Phylogenetic Tree Inference with Tropical Axial Attention

• URL: http://arxiv.org/abs/2605.13894v1
• Date: Tue, 12 May 2026 10:54:37 GMT
• Title: Phylogenetic Tree Inference with Tropical Axial Attention
• Abstract summary: We introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators.<n>From multi-species sequence alignments, our model learns all possible pairwise distances.<n>We show that tropical attention provides a natural geometric framework for phylogenetic inference.
• Score: 1.43494686131174
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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