相关论文: Tropical Bisectors and Carlini-Wagner Attacks

Robustness against adversarial attack in neural networks is an important research topic in the machine learning community. We observe one major source of vulnerability of neural nets is from overparameterized fully-connected layers. In this…

While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…

Progress in making neural networks more robust against adversarial attacks is mostly marginal, despite the great efforts of the research community. Moreover, the robustness evaluation is often imprecise, making it difficult to identify…

Deep learning-based weather forecasting (DLWF) models leverage past weather observations to generate future forecasts, supporting a wide range of downstream applications, including tropical cyclone (TC) prediction. In this paper, we…

We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReLU neural networks is contained as a semialgebraic set inside…

Maxmin-$\omega$ is a new threshold model, where each node in a network waits for the arrival of states from a fraction $\omega$ of neighborhood nodes before processing its own state, and subsequently transmitting it to downstream nodes.…

In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…

This article discusses a combinatorial extension of tropical intersection theory to spaces given by glueing quotients of partially open convex polyhedral cones by finitely many automorphisms. This extension is done in terms of linear…

Deep learning algorithms have been recently targeted by attackers due to their vulnerability. Several research studies have been conducted to address this issue and build more robust deep learning models. Non-continuous deep models are…

Robustness of convolutional neural networks (CNNs) has gained in importance on account of adversarial examples, i.e., inputs added as well-designed perturbations that are imperceptible to humans but can cause the model to predict…

We give several characterizations of stable intersections of tropical cycles and establish their fundamental properties. We prove that the stable intersection of two tropical varieties is the tropicalization of the intersection of the…

We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…

We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is arXiv:1509.07453, where a tropical-algebraic correspondence theorem…

Distributed deep neural networks (DNNs) have been shown to reduce the computational burden of mobile devices and decrease the end-to-end inference latency in edge computing scenarios. While distributed DNNs have been studied, to the best of…

We fix the supports A=(A_1,...,A_k) of a list of tropical polynomials and define the tropical resultant TR(A) to be the set of choices of coefficients such that the tropical polynomials have a common solution. We prove that TR(A) is the…

We discuss a novel analysis method for reaction network systems with polynomial or rational rate functions. This method is based on computing tropical equilibrations defined by the equality of at least two dominant monomials of opposite…

The Lightning Network is the most widely used payment channel network (PCN) to date, making it an attractive attack surface for adversaries. In this paper, we analyze the Lightning Network's PCN topology and investigate its resilience…

Recently, adversarial deception becomes one of the most considerable threats to deep neural networks. However, compared to extensive research in new designs of various adversarial attacks and defenses, the neural networks' intrinsic…

We develop a combinatorial framework to study certain polyhedral maps which are higher-dimensional analogues of tropical covers between metric graphs. Under a mild combinatorial assumption, we show that a map satisfies the so-called…

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their…