# GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologies

arXiv: https://arxiv.org/abs/2307.03675 · HTML: https://mlsanity.com/paper/2307.03675/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Variational inference for Monte Carlo objectives](https://mlsanity.com/paper/1602.06725/) (2016)
- [VarGrad: A Low-Variance Gradient Estimator for Variational Inference](https://mlsanity.com/paper/2010.10436/) (2020)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows](https://mlsanity.com/paper/2012.00459/) (2020)
- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference](https://mlsanity.com/paper/2106.00075/) (2021)
- [VaiPhy: a Variational Inference Based Algorithm for Phylogeny](https://mlsanity.com/paper/2203.01121/) (2022)
- [Leveraging Recursive Gumbel-Max Trick for Approximate Inference in Combinatorial Spaces](https://mlsanity.com/paper/2110.15072/) (2021)
- [Learning phylogenetic trees as hyperbolic point configurations](https://mlsanity.com/paper/2104.11430/) (2021)
- [HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering](https://mlsanity.com/paper/2205.09721/) (2022)

## Built on by (most cited first, 10 of 10)

- [PhyloGFN: Phylogenetic inference with generative flow networks](https://mlsanity.com/paper/2310.08774/) (2023)
- [Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation](https://mlsanity.com/paper/2410.08125/) (2024)
- [Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation](https://mlsanity.com/paper/2412.18827/) (2024)
- [Variational Bayesian Phylogenetic Inference with Semi-implicit Branch Length Distributions](https://mlsanity.com/paper/2408.05058/) (2024)
- [Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree](https://mlsanity.com/paper/2510.09328/) (2025)
- [Solving the Tree Containment Problem Using Graph Neural Networks](https://mlsanity.com/paper/2404.09812/) (2024)
- [Variational phylogenetic inference with products over bipartitions](https://mlsanity.com/paper/2502.15110/) (2025)
- [PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference](https://mlsanity.com/paper/2605.21859/) (2026)
- [Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes](https://mlsanity.com/paper/2610.19053/) (2026)

## Abstract (arXiv)

Phylogenetic inference, grounded in molecular evolution models, is essential for understanding the evolutionary relationships in biological data. Accounting for the uncertainty of phylogenetic tree variables, which include tree topologies and evolutionary distances on branches, is crucial for accurately inferring species relationships from molecular data and tasks requiring variable marginalization. Variational Bayesian methods are key to developing scalable, practical models; however, it remains challenging to conduct phylogenetic inference without restricting the combinatorially vast number of possible tree topologies. In this work, we introduce a novel, fully differentiable formulation of phylogenetic inference that leverages a unique representation of topological distributions in continuous geometric spaces. Through practical considerations on design spaces and control variates for gradient estimations, our approach, GeoPhy, enables variational inference without limiting the topological candidates. In experiments using real benchmark datasets, GeoPhy significantly outperformed other approximate Bayesian methods that considered whole topologies.