3 citations · 3 across the 9 of their papers we have counts for
9 papers
On the Representational Geometry of Dynamic Programs
Richard F. M. Lim, Ruriko Yoshida
Standard neural architectures often fail to generalize to longer inputs for dynamic programming (DP) targets. We investigate what makes this hard geometrically. Every finite min-pl…
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…
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…
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…
Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attacks
Kurt Pasque, Christopher Teska, Ruriko Yoshida +2
We introduce a simple, easy to implement, and computationally efficient tropical convolutional neural network architecture that is robust against adversarial attacks. We exploit th…
Tropical Geometric Tools for Machine Learning: the TML package
David Barnhill, Ruriko Yoshida, Georgios Aliatimis +1
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package…