11. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  12. 2018Hyperbolic Neural Networkscited by 393
24 more
  1. 2019TuckER: Tensor Factorization for Knowledge Graph Completioncited by 290
  2. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 261
  3. 2017OpenNMT: Open-source Toolkit for Neural Machine Translationcited by 251
  4. 2019Hyperbolic Graph Neural Networkscited by 244
  5. 2020Low-Dimensional Hyperbolic Knowledge Graph Embeddingscited by 195
  6. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  7. 2019Multi-relational Poincar'e Graph Embeddingscited by 126
  8. 2018Hyperbolic Attention Networkscited by 122
  9. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  10. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  11. 2018Ultra-Fine Entity Typingcited by 87
  12. 2019Hyperspherical Prototype Networkscited by 85
  13. 2017Knowledge Graph Completion via Complex Tensor Factorizationcited by 80
  14. 2019Hyperbolic Graph Attention Networkcited by 69
  15. 2021Lorentzian Graph Convolutional Networkscited by 66
  16. 2020Differentiating through the Fr'echet Meancited by 52
  17. 2021Probing BERT in Hyperbolic Spacescited by 50
  18. 2020Latent Variable Modelling with Hyperbolic Normalizing Flowscited by 49
  19. 2020HyperText: Endowing FastText with Hyperbolic Geometrycited by 28
  20. 2017Hyperbolic Representation Learning for Fast and Efficient Neural Question Answeringcited by 23
  21. 2020A Fully Hyperbolic Neural Model for Hierarchical Multi-Class Classificationcited by 23
  22. 2019Imposing Label-Relational Inductive Bias for Extremely Fine-Grained Entity Typingcited by 22
  23. 2019HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completioncited by 20
  24. 2019Fine-Grained Entity Typing in Hyperbolic Spacecited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 10; 2023: 14; 2024: 21; 2025: 28; 2026: 31.

107 papers.

Sort:

By area:

  1. 2022VLP: A Survey on Vision-Language Pre-trainingcited by 159
  2. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  3. 2021CPM-2: Large-scale Cost-effective Pre-trained Language Modelscited by 52
  4. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 48
  5. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  6. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  7. 2024Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Spacecited by 39
  8. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  9. 2023Poincar'e ResNetcited by 24
  10. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 24
  11. 2025HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Expertscited by 22
  12. 2022Graph Neural Networks Designed for Different Graph Types: A Surveycited by 21
38 more
  1. 2023Riemannian Residual Neural Networkscited by 21
  2. 2022Ultrahyperbolic Knowledge Graph Embeddingscited by 20
  3. 2024LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clusteringcited by 20
  4. 2025Hyperbolic Category Discoverycited by 20
  5. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  6. 2024Lorentzian Residual Neural Networkscited by 17
  7. 2025HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learningcited by 17
  8. 2023Contrastive Graph Clustering in Curvature Spacescited by 15
  9. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 15
  10. 2024Spiking Graph Neural Network on Riemannian Manifoldscited by 15
  11. 2025Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometriescited by 15
  12. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  13. 2022Hyperbolic VAE via Latent Gaussian Distributionscited by 14
  14. 2024Matrix Manifold Neural Networks++cited by 13
  15. 2023Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Spacecited by 12
  16. 2025HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modulescited by 12
  17. 2024Cross-Modal Fusion and Attention Mechanism for Weakly Supervised Video Anomaly Detectioncited by 10
  18. 2021D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learningcited by 8
  19. 2023Geometric Relational Embeddings: A Surveycited by 8
  20. 2023HyperFed: Hyperbolic Prototypes Exploration with Consistent Aggregation for Non-IID Data in Federated Learningcited by 8
  21. 2022Autoencoding Hyperbolic Representation for Adversarial Generationcited by 7
  22. 2023Fast hyperboloid decision tree algorithmscited by 7
  23. 2023Hyperbolic Graph Diffusion Modelcited by 6
  24. 2023Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coincited by 6
  25. 2025Is Hyperbolic Space All You Need for Medical Anomaly Detection?cited by 5
  26. 2023DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networkscited by 4
  27. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  28. 2024Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networkscited by 4
  29. 2025ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Spacecited by 4
  30. 2026Path-Decoupled Hyperbolic Flow Matching for Few-Shot Adaptationcited by 4
  31. 2022Towards Scalable Hyperbolic Neural Networks using Taylor Series Approximationscited by 3
  32. 2024Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spacescited by 3
  33. 2024Three Revisits to Node-Level Graph Anomaly Detection: Outliers, Message Passing and Hyperbolic Neural Networkscited by 3
  34. 2024Klein Model for Hyperbolic Neural Networkscited by 3
  35. 2024Fully Hyperbolic Rotation for Knowledge Graph Embeddingcited by 3
  36. 2024Shedding Light on Problems with Hyperbolic Graph Learningcited by 3
  37. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  38. 2025Hyperbolic recurrent neural network as the first type of non-Euclidean neural quantum state ansatzcited by 3

50 most cited of 107 All 107 (JSON)