Phylogenetic Tree Inference with Tropical Axial Attention

TL;DR

This paper introduces Tropical Axial Attention, a neural architecture that uses tropical geometry to improve phylogenetic tree inference from sequence data, outperforming baseline models in distance accuracy.

Contribution

It proposes a novel tropical attention mechanism aligned with phylogenetic geometry, enhancing neural inference of evolutionary trees.

Findings

Tropical attention produces distance matrices closer to true tree metrics.

Model performs well under distribution shift.

Outperforms baseline models on empirical alignments.

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 $\ell_1$ 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 produces distance matrices that are substantially closer to their BME-induced tree metrics than the baseline models. 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.