6 papers
Tropical Fermat--Weber Problems over Non-Finite Data and their Inverse Formulations
John Sabol, Ruriko Yoshida
The term tropical pseudonorm refers to a family of (not necessarily symmetric) gauge functions that arise in tropical or idempotent geometry. An important characteristic of these g…
Tropical Fermat-Weber Polytropes
John Sabol, David Barnhill, Ruriko Yoshida +1
We study the geometry of tropical Fermat--Weber points, that is, optimal solutions to a location problem over a projective space using a dissimilarity measure derived from the trop…
Phylogenetic Tree Inference with Tropical Axial Attention
Chris Teska, Kurt Pasque, Ruriko Yoshida +1
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 piecewis…
Phylogenetics in a warm place: computational aspects of the Tropical Grassmannian
Samir Bhatt, John Sabol, Papri Dey +3
Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally…
Tropical Attention: Neural Algorithmic Reasoning for Combinatorial Algorithms
Baran Hashemi, Kurt Pasque, Chris Teska +1
Can algebraic geometry enhance the sharpness, robustness, and interpretability of modern neural reasoning models by equipping them with a mathematically grounded inductive bias? To…
Tropical Fermat-Weber Points over Spaces of -Ultrametrics
Shelby Cox, John Sabol, Roan Talbut +1
We extend reconstruction methods for phylogenetic trees to ultrametrics of arbitrary matroids and study the stability of these data analysis methods in the combinatorial spirit of…