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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…

Generating adversarial examples is an intriguing problem and an important way of understanding the working mechanism of deep neural networks. Most existing approaches generated perturbations in the image space, i.e., each pixel can be…

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

Adversarial robustness corresponds to the susceptibility of deep neural networks to imperceptible perturbations made at test time. In the context of image tasks, many algorithms have been proposed to make neural networks robust to…

Adversarial examples are inevitable on the road of pervasive applications of deep neural networks (DNN). Imperceptible perturbations applied on natural samples can lead DNN-based classifiers to output wrong prediction with fair confidence…

Adversarial attacks are widely used to identify model vulnerabilities; however, their validity as proxies for robustness to random perturbations remains debated. We ask whether an adversarial example provides a representative estimate of…

This paper studies the problem of detecting adversarial perturbations in a sequence of observations. Given a data sample $X_1, \ldots, X_n$ drawn from a standard normal distribution, an adversary, after observing the sample, can perturb…

Machine learning is vulnerable to adversarial examples-inputs designed to cause models to perform poorly. However, it is unclear if adversarial examples represent realistic inputs in the modeled domains. Diverse domains such as networks and…

The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability. While many deep neural networks have shown impressive performance in terms of predictive accuracy, it has been shown that…

Deep neural networks are at the forefront of machine learning research. However, despite achieving impressive performance on complex tasks, they can be very sensitive: Small perturbations of inputs can be sufficient to induce incorrect…

Deep neural networks are vulnerable to adversarial examples, i.e., carefully-perturbed inputs aimed to mislead classification. This work proposes a detection method based on combining non-linear dimensionality reduction and density…

Adversarial examples are a challenging open problem for deep neural networks. We propose in this paper to add a penalization term that forces the decision function to be at in some regions of the input space, such that it becomes, at least…

The existence of adversarial attacks on machine learning models imperceptible to a human is still quite a mystery from a theoretical perspective. In this work, we introduce two notions of adversarial attacks: natural or on-manifold attacks,…

A wide range of defenses have been proposed to harden neural networks against adversarial attacks. However, a pattern has emerged in which the majority of adversarial defenses are quickly broken by new attacks. Given the lack of success at…

Intentionally crafted adversarial samples have effectively exploited weaknesses in deep neural networks. A standard method in adversarial robustness assumes a framework to defend against samples crafted by minimally perturbing a sample such…

We establish a theoretical link between adversarial training and operator norm regularization for deep neural networks. Specifically, we prove that $\ell_p$-norm constrained projected gradient ascent based adversarial training with an…

State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the perturbations can \textit{transfer across models}:…

It has been suggested that adversarial examples cause deep learning models to make incorrect predictions with high confidence. In this work, we take the opposite stance: an overly confident model is more likely to be vulnerable to…

The burgeoning success of deep learning has raised the security and privacy concerns as more and more tasks are accompanied with sensitive data. Adversarial attacks in deep learning have emerged as one of the dominating security threat to a…

Robustness is a key requirement for widespread deployment of machine learning algorithms, and has received much attention in both statistics and computer science. We study a natural model of robustness for high-dimensional statistical…