Ensemble Robustness of Deep Learning Algorithms

The question why deep learning algorithms perform so well in practice has puzzled machine learning theoreticians and practitioners alike. However, most of well-established approaches, such as hypothesis capacity, robustness or sparseness, have not provided complete explanations, due to the high complexity of the deep learning algorithms and their inherent randomness. In this work, we introduce a new approach – ensemble robustness – towards characterizing the generalization performance of generic deep learning algorithms. Ensemble robustness concerns robustness of the population of the hypotheses that may be output by a learning algorithm. Through the lens of ensemble robustness, we reveal that a stochastic learning algorithm can generalize well as long as its sensitiveness to adversarial perturbation is bounded in average, or equivalently, the performance variance of the algorithm is small. Quantifying the ensemble robustness of various deep learning algorithms may be difficult analytically. However, extensive simulations for seven common deep learning algorithms for different network architectures provide supporting evidence for our claims. In addition, as an example for utilizing ensemble robustness, we propose a novel semi-supervised learning method that outperforms the state-of-the-art. Furthermore, our work explains the good performance of several published deep learning algorithms.