title: Ensemble Robustness and Generalization of Stochastic Deep Learning Algorithms
abstract: 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.
authors: Tom Zahavy Bingyi Kang Alex Sivak Jiashi Feng Huan Xu Shie Mannor
hIndex: Jiashi Feng 76