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We propose the first general PAC-Bayesian generalization bounds for adversarial robustness, that estimate, at test time, how much a model will be invariant to imperceptible perturbations in the input. Instead of deriving a worst-case analysis of the risk of a hypothesis over all the possible perturbations, we leverage the PAC-Bayesian framework to bound the averaged risk on the perturbations for majority votes (over the whole class of hypotheses). Our theoretically founded analysis has the advantage to provide general bounds (i) independent from the type of perturbations (i.e., the adversarial attacks), (ii) that are tight thanks to the PAC-Bayesian framework, (iii) that can be directly minimized during the learning phase to obtain a robust model on different attacks at test time.
This paper proposes a black box based approach for analysing deep neural networks (DNNs). We view a DNN as a function $boldsymbol{f}$ from inputs to outputs, and consider the local robustness property for a given input. Based on scenario optimization
The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of clas
We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows
Owing to the susceptibility of deep learning systems to adversarial attacks, there has been a great deal of work in developing (both empirically and certifiably) robust classifiers. While most work has defended against a single type of attack, recent
One popular hypothesis of neural network generalization is that the flat local minima of loss surface in parameter space leads to good generalization. However, we demonstrate that loss surface in parameter space has no obvious relationship with gener