mlsanityData to 14 Oct 2026

Hyperbolic Busemann Neural Networks

arXiv 2602.18858 ↗First posted 21 Feb 2026cs.LG cs.AI cs.CVcited by 5

Not on the map. Why?

Abstract (arXiv)

Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate directly in hyperbolic space. In this work, we lift two core components of neural networks, Multinomial Logistic Regression (MLR) and Fully Connected (FC) layers, into hyperbolic space via Busemann functions, resulting in Busemann MLR (BMLR) and Busemann FC (BFC) layers with a unified mathematical interpretation. BMLR provides compact parameters, a point-to-horosphere distance interpretation, batch-efficient computation, and a Euclidean limit, while BFC generalizes FC and activation layers with comparable complexity. Experiments on image classification, genome sequence learning, node classification, and link prediction demonstrate improvements in effectiveness and efficiency over prior hyperbolic layers. The code is available at https://github.com/GitZH-Chen/HBNN.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 40 of its 58 references that are in the map. First posted on arXiv 21 Feb 2026.

Builds on

40 of 58 references.

References · 40

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
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  7. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  8. 2019Hyperbolic Graph Neural Networkscited by 244
  9. 2019Hyperbolic Image Embeddingscited by 221
  10. 2023DNABERT-2: Efficient Foundation Model and Benchmark For Multi-Species Genomecited by 143
  11. 2023Hyperbolic Image-Text Representationscited by 136
  12. 2018Hyperbolic Attention Networkscited by 122
28 more
  1. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 111
  2. 2019Constant Curvature Graph Convolutional Networkscited by 108
  3. 2021Fully Hyperbolic Neural Networkscited by 108
  4. 2019Mixed-curvature Variational Autoencoderscited by 86
  5. 2024Compositional Entailment Learning for Hyperbolic Vision-Language Modelscited by 74
  6. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 57
  7. 2020Differentiating through the Fr'echet Meancited by 53
  8. 2021A Hyperbolic-to-Hyperbolic Graph Convolutional Networkcited by 53
  9. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 49
  10. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  11. 2024Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Spacecited by 43
  12. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 41
  13. 2024Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifoldscited by 28
  14. 2024Hyperbolic Fine-Tuning for Large Language Modelscited by 27
  15. 2025HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Expertscited by 26
  16. 2023Poincar'e ResNetcited by 25
  17. 2023Riemannian Residual Neural Networkscited by 21
  18. 2024Hyperbolic Geometric Latent Diffusion Model for Graph Generationcited by 20
  19. 2025Hyperbolic Category Discoverycited by 20
  20. 2024Lorentzian Residual Neural Networkscited by 17
  21. 2023Exploring Data Geometry for Continual Learningcited by 15
  22. 2023Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Spacecited by 11
  23. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  24. 2025Riemannian Batch Normalization: A Gyro Approachcited by 6
  25. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 6
  26. 2024Robust Hyperbolic Learning with Curvature-Aware Optimizationcited by 4
  27. 2025Galaxy Walker: Geometry-aware VLMs For Galaxy-scale Understandingcited by 4
  28. 2025Wasserstein-Aligned Hyperbolic Multi-View Clusteringcited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026hyperbolix: Hyperbolic Deep Learning in JAXcited by 1
  2. 2026Busemann energy-based attention for emotion analysis in Poincar'e discscited by 0
  3. 2026Rethinking the Fully Hyperbolic Vision Transformer in Polar Coordinatescited by 0
  4. 2026Hesitation Has a Geometry: Entropy-Trained Hyperbolic Probes for Sparse Activation Steeringcited by 0
  5. 2026The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspectivecited by 0