# Leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees

arXiv: https://arxiv.org/abs/2306.05739 · HTML: https://mlsanity.com/paper/2306.05739/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 130 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Learning phylogenetic trees as hyperbolic point configurations](https://mlsanity.com/paper/2104.11430/) (2021)
- [Computing nearest neighbour interchange distances between ranked phylogenetic trees](https://mlsanity.com/paper/2007.12307/) (2020)
- [Phylo2Vec: a vector representation for binary trees](https://mlsanity.com/paper/2304.12693/) (2023)

## Built on by (most cited first, 1 of 1)

- [Enhancing Group Fairness in Online Settings Using Oblique Decision Forests](https://mlsanity.com/paper/2310.11401/) (2023)

## Abstract (arXiv)

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains challenging. To address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. This continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. Our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. The approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. Indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrates. Optimisation is possible via automatic differentiation and our method presents an effective way forwards for exploring the most difficult, data-deficient phylogenetic questions.