# Fast hyperboloid decision tree algorithms

arXiv: https://arxiv.org/abs/2310.13841 · HTML: https://mlsanity.com/paper/2310.13841/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [Large-Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/1806.00437/) (2018)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [Hyperbolic Representation Learning for Fast and Efficient Neural Question Answering](https://mlsanity.com/paper/1707.07847/) (2017)
- [Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features](https://mlsanity.com/paper/2206.11844/) (2022)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/2302.06807/) (2023)
- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)

## Built on by (most cited first, 7 of 7)

- [Hyperbolic Genome Embeddings](https://mlsanity.com/paper/2507.21648/) (2025)
- [Mixed-curvature decision trees and random forests](https://mlsanity.com/paper/2410.13879/) (2024)
- [Manify: A Python Library for Learning Non-Euclidean Representations](https://mlsanity.com/paper/2503.09576/) (2025)
- [Tempered Calculus for ML: Application to Hyperbolic Model Embedding](https://mlsanity.com/paper/2402.04163/) (2024)
- [Mixed-Curvature Decision Trees and Random Forests](https://mlsanity.com/paper/2406.05227/) (2024)
- [Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approach](https://mlsanity.com/paper/2506.04360/) (2025)
- [Hyperbolic Manifold Constrained Tabular Neural Network](https://mlsanity.com/paper/2607.09710/) (2026)

## Abstract (arXiv)

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and consistently deliver state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present hyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, hyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.