We conduct a large experimental comparison of various robustness metrics for image classification. The main question of our study is to what extent current synthetic robustness interventions ( p -adversarial examples, noise corruptions, etc.) promote robustness under natural distribution shifts occuring in real data. To this end, we evaluate 147 ImageNet models under 199 different evaluation settings. We find that no current robustness intervention improves robustness on natural distribution shifts beyond a baseline given by standard models without a robustness intervention. The only exception is the use of larger training datasets, which provides a small increase in robustness on one natural distribution shift. Our results indicate that robustness improvements on real data may require new methodology and more evaluations on test sets representing natural distribution shifts.
============================================ Update after rebuttal =========================================
I thank the authors for their detailed rebuttal. I'm in general satisfied with the authors' response to my concerns, so as promised, I'm happy to increase my score.
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This paper considers the relationship between various measures of synthetic robustness and two distinct measures of natural robustness in large scale image classification models. The authors argue that the synthetic robustness measures considered in this paper are not predictive of natural robustness when the effect of baseline accuracy is subtracted. I think, if true, this is an important message that researchers in this area need to be aware of. However, I have a number of questions and concerns about the results. I would be happy to increase my score if the authors could address some of these issues:
1) Another important recent benchmark not mentioned in the paper is ImageNet-A (https://github.com/hendrycks/natural-adv-examples). I would encourage the authors to include this benchmark among their natural robustness measures (in addition to ImageNetV2 and ImageNetVidRobust). The advantage of this dataset is that because it samples from the error distribution of a high-performing ImageNet model, to a large extent, it already comes with the baseline subtracted, so it essentially obviates the need for the indirect effective robustness measure introduced here. The raw accuracies on ImageNet-A would be directly interpretable and they would also answer the question “why should we care?” in a more visceral way, because even the Instagram trained state-of-the-art ImageNet models seem to achieve a mere 17% accuracy on this benchmark: https://arxiv.org/abs/1907.07640
2) There seems to be a direct conflict between the main conclusion of this paper (that synthetic robustness measures do not predict natural robustness) and an opposite conclusion reached in an earlier paper (https://arxiv.org/abs/1904.10076) where the authors claim that robustness against synthetic perturbations like translation, hue, and saturation are actually highly predictive of video robustness (not sure if this would generalize to ImageNetV2). As far as I can see, these particular perturbation types are not included among the synthetic perturbations considered in this paper. Can you please clarify this discrepancy? 
3) Relatedly, looking at the scatter plots of effective robustness vs. robustness against individual perturbations in the appendix, especially for the video robustness measure, some of the correlations seem to be pretty significant (for example, video robustness vs. jpeg compression robustness, p. 19). So, I am wondering to what extent the main conclusion of this paper might just be driven by the averaging of a large number of non-predictive perturbations and a smaller number of more predictive perturbations. 
4) Also, ImageNet-P perturbations are not included in the paper. If the authors want to make their claims more reliable, I would encourage them to consider these among their synthetic perturbations as well. The translation perturbation in ImageNet-P, in particular, would be particularly important to consider for video robustness given the results from the arxiv pre-print mentioned in 2) above.