mlsanityData to 7 Oct 2026

Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers

arXiv 2107.11472 ↗First posted 23 Jul 2021cs.LG cs.CVcited by 56

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Abstract (arXiv)

Hyperbolic space can naturally embed hierarchies, unlike Euclidean space. Hyperbolic Neural Networks (HNNs) exploit such representational power by lifting Euclidean features into hyperbolic space for classification, outperforming Euclidean neural networks (ENNs) on datasets with known semantic hierarchies. However, HNNs underperform ENNs on standard benchmarks without clear hierarchies, greatly restricting HNNs' applicability in practice. Our key insight is that HNNs' poorer general classification performance results from vanishing gradients during backpropagation, caused by their hybrid architecture connecting Euclidean features to a hyperbolic classifier. We propose an effective solution by simply clipping the Euclidean feature magnitude while training HNNs. Our experiments demonstrate that clipped HNNs become super-hyperbolic classifiers: They are not only consistently better than HNNs which already outperform ENNs on hierarchical data, but also on-par with ENNs on MNIST, CIFAR10, CIFAR100 and ImageNet benchmarks, with better adversarial robustness and out-of-distribution detection.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). Builds on 30 of its 59 references that are in the map. First posted on arXiv 23 Jul 2021.

Builds on

30 of 59 references.

References · 30

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
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18 more
  1. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  2. 2015Empirical Evaluation of Rectified Activations in Convolutional Networkcited by 515
  3. 2018Hyperbolic Neural Networkscited by 393
  4. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 261
  5. 2019Hyperbolic Graph Neural Networkscited by 244
  6. 2019Hyperbolic Image Embeddingscited by 219
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  8. 2015TurkerGaze: Crowdsourcing Saliency with Webcam based Eye Trackingcited by 165
  9. 2017Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practicecited by 132
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  11. 2018Hyperbolic Attention Networkscited by 122
  12. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  13. 2018Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?cited by 94
  14. 2015Beyond Convexity: Stochastic Quasi-Convex Optimizationcited by 75
  15. 2018The Emergence of Spectral Universality in Deep Networkscited by 74
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 13; 2024: 13; 2025: 15; 2026: 13.

56 papers.

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  1. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  2. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 48
  3. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  4. 2023HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representationscited by 42
  5. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  6. 2023Poincar'e ResNetcited by 24
  7. 2025Hyperbolic Category Discoverycited by 20
  8. 2023Hyperbolic Active Learning for Semantic Segmentation under Domain Shiftcited by 18
  9. 2024Learning Structured Representations with Hyperbolic Embeddingscited by 16
  10. 2023Hyperbolic Contrastive Learningcited by 15
  11. 2025HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modulescited by 12
  12. 2024Hyperbolic Learning with Synthetic Captions for Open-World Detectioncited by 11
38 more
  1. 2024Understanding Hyperbolic Metric Learning through Hard Negative Samplingcited by 10
  2. 2024Hyperbolic Learning with Multimodal Large Language Modelscited by 10
  3. 2024Flattening the Parent Bias: Hierarchical Semantic Segmentation in the Poincar'e Ballcited by 9
  4. 2024Learning Visual Hierarchies in Hyperbolic Space for Image Retrievalcited by 8
  5. 2023Equiangular Basis Vectorscited by 7
  6. 2024A Fashion Item Recommendation Model in Hyperbolic Spacecited by 7
  7. 2023Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coincited by 6
  8. 2023HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypescited by 5
  9. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  10. 2023Hyperbolic Geometry in Computer Vision: A Surveycited by 4
  11. 2024When Cars meet Drones: Hyperbolic Federated Learning for Source-Free Domain Adaptation in Adverse Weathercited by 4
  12. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  13. 2025Continual Hyperbolic Learning of Instances and Classescited by 4
  14. 2023Hyp-UML: Hyperbolic Image Retrieval with Uncertainty-aware Metric Learningcited by 3
  15. 2024Hyperbolic Metric Learning for Visual Outlier Detectioncited by 3
  16. 2024Hyp-OC: Hyperbolic One Class Classification for Face Anti-Spoofingcited by 3
  17. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  18. 2025Curvature Learning for Generalization of Hyperbolic Neural Networkscited by 3
  19. 2025Modality Alignment across Trees on Heterogeneous Hyperbolic Manifoldscited by 3
  20. 2026Intrinsic Lorentz Neural Networkcited by 3
  21. 2023Unsupervised Feature Learning with Emergent Data-Driven Prototypicalitycited by 2
  22. 2023Knowledge-based Multiple Adaptive Spaces Fusion for Recommendationcited by 2
  23. 2025Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spacescited by 2
  24. 2025HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discoverycited by 2
  25. 2026Hyperbolic Busemann Neural Networkscited by 2
  26. 2025Deep Change Monitoring: A Hyperbolic Representative Learning Framework and a Dataset for Long-term Fine-grained Tree Change Detectioncited by 1
  27. 2025Machine Unlearning in Hyperbolic vs. Euclidean Multimodal Contrastive Learning: Adapting Alignment Calibration to MERUcited by 1
  28. 2025Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectorscited by 1
  29. 2025Understanding and Improving Hyperbolic Deep Reinforcement Learningcited by 1
  30. 2024Siamese networks for Poincar'e embeddings and the reconstruction of evolutionary treescited by 0
  31. 2025A Set-to-Set Distance Measure in Hyperbolic Spacecited by 0
  32. 2025Sharpness-Aware Geometric Defense for Robust Out-Of-Distribution Detectioncited by 0
  33. 2025HyperHELM: Hyperbolic Hierarchy Encoding for mRNA Language Modelingcited by 0
  34. 2025Adaptive Hyperbolic Kernels: Modulated Embedding in de Branges-Rovnyak Spacescited by 0
  35. 2026HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysiscited by 0
  36. 2026Comparing Euclidean and Hyperbolic K-Means for Generalized Category Discoverycited by 0
  37. 2026Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Modelscited by 0
  38. 2026Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Modelscited by 0

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