The question why deep learning algorithms generalize so well has attracted increasing
 research interest. However, most of the well-established approaches,
 such as hypothesis capacity, stability or sparseness, have not provided complete
 explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this work, we focus
 on the robustness approach (Xu & Mannor, 2012), i.e., if the error of a hypothesis
 will not change much due to perturbations of its training examples, then it
 will also generalize well. As most deep learning algorithms are stochastic (e.g.,
 Stochastic Gradient Descent, Dropout, and Bayes-by-backprop), we revisit the robustness
 arguments of Xu & Mannor, and introduce a new approach – ensemble
 robustness – that concerns the robustness of a population of hypotheses. Through
 the lens of ensemble robustness, we reveal that a stochastic learning algorithm can
 generalize well as long as its sensitiveness to adversarial perturbations is bounded
 in average over training examples. Moreover, an algorithm may be sensitive to
 some adversarial examples (Goodfellow et al., 2015) but still generalize well. To
 support our claims, we provide extensive simulations for different deep learning
 algorithms and different network architectures exhibiting a strong correlation between
 ensemble robustness and the ability to generalize.
Explaining the generalization of stochastic deep learning algorithms, theoretically and empirically, via ensemble robustness This paper presents an adaptation of the algorithmic robustness of Xu&Mannor'12 and presents learning bounds and an experimental showing correlation between empirical ensemble robustness and generalization error.  Proposes a study of the generalization ability of deep learning algorithms using an extension of notion of stability called ensemble robustness and gives bounds on generalization error of a randomized algorithm in terms of stability parameter and provides empirical study attempting to connect theory with practice. The paper studied the generalization ability of learning algorithms from the robustness viewpoint in a deep learning context