mlsanityData to 7 Oct 2026

Poincar'e ResNet

arXiv 2303.14027 ↗First posted 24 Mar 2023cs.CVcited by 24

Not on the map. Why?

Abstract (arXiv)

This paper introduces an end-to-end residual network that operates entirely on the Poincar'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar'e 2D convolutions up to Poincar'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr'echet mean calculations in hyperbolic space. We introduce Poincar'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 39 of its 63 references that are in the map. First posted on arXiv 24 Mar 2023.

Builds on

39 of 63 references.

References · 39

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,690
  4. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  5. 2013Describing Textures in the Wildcited by 2,110
  6. 2020Energy-based Out-of-distribution Detectioncited by 1,296
  7. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  8. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  9. 2018Hyperbolic Neural Networkscited by 393
  10. 2019Hyperbolic Graph Neural Networkscited by 244
  11. 2019Hyperbolic Image Embeddingscited by 219
  12. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 204
27 more
  1. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 160
  2. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  3. 2020Riemannian Continuous Normalizing Flowscited by 143
  4. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  5. 2019Multi-relational Poincar'e Graph Embeddingscited by 126
  6. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  7. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 109
  8. 2021Fully Hyperbolic Neural Networkscited by 107
  9. 2022Hyperbolic Image Segmentationcited by 101
  10. 2018Embedding Text in Hyperbolic Spacescited by 76
  11. 2019Hyperbolic Graph Attention Networkcited by 69
  12. 2020From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clusteringcited by 65
  13. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 56
  14. 2021A Hyperbolic-to-Hyperbolic Graph Convolutional Networkcited by 53
  15. 2020Differentiating through the Fr'echet Meancited by 52
  16. 2020Latent Variable Modelling with Hyperbolic Normalizing Flowscited by 49
  17. 2021Learning the Predictability of the Futurecited by 48
  18. 2020Hierarchical Image Classification using Entailment Cone Embeddingscited by 46
  19. 2023HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representationscited by 42
  20. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 40
  21. 2021Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervisioncited by 39
  22. 2020Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representationscited by 24
  23. 2022Skin Lesion Recognition with Class-Hierarchy Regularized Hyperbolic Embeddingscited by 19
  24. 2022Hyperbolic Uncertainty Aware Semantic Segmentationcited by 17
  25. 2021Adaptive Poincar'e Point to Set Distance for Few-Shot Classificationcited by 15
  26. 2022On Hyperbolic Embeddings in 2D Object Detectioncited by 6
  27. 2021Hyperbolic Generative Adversarial Networkcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 8; 2025: 6; 2026: 8.

24 papers.

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  1. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 24
  2. 2025Hyperbolic Safety-Aware Vision-Language Modelscited by 17
  3. 2024Hyperbolic Learning with Multimodal Large Language Modelscited by 10
  4. 2023Hyperbolic Random Forestscited by 9
  5. 2024Flattening the Parent Bias: Hierarchical Semantic Segmentation in the Poincar'e Ballcited by 9
  6. 2023HypLL: The Hyperbolic Learning Librarycited by 6
  7. 2024When Cars meet Drones: Hyperbolic Federated Learning for Source-Free Domain Adaptation in Adverse Weathercited by 4
  8. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  9. 2024Hyperbolic Metric Learning for Visual Outlier Detectioncited by 3
  10. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  11. 2025GGBall: Graph Generative Model on Poincar'e Ballcited by 3
  12. 2026Intrinsic Lorentz Neural Networkcited by 3
12 more
  1. 2026Fast and Geometrically Grounded Lorentz Neural Networkscited by 2
  2. 2026Hyperbolic Busemann Neural Networkscited by 2
  3. 2024Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphscited by 1
  4. 2025H2em: Learning Hierarchical Hyperbolic Embeddings for Compositional Zero-Shot Learningcited by 1
  5. 2026A Neural Tension Operator for Curve Subdivision across Constant Curvature Geometriescited by 1
  6. 2025A Set-to-Set Distance Measure in Hyperbolic Spacecited by 0
  7. 2025Hyperbolic Multimodal Representation Learning for Biological Taxonomiescited by 0
  8. 2025HyperHELM: Hyperbolic Hierarchy Encoding for mRNA Language Modelingcited by 0
  9. 2026Group-Equivariant Poincar'e Convolutional Networkscited by 0
  10. 2026Adaptive Interpolatory Curve Subdivision with Learned Local Anglescited by 0
  11. 2026Geometry-Aware Hyperbolic Residual-Quantized Variational Autoencoderscited by 0
  12. 2026hyperbolix: Hyperbolic Deep Learning in JAXcited by 0