Related papers: Tropical Bisectors and Carlini-Wagner Attacks

In recent years, deep neural networks demonstrated state-of-the-art performance in a large variety of tasks and therefore have been adopted in many applications. On the other hand, the latest studies revealed that neural networks are…

Complex-valued neural networks (CVNNs) are rising in popularity for all kinds of applications. To safely use CVNNs in practice, analyzing their robustness against outliers is crucial. One well known technique to understand the behavior of…

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 piecewise-linear structure aligned with dynamic programming…

We present an alternative layer to convolution layers in convolutional neural networks (CNNs). Our approach reduces the complexity of convolutions by replacing it with binary decisions. Those binary decisions are used as indexes to…

Given an algebraic variety defined over a discrete valuation field and a skeleton of its Berkovich analytification, the tropicalization process transforms function field of the variety to a semifield of tropical functions on the skeleton.…

Despite great success in many applications, deep neural networks are not always robust in practice. For instance, a convolutional neuron network (CNN) model for classification tasks often performs unsatisfactorily in classifying some…

Tropical Cyclones (TCs) are counted among the most destructive phenomena that can be found in nature. Every year, globally an average of 90 TCs occur over tropical waters, and global warming is making them stronger, larger and more…

Deploying convolutional neural networks (CNNs) for embedded applications presents many challenges in balancing resource-efficiency and task-related accuracy. These two aspects have been well-researched in the field of CNN compression. In…

Machine-learning architectures, such as Convolutional Neural Networks (CNNs) are vulnerable to adversarial attacks: inputs crafted carefully to force the system output to a wrong label. Since machine-learning is being deployed in…

Neural networks, being susceptible to adversarial attacks, should face a strict level of scrutiny before being deployed in critical or adversarial applications. This paper uses ideas from Chaos Theory to explain, analyze, and quantify the…

Network intrusion detection is critical for securing modern networks, yet the complexity of network traffic poses significant challenges to traditional methods. This study proposes a Temporal Convolutional Network(TCN) model featuring a…

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…

With the tremendous advances in the architecture and scale of convolutional neural networks (CNNs) over the past few decades, they can easily reach or even exceed the performance of humans in certain tasks. However, a recently discovered…

Network controllability robustness reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network…

In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…

Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial…

Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added…

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we…

Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…

We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a tropical variety, and whether it is connected, as well as…