mlsanityData to 14 Oct 2026

Hyperbolic Random Forests

arXiv 2308.13279 ↗First posted 25 Aug 2023cs.LG cs.AIcited by 9

Not on the map. Why?

Abstract (arXiv)

Hyperbolic space is becoming a popular choice for representing data due to the hierarchical structure - whether implicit or explicit - of many real-world datasets. Along with it comes a need for algorithms capable of solving fundamental tasks, such as classification, in hyperbolic space. Recently, multiple papers have investigated hyperbolic alternatives to hyperplane-based classifiers, such as logistic regression and SVMs. While effective, these approaches struggle with more complex hierarchical data. We, therefore, propose to generalize the well-known random forests to hyperbolic space. We do this by redefining the notion of a split using horospheres. Since finding the globally optimal split is computationally intractable, we find candidate horospheres through a large-margin classifier. To make hyperbolic random forests work on multi-class data and imbalanced experiments, we furthermore outline a new method for combining classes based on their lowest common ancestor and a class-balanced version of the large-margin loss. Experiments on standard and new benchmarks show that our approach outperforms both conventional random forest algorithms and recent hyperbolic classifiers.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 37 of its 65 references that are in the map. First posted on arXiv 25 Aug 2023.

Builds on

37 of 65 references.

References · 37

  1. 2019Class-Balanced Loss Based on Effective Number of Samplescited by 1,245
  2. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  3. 2018Hyperbolic Neural Networkscited by 402
  4. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  5. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  6. 2019Hyperbolic Graph Neural Networkscited by 244
  7. 2019Hyperbolic Image Embeddingscited by 221
  8. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 162
  9. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 156
  10. 2021Hyperbolic Deep Neural Networks: A Surveycited by 139
  11. 2023Hyperbolic Image-Text Representationscited by 136
  12. 2017Cooperative Game Theory Approaches for Network Partitioningcited by 135
25 more
  1. 2022Hyperbolic Image Segmentationcited by 102
  2. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 73
  3. 2020From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clusteringcited by 65
  4. 2017Neural Embeddings of Graphs in Hyperbolic Spacecited by 58
  5. 2020Differentiating through the Fr'echet Meancited by 53
  6. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
  7. 2021Learning the Predictability of the Futurecited by 49
  8. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  9. 2018Large-Margin Classification in Hyperbolic Spacecited by 41
  10. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 41
  11. 2022Hyperbolic Graph Neural Networks: A Review of Methods and Applicationscited by 40
  12. 2022Learning Hierarchy Aware Features for Reducing Mistake Severitycited by 26
  13. 2023Poincar'e ResNetcited by 25
  14. 2021ARM-Net: Adaptive Relation Modeling Network for Structured Datacited by 24
  15. 2020Robust Large-Margin Learning in Hyperbolic Spacecited by 21
  16. 2021No Cost Likelihood Manipulation at Test Time for Making Better Mistakes in Deep Networkscited by 21
  17. 2022Maximum Class Separation as Inductive Bias in One Matrixcited by 21
  18. 2022Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysiscited by 14
  19. 2022FisheyeHDK: Hyperbolic Deformable Kernel Learning for Ultra-Wide Field-of-View Image Recognitioncited by 10
  20. 2021Highly Scalable and Provably Accurate Classification in Poincare Ballscited by 8
  21. 2023HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypescited by 6
  22. 2020Hyperbolic Manifold Regressioncited by 5
  23. 2021Hyperbolic Disentangled Representation for Fine-Grained Aspect Extractioncited by 3
  24. 2018Enhancing Multi-Class Classification of Random Forest using Random Vector Functional Neural Network and Oblique Decision Surfacescited by 2
  25. 2022Provably Accurate and Scalable Linear Classifiers in Hyperbolic Spacescited by 2

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 5; 2025: 3.

9 papers.

  1. 2023Fast hyperboloid decision tree algorithmscited by 7
  2. 2025Continual Hyperbolic Learning of Instances and Classescited by 5
  3. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  4. 2024Mixed-curvature decision trees and random forestscited by 2
  5. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  6. 2025Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicingcited by 1
  7. 2024Tempered Calculus for ML: Application to Hyperbolic Model Embeddingcited by 0
  8. 2024Mixed-Curvature Decision Trees and Random Forestscited by 0
  9. 2025Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approachcited by 0