Related papers: Empirically Measuring Concentration: Fundamental L…
Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find…
The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data…
A fundamental question in adversarial machine learning is whether a robust classifier exists for a given task. A line of research has made some progress towards this goal by studying the concentration of measure, but we argue standard…
Recent work in adversarial robustness suggests that natural data distributions are localized, i.e., they place high probability in small volume regions of the input space, and that this property can be utilized for designing classifiers…
Starting with Gilmer et al. (2018), several works have demonstrated the inevitability of adversarial examples based on different assumptions about the underlying input probability space. It remains unclear, however, whether these results…
Many modern machine learning classifiers are shown to be vulnerable to adversarial perturbations of the instances. Despite a massive amount of work focusing on making classifiers robust, the task seems quite challenging. In this work,…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
Recent studies have shown that modern deep neural network classifiers are easy to fool, assuming that an adversary is able to slightly modify their inputs. Many papers have proposed adversarial attacks, defenses and methods to measure…
Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp…
Making classifiers robust to adversarial examples is hard. Thus, many defenses tackle the seemingly easier task of detecting perturbed inputs. We show a barrier towards this goal. We prove a general hardness reduction between detection and…
Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
Machine learning models are vulnerable to tiny adversarial input perturbations optimized to cause a very large output error. To measure this vulnerability, we need reliable methods that can find such adversarial perturbations. For image…
Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…
Adversarial examples are a type of attack on machine learning (ML) systems which cause misclassification of inputs. Achieving robustness against adversarial examples is crucial to apply ML in the real world. While most prior work on…
Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…
Over the last few years, the phenomenon of adversarial examples --- maliciously constructed inputs that fool trained machine learning models --- has captured the attention of the research community, especially when the adversary is…
Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization. Specifically, an $\ell_2$ bounded adversary cannot alter the ensemble prediction generated by an additive isotropic…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…