Related papers: Tropical Bisectors and Carlini-Wagner Attacks
Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case…
To quantify the geometric expressivity of transformers, we introduce a tropical geometry framework to characterize their exact spatial partitioning capabilities. By modeling self-attention as a vector-valued tropical rational map, we prove…
Deep learning algorithms have been known to be vulnerable to adversarial perturbations in various tasks such as image classification. This problem was addressed by employing several defense methods for detection and rejection of particular…
Neural networks are vulnerable to adversarial attacks, and several defenses have been proposed. Designing a robust network is a challenging task given the wide range of attacks that have been developed. Therefore, we aim to provide insight…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
Heavy precipitation from tropical cyclones (TCs) may result in disasters, such as floods and landslides, leading to substantial economic damage and loss of life. Prediction of TC precipitation based on ensemble post-processing procedures…
We study the classical result by Bruijn and Erd\H os regarding the bound on the number of lines determined by a $n$-point configuration in the plane, and in the light of the recently proven Tropical Sylvester-Gallai theorem, come up with a…
This paper presents numerical solutions and idealized analytical solutions of axisymmetric, $f$-plane models of the tropical cyclone boundary layer. In the numerical model, the boundary layer radial and tangential flow is forced by a…
In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
Due to the gap between a substitute model and a victim model, the gradient-based noise generated from a substitute model may have low transferability for a victim model since their gradients are different. Inspired by the fact that the…
Traditional methods for enhancing tropical cyclone (TC) intensity from climate model outputs or projections have primarily relied on either dynamical or statistical downscaling. With recent advances in deep learning (DL) techniques, a…
We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is…
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The purpose of this paper is to advertise tropical modifications as a tool to locally repair bad embeddings of plane curves, allowing the…
In recent times, a wide variety of combinatorics has been introduced in order to solve problems from algebraic geometry. Newton-Okounkov bodies and tropical geometry are two such combinatorial theories. As shown by Kaveh and Manon, there is…
The paper studies intrinsic geometry in the tropical plane. Tropical structure in the real affine $n$-space is determined by the integer tangent vectors. Tropical isomorphisms are affine transformations preserving the integer lattice of the…
A valuation-theoretic framework is developed for studying tropical degenerations of multilinear network games. Equilibrium conditions are modeled by an ideal over the Puiseux field, and valuation classes and cluster multiplicities are used…
To advance automated detection of extreme weather events, which are increasing in frequency and intensity with climate change, we explore modifications to a novel light-weight Context Guided convolutional neural network architecture trained…
This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…
The entropic barrier, studied by Bubeck and Eldan (Proc. Mach. Learn. Research, 2015), is a self-concordant barrier with asymptotically optimal self-concordance parameter. In this paper, we study the tropicalization of the central path…