Ensemble Robustness and Generalization of Stochastic Deep Learning Algorithms
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.
 The paper studied the generalization ability of learning algorithms from the robustness viewpoint in a deep learning context. To achieve this goal, the authors extended the notion of the (K, .epsilon)- robustness proposed in Xu and Mannor, 2012 and introduced the ensemble robustness. Pros: 1, The problem studied in this paper is interesting. Both robustness and generalization are important properties of learning algorithms. It is good to see that the authors made some efforts towards this direction. 2, The paper is well shaped and is easy to follow. The analysis conducted in this paper is sound. Numerical experiments are also convincing. 3, The extended notion "ensemble robustness" is shown to be very useful in studying the generalization properties of several deep learning algorithms. Cons: 1, The terminology "ensemble" seems odd to me, and seems not to be informative enough. 2, Given that the stability is considered as a weak notion of robustness, and the fact that the stability of a learning algorithm and its relations to the generalization property have been well studied, in my view, it is quite necessary to mention the relation of the present study with stability arguments. 3, After Definition 3, the author stated that ensemble robustness is a weak notion of robustness proposed in Xu and Manner, 2012. It is better to present an example here immediately to illustrate.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Ensemble Robustness and Generalization of Stochastic Deep Learning Algorithms
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.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper studied the generalization ability of learning algorithms from the robustness viewpoint in a deep learning context. To achieve this goal, the authors extended the notion of the (K, .epsilon)- robustness proposed in Xu and Mannor, 2012 and introduced the ensemble robustness. Pros: 1, The problem studied in this paper is interesting. Both robustness and generalization are important properties of learning algorithms. It is good to see that the authors made some efforts towards this direction. 2, The paper is well shaped and is easy to follow. The analysis conducted in this paper is sound. Numerical experiments are also convincing. 3, The extended notion "ensemble robustness" is shown to be very useful in studying the generalization properties of several deep learning algorithms. Cons: 1, The terminology "ensemble" seems odd to me, and seems not to be informative enough. 2, Given that the stability is considered as a weak notion of robustness, and the fact that the stability of a learning algorithm and its relations to the generalization property have been well studied, in my view, it is quite necessary to mention the relation of the present study with stability arguments. 3, After Definition 3, the author stated that ensemble robustness is a weak notion of robustness proposed in Xu and Manner, 2012. It is better to present an example here immediately to illustrate.
assistant
 The paper studied the generalization ability of learning algorithms from the robustness viewpoint in a deep learning context. To achieve this goal, the authors extended the notion of the (K, .epsilon)- robustness proposed in Xu and Mannor, 2012 and introduced the ensemble robustness. Pros: 1, The problem studied in this paper is interesting. Both robustness and generalization are important properties of learning algorithms. It is good to see that the authors made some efforts towards this direction. 2, The paper is well shaped and is easy to follow. The analysis conducted in this paper is sound. Numerical experiments are also convincing. 3, The extended notion "ensemble robustness" is shown to be very useful in studying the generalization properties of several deep learning algorithms. Cons: 1, The terminology "ensemble" seems odd to me, and seems not to be informative enough. 2, Given that the stability is considered as a weak notion of robustness, and the fact that the stability of a learning algorithm and its relations to the generalization property have been well studied, in my view, it is quite necessary to mention the relation of the present study with stability arguments. 3, After Definition 3, the author stated that ensemble robustness is a weak notion of robustness proposed in Xu and Manner, 2012. It is better to present an example here immediately to illustrate.