相关论文: Tropical Bisectors and Carlini-Wagner Attacks

In this research, we investigate a tropical principal component analysis (PCA) as a best-fit Stiefel tropical linear space to a given sample over the tropical projective torus for its dimensionality reduction and visualization. Especially,…

Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of…

We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is…

When modeling the dynamics of infectious disease, the incorporation of contact network information allows for the capture of the non-randomness and heterogeneity of realistic contact patterns. Oftentimes, it is assumed that the underlying…

Although convolutional neural networks (CNNs) are now widely used in various computer vision applications, its huge resource demanding on parameter storage and computation makes the deployment on mobile and embedded devices difficult.…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr$_0(3,8)$, and show that it refines the…

This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…

Deep neural networks (DNN) are increasingly applied in safety-critical systems, e.g., for face recognition, autonomous car control and malware detection. It is also shown that DNNs are subject to attacks such as adversarial perturbation and…

We study algebraic and combinatorial aspects of (classical) projections of $m$-dimensional tropical varieties onto $(m+1)$-dimensional planes. Building upon the work of Sturmfels, Tevelev, and Yu on tropical elimination as well as the work…

Geometry and topology of decision regions are closely related with classification performance and robustness against adversarial attacks. In this paper, we use differential geometry to theoretically explore the geometrical and topological…

From transportation networks to complex infrastructures, and to social and economic networks, a large variety of systems can be described in terms of multiplex networks formed by a set of nodes interacting through different network layers.…

Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this…

Woven fabrics play an essential role in everyday textiles for clothing/sportswear, water filtration, and retaining walls, to reinforcements in stiff composites for lightweight structures like aerospace, sporting, automotive, and marine…

Lightning plays a crucial role in the Earth's climate system, yet existing parameterizations for use in forecasting and earth system models show room for improvement in capturing spatial and temporal variations in its frequency. This study…

A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…

In this paper we generalize correspondence theorems of Mikhalkin and Nishinou-Siebert providing a correspondence between algebraic and parameterized tropical curves. We also give a description of a canonical tropicalization procedure for…

We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the…

Adversarial attacks have been proven to be potential threats to Deep Neural Networks (DNNs), and many methods are proposed to defend against adversarial attacks. However, while enhancing the robustness, the clean accuracy will decline to a…

We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges, and subgraphs, our metric graph kernels are purely based on…