Related papers: Tail Adversarial Stability for Regularly Varying L…

The safety and robustness of learning-based decision-making systems are under threats from adversarial examples, as imperceptible perturbations can mislead neural networks to completely different outputs. In this paper, we present an…

Current research on defending against adversarial examples focuses primarily on achieving robustness against a single attack type such as $\ell_2$ or $\ell_{\infty}$-bounded attacks. However, the space of possible perturbations is much…

Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…

We introduce the relative tail entropy to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail entropy is conserved by the principal extension.

Despite extraordinary progress, current machine learning systems have been shown to be brittle against adversarial examples: seemingly innocuous but carefully crafted perturbations of test examples that cause machine learning predictors to…

In this paper, we consider a simple estimator for tail dependence coefficients of a max-stable time series and show its asymptotic normality under a mild condition. The novelty of our result is that this condition does not involve mixing…

For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…

The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…

This work studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via…

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…

Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when implemented as digital tasks on an embedded platform. This…

Adversarial training is one of the most effective approaches defending against adversarial examples for deep learning models. Unlike other defense strategies, adversarial training aims to promote the robustness of models intrinsically.…

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is…

Adversarial robustness studies the worst-case performance of a machine learning model to ensure safety and reliability. With the proliferation of deep-learning-based technology, the potential risks associated with model development and…

We study the model robustness against adversarial examples, referred to as small perturbed input data that may however fool many state-of-the-art deep learning models. Unlike previous research, we establish a novel theory addressing the…

Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we…