# Learning phylogenetic trees as hyperbolic point configurations

arXiv: https://arxiv.org/abs/2104.11430 · HTML: https://mlsanity.com/paper/2104.11430/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 23 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [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)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Skip-gram word embeddings in hyperbolic space](https://mlsanity.com/paper/1809.01498/) (2018)
- [Gradient descent in hyperbolic space](https://mlsanity.com/paper/1805.08207/) (2018)

## Built on by (most cited first, 3 of 3)

- [GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologies](https://mlsanity.com/paper/2307.03675/) (2023)
- [Leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees](https://mlsanity.com/paper/2306.05739/) (2023)
- [Hyperbolic Residual Quantization: Discrete Representations for Data with Latent Hierarchies](https://mlsanity.com/paper/2505.12404/) (2025)

## Abstract (arXiv)

We propose a novel method for the inference of phylogenetic trees that utilises point configurations on hyperbolic space as its optimisation landscape. Each taxon corresponds to a point of the point configuration, while the evolutionary distance between taxa is represented by the geodesic distance between their corresponding points. The point configuration is iteratively modified to increase an objective function that additively combines pairwise log-likelihood terms. After convergence, the final tree is derived from the inter-point distances using a standard distance-based method. The objective function, which is shown to mimic the log-likelihood on tree space, is a differentiable function on a Riemannian manifold. Thus gradient-based optimisation techniques can be applied, avoiding the need for combinatorial rearrangements of tree topology.