Phylogenetic tree inference with tropical axial attention
- 1Department of Operations Research, Naval Postgraduate School, Monterey, CA, United States
- 2Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Abstract
In this work, we introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators, inducing a piecewise-linear structure aligned with dynamic programming formulations. From multi-species sequence alignments, our model learns all possible pairwise distances and is trained using a combination of ℓ1 and tropical symmetric distance metric losses with an ultrametric violation penalty. We leverage the well known isomorphic relationship between the space of all phylogenetic trees with n species and tropical Grassmannian to show that tropical attention provides a natural geometric framework for phylogenetic inference. On empirical DS1−DS11 alignments, where true trees are unknown, the tropical model achieves the lowest MAE to its FastME-induced tree metric on every dataset, with a MAE reductions averaging 81.5% relative to Phyloformer and 98.4% relative than Phyloformer 2. These results suggest that tropical attention is a useful geometric inductive bias for neural phylogenetic inference, especially under distribution shift and when tree-metric consistency is important.
Related
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BibTeX
@article{teska2026phylogenetic,
title = {{Phylogenetic tree inference with tropical axial attention}},
author = {Chris Teska and Kurt Pasque and Ruriko Yoshida and Baran Hashemi},
journal = {Frontiers in Systems Biology},
year = {2026},
month = oct,
doi = {10.3389/fsysb.2026.1886918},
url = {https://doi.org/10.3389/fsysb.2026.1886918},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Phylogenetic tree inference with tropical axial attention
AU - Chris Teska
AU - Kurt Pasque
AU - Ruriko Yoshida
AU - Baran Hashemi
PY - 2026
DA - 2026/10/12
JO - Frontiers in Systems Biology
DO - 10.3389/fsysb.2026.1886918
UR - https://doi.org/10.3389/fsysb.2026.1886918
AB - In this work, we introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators, inducing a piecewise-linear structure aligned with dynamic programming formulations. From multi-species sequence alignments, our model learns all possible pairwise distances and is trained using a combination of ℓ1 and tropical symmetric distance metric losses with an ultrametric violation penalty. We leverage the well known isomorphic relationship between the space of all phylogenetic trees with n species and tropical Grassmannian to show that tropical attention provides a natural geometric framework for phylogenetic inference. On empirical DS1−DS11 alignments, where true trees are unknown, the tropical model achieves the lowest MAE to its FastME-induced tree metric on every dataset, with a MAE reductions averaging 81.5% relative to Phyloformer and 98.4% relative than Phyloformer 2. These results suggest that tropical attention is a useful geometric inductive bias for neural phylogenetic inference, especially under distribution shift and when tree-metric consistency is important.
SN - 2674-0702
ER -