Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: This paper examines generalization performance of various neural network architectures in terms of a sensitivity metric that approximates how the error responds to perturbations of the input. A crude argument is presented for how the proposed sensitivity metric captures the variance term in the standard bias-variance decomposition of the loss. A number of experimental results are presented that show strong correlation between the sensitivity metric and the empirical test loss.

Understanding the distinguishing characteristics of networks that generalize well versus networks that generalize poorly is a central challenge in modern deep learning research, so the topic and analyses presented in this paper are salient and will be of interest to most of the community. The experimental results are intriguing and the presentation is clear and easy to read. While some may object to the egregious simplifications utilized in "deriving" the sensitivity metric, I believe this kind of analysis should be welcomed if it produces new insights and helps explain otherwise opaque empirical phenomena. All told, if taken in isolation from prior work, I think the insights and empirical results presented in this paper are quite interesting and certainly sufficient for acceptance to ICLR.

However, there is significant overlap with prior work that severely detracts from the novelty of the results presented here, and I think the community is already familiar with the paper's main conclusions. From the empirical viewpoint, [1] performs a very similar (and actually quite a bit more thorough) analysis, and reaches very similar conclusions. The authors do cite [1], but unless I missed something, their main argument for uniqueness is basically "in experiments, we prefer S to the Jacobian, because in order to compute S it is enough to look at the network as a black box that given an input, generates an output, without requiring further knowledge of the model." While this may be useful from the practical standpoint for some non-differentiable models, I'm not convinced that this distinction is really significant in terms of building insights or new understanding. 

One additional way this paper is distinct from [1] is that it includes a theoretical "derivation" for the sensitivity metric. While I found the argument interesting, from the theoretical perspective, [2] gives much more rigorous and insightful arguments that help explain the observed phenomena. 

Overall, I'm just not convinced this paper is novel enough to merit publication. But perhaps I've overlooked something, in which case I hope the author's response can highlight their unique contributions relative to prior work.

[1] Novak, Roman, et al. "Sensitivity and generalization in neural networks: an empirical study." arXiv preprint arXiv:1802.08760 (2018).
[2] Arora, Sanjeev, et al. "Stronger Generalization Bounds for Deep Nets via a Compression Approach." International Conference on Machine Learning. 2018.
review_title: Official Blind Review #3

final_score: rating: 3: Weak Reject
review_content: This paper studies the connection between sensitivity and generalization where sensitivity is roughly defined as the variance of the output of the network when gaussian noise is added to the input data (generated from the same distribution as the training error).

The paper is well-written and the experiments are very comprehensive. There are however 3 major issues with the current approach:

1- Novelty: Novak et al. 2018 suggests a very similar notation of sensitivity and they show correlation with generalization. Even though the authors site this work, they don't discuss the connection very clearly. In light of that work, there is very limited novelty in this paper.

2- Definition of test loss: Authors define the test loss to be cross-entropy but in almost all these tasks, what we care about is the task-loss which is 0/1 classification error on the test data and not the cross-entropy loss. These two loss behave very differently. In particular, the cross-entropy loss is very sensitive to the of variance of the output while 0/1 classification loss does not depend on it. Therefore, it is not surprising that there is high correlation between the output variance and the cross-entropy loss but it is not clear if this has anything to do with the test error.

3- Using test data in the complexity measure: The goal of understanding generalization is not just to get correlation with the test error. One can always use a validation set to get a very good correlation. Even when we have limited data, we can always put a small portion of the data for validation without loosing much in the final performance. The main goal is to predict generalization without using any access to the distribution. In particular, we need properties that show how networks behave on new data instead of simply measuring a property on the new data. Therefore, using a measure that is evaluated on new data is not really helpful.


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After author rebuttals:

Authors have addressed one of my concerns (no 3) but the other two concerns are not addressed adequately. I increase my score to "weak reject" but not higher because of my concern about the novelty of the work in light of Novak et al. 2018.
review_title: Official Blind Review #2

Meta-review: The paper proposes a definition of the sensitivity of the output to random perturbations of the input and its link to generalization.

While both reviewers appreciated the timeliness of this research, they were taken aback by the striking similarity with the work of Novak et al. I encourage the authors to resubmit to a later conference with a lengthier analysis of the differences between the two frameworks, as they started to do in their rebuttal.
Decision: Reject