# Phylogenetic Tree Inference with Tropical Axial Attention

arXiv: https://arxiv.org/abs/2605.13894 · HTML: https://mlsanity.com/paper/2605.13894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 44 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Axial-DeepLab: Stand-Alone Axial-Attention for Panoptic Segmentation](https://mlsanity.com/paper/2003.07853/) (2020)
- [A Tutorial on LLM Reasoning: Relevant Methods behind ChatGPT o1](https://mlsanity.com/paper/2502.10867/) (2025)
- [Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms](https://mlsanity.com/paper/2505.17190/) (2025)
- [Capacitated Dynamic Programming: Faster Knapsack and Graph Algorithms](https://mlsanity.com/paper/1802.06440/) (2018)
- [Parametric shortest-path algorithms via tropical geometry](https://mlsanity.com/paper/1904.01082/) (2019)

## Abstract (arXiv)

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.