mlsanityData to 7 Oct 2026

Fully Hyperbolic Convolutional Neural Networks for Computer Vision

arXiv 2303.15919 ↗First posted 28 Mar 2023cs.CV cs.LGcited by 48

Not on the map. Why?

Abstract (arXiv)

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current HNNs in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, a fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression. {Experiments on standard vision tasks demonstrate the promising performance of our HCNN framework in both hybrid and fully hyperbolic settings.} Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). Builds on 28 of its 54 references that are in the map. First posted on arXiv 28 Mar 2023.

Builds on

28 of 54 references.

References · 28

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  4. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  5. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  6. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  7. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  8. 2017Improved Regularization of Convolutional Neural Networks with Cutoutcited by 1,623
  9. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  10. 2018Hyperbolic Neural Networkscited by 393
  11. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 261
  12. 2019Hyperbolic Image Embeddingscited by 219
16 more
  1. 2018Riemannian Adaptive Optimization Methodscited by 187
  2. 2016A guide to convolution arithmetic for deep learningcited by 182
  3. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  4. 2019From Variational to Deterministic Autoencoderscited by 131
  5. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  6. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  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. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 56
  11. 2020Differentiating through the Fr'echet Meancited by 52
  12. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  13. 2018Large-Margin Classification in Hyperbolic Spacecited by 41
  14. 2020Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representationscited by 24
  15. 2022Skin Lesion Recognition with Class-Hierarchy Regularized Hyperbolic Embeddingscited by 19
  16. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 20; 2026: 19.

48 papers.

Sort:

By area:

  1. 2025HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Expertscited by 22
  2. 2025Hyperbolic Category Discoverycited by 20
  3. 2024Lorentzian Residual Neural Networkscited by 17
  4. 2025Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometriescited by 15
  5. 2025Hyperbolic Dataset Distillationcited by 15
  6. 2025HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modulescited by 12
  7. 2025Geo-Sign: Hyperbolic Contrastive Regularisation for Geometrically Aware Sign Language Translationcited by 11
  8. 2024Hyperbolic Learning with Multimodal Large Language Modelscited by 10
  9. 2025Is Hyperbolic Space All You Need for Medical Anomaly Detection?cited by 5
  10. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  11. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  12. 2025Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learningcited by 4
36 more
  1. 2024Hyperbolic Metric Learning for Visual Outlier Detectioncited by 3
  2. 2024Fully Hyperbolic Rotation for Knowledge Graph Embeddingcited by 3
  3. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  4. 2025Hyperbolic Genome Embeddingscited by 3
  5. 2026Intrinsic Lorentz Neural Networkcited by 3
  6. 2024HYDEN: Hyperbolic Density Representations for Medical Images and Reportscited by 2
  7. 2024On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networkscited by 2
  8. 2024Hgformer: Hyperbolic Graph Transformer for Recommendationcited by 2
  9. 2025Hyperbolic Dual Feature Augmentation for Open-Environmentcited by 2
  10. 2025Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spacescited by 2
  11. 2025Learning Protein-Ligand Binding in Hyperbolic Spacecited by 2
  12. 2025HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discoverycited by 2
  13. 2026HEEGNet: Hyperbolic Embeddings for EEGcited by 2
  14. 2026Fast and Geometrically Grounded Lorentz Neural Networkscited by 2
  15. 2026Hyperbolic Busemann Neural Networkscited by 2
  16. 2025Siegel Neural Networkscited by 1
  17. 2025LIHE: Linguistic Instance-Split Hyperbolic-Euclidean Framework for Generalized Weakly-Supervised Referring Expression Comprehensioncited by 1
  18. 2025Understanding and Improving Hyperbolic Deep Reinforcement Learningcited by 1
  19. 2026HexFormer: Hyperbolic Vision Transformer with Exponential Map Aggregationcited by 1
  20. 2026HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generationcited by 1
  21. 2026Parameter-Efficient Fine-Tuning of LLMs with Mixture of Space Expertscited by 1
  22. 2026EEG-Based Multimodal Learning via Hyperbolic Mixture-of-Curvature Expertscited by 1
  23. 2026Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representationscited by 1
  24. 2025Cartan Networks: Group theoretical Hyperbolic Deep Learningcited by 0
  25. 2025A Set-to-Set Distance Measure in Hyperbolic Spacecited by 0
  26. 2025HANS-Net: Hyperbolic Convolution and Adaptive Temporal Attention for Accurate and Generalizable Liver and Tumor Segmentation in CT Imagingcited by 0
  27. 2025More Than A Shortcut: A Hyperbolic Approach To Early-Exit Networkscited by 0
  28. 2026LAtte: Hyperbolic Lorentz Attention for Cross-Subject EEG Classificationcited by 0
  29. 2026Batch Normalization for Neural Networks on Complex Domainscited by 0
  30. 2026HyNeuralMap: Hyperbolic Mapping of Visual Semantics to Neural Hierarchiescited by 0
  31. 2026Riemannian Networks over Full-Rank Correlation Matricescited by 0
  32. 2026HyCoSeq: Contextual Hyperbolic Representation Learning for Genomic Sequencescited by 0
  33. 2026Geometry-Aware Hyperbolic Residual-Quantized Variational Autoencoderscited by 0
  34. 2026hyperbolix: Hyperbolic Deep Learning in JAXcited by 0
  35. 2026Rethinking the Fully Hyperbolic Vision Transformer in Polar Coordinatescited by 0
  36. 2026Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagationcited by 0