# Differentiable phylogenetics via hyperbolic embeddings with Dodonaphy

## TL;DR

This paper introduces a new method for phylogenetics using hyperbolic embeddings and a differentiable tree decoder to improve tree optimization.

## Contribution

The novel contribution is soft-NJ, a differentiable version of neighbour joining for gradient-based tree optimization.

## Key findings

- Soft-NJ enables differentiable optimization over tree space for maximum likelihood inference.
- Variational Bayesian phylogenetics using hyperbolic embeddings shows promise despite susceptibility to local optima.
- The method is compared to state-of-the-art techniques on eight benchmark datasets.

## Abstract

Navigating the high dimensional space of discrete trees for phylogenetics presents a challenging problem for tree optimization. To address this, hyperbolic embeddings of trees offer a promising approach to encoding trees efficiently in continuous spaces. However, they require a differentiable tree decoder to optimize the phylogenetic likelihood. We present soft-NJ, a differentiable version of neighbour joining that enables gradient-based optimization over the space of trees.

We illustrate the potential for differentiable optimization over tree space for maximum likelihood inference. We then perform variational Bayesian phylogenetics by optimizing embedding distributions in hyperbolic space. We compare the performance of this approximation technique on eight benchmark datasets to state-of-the-art methods. Results indicate that, while this technique is not immune from local optima, it opens a plethora of powerful and parametrically efficient approach to phylogenetics via tree embeddings.

Dodonaphy is freely available on the web at https://www.github.com/mattapow/dodonaphy. It includes an implementation of soft-NJ.