# Approximating SPR Distance Between Phylogenetic Trees with Graph Neural Networks

arXiv: https://arxiv.org/abs/2607.18311 · HTML: https://mlsanity.com/paper/2607.18311/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [SimGNN: A Neural Network Approach to Fast Graph Similarity Computation](https://mlsanity.com/paper/1808.05689/) (2018)
- [Calculating the Unrooted Subtree Prune-and-Regraft Distance](https://mlsanity.com/paper/1511.07529/) (2015)
- [Distance-based phylogenetic inference from typing data: a unifying view](https://mlsanity.com/paper/2006.07016/) (2020)

## Abstract (arXiv)

Comparing phylogenetic tree topologies is essential for understanding epidemic dynamics, yet biologically meaningful distances such as the Subtree Prune and Regraft (SPR) distance are NP-hard to compute and intractable on large datasets. We investigate whether a Graph Neural Network (GNN) can approximate SPR distances in near-constant time per comparison after training. Our contributions are fourfold. First, we build and publicly release a dataset of 864 phylogenetic trees inferred with UPGMA and Neighbor-Joining over four bacterial species, spanning up to 9,500 isolates, together with 388 labelled tree pairs. Second, we establish a reproducible pre-processing pipeline including midpoint re-rooting, which reduces tree depth and supplies the rooting required for exact distance computation and for the model's root-based features. Third, we validate the supervision target: on small trees, where exact SPR is tractable, the unrooted phangorn::SPR.dist heuristic correlates almost perfectly with the exact rooted distance computed by rspr (Pearson 0.98--0.99), making it an excellent monotonic surrogate. Lastly, we train a Siamese Graph Isomorphism Network (GIN) regressor. In-distribution, i.e., held-out trees from the same species and size range as training, it explains roughly 87--90% of the variance (R2 ≈ 0.87 on a held-out split; 0.90 ± 0.19 under stratified cross-validation), with about four times lower error than a mean-predictor baseline, and shows partial transfer to unseen species (R2 ≈ 0.37). Its main limitation is extrapolation to trees larger than those seen in training, where accuracy collapses. The released dataset and the validated heuristic versus exact relationship provide a reproducible basis for scaling learned SPR approximation.