Ensemble Robustness and Generalization of Stochastic Deep Learning Algorithms
This work addresses the fundamental challenge of understanding generalization in deep learning for researchers, offering a novel perspective that could inform algorithm design, though it appears incremental as it builds on existing robustness theory.
The paper tackles the problem of explaining generalization in deep learning by introducing ensemble robustness, a new approach focusing on the robustness of a population of hypotheses, and shows through simulations that stochastic algorithms can generalize well if their average sensitivity to perturbations is bounded, even if sensitive to some adversarial examples.
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.