Title: WHEN ROBUSTNESS DOESN'T PROMOTE ROBUST-NESS: SYNTHETIC VS. NATURAL DISTRIBUTION SHIFTS ON IMAGENET

Abstract: 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.

1. INTRODUCTION:

Reliable classification under distribution shift is still out of reach for current machine learning (Torralba et al., 2011; Recht et al., 2019) . As a result, the research community has proposed a wide range of evaluation protocols that go beyond a single, static test set. Common examples include adversarial examples (Szegedy et al., 2013; Biggio et al., 2013) , noise perturbations (Geirhos et al., 2018; Hendrycks & Dietterich, 2019) , and spatial transformations (Fawzi & Frossard, 2015; Engstrom et al., 2019) . Encouragingly, the past few years have seen substantial progress in robustness to these distribution shifts, e.g., see (Madry et al., 2018; Zhang et al., 2019; Geirhos et al., 2019; Zhang, 2019; Engstrom et al., 2019; Yang et al., 2019) and many others. However, an implicit assumption underlying this research direction is that robustness to such synthetic distribution shifts will lead to models that also perform more reliably on natural distribution shifts.

We challenge that assumption. We conduct a large experimental study involving 147 ImageNet models evaluated under 199 different evaluation settings for a total of 29,253 test set evaluations. Our model testbed contains a wide range of standard models and most proposed robustness interventions (adversarial training, various forms of data augmentation, etc.). In order to measure robustness under natural distribution shift, we utilize two recently proposed variants of ImageNet (Deng et al., 2009; Russakovsky et al., 2015) and ImageNetVid (Berg et al., 2015) . Both test sets consist entirely of unperturbed images drawn from the same sources as the original datasets, but also exhibit substantial accuracy drops for all current model architectures (Recht et al., 2019; Shankar et al., 2019) .

Figure 1 shows the main result of our evaluation. The plots display model accuracies for the two natural distribution shifts. As noted in prior work, there is a substantial drop in accuracy when going from the original test set to the test set with distribution shift. A priori, one may hope that a more robust model would see a smaller drop than baseline approaches without a robustness intervention. But we find that in both cases, current robustness interventions offer little to no benefit over standard models. In particular, the accuracy on the original test set alone almost perfectly predicts the accuracy on the test sets with distribution shift. Importantly, the same relationship between original and "shifted" accuracy holds for both standard models and models with an explicit robustness intervention. This implies that the robustness interventions do not close the gap between original and "shifted" test accuracies any more than standard models with the same accuracy.

Figure 1 : Model accuracy on the two natural distribution shifts, ImageNetV2 (left) and Ima-geNetVidRobust (right) . Each data point corresponds to one model in our testbed and is shown with 99.5% Clopper-Pearson confidence intervals. The plots demonstrate that the standard test accuracy (x-axis) is an almost perfect predictor for the test accuracy under distribution shift (y-axis). This holds regardless of whether the model was trained with a robustness intervention. Current robustness interventions reduce the accuracy drops under these distribution shifts only by a small amount (on ImageNetVidRobust) or not at all (on ImageNetV2). The axes were adjusted using logit scaling and the linear fit was computed in the scaled space. The red shaded region is a 95% confidence region for the linear fit from 100,000 bootstrap samples.

There are only two significant deviations away from the otherwise universal relationship between original and shifted accuracy. The first is that p -adversarially robust models do offer increased accuracy against the distribution shift on ImageNetVidRobust. However, this increase is in a regime of overall low accuracy. As we will demonstrate in Section 5, interpolating between a standard model and a random classifier yields a comparable robustness increase in this accuracy regime. So the current p -robust models do not provide a truly new robustness trade-off.

The second class of outliers are models trained on substantially different data. In particular, the two most pronounced outliers on ImageNetV2 correspond to models trained on 10× to 1,000× more training examples. This shows that adding more training data does indeed increase robustness on ImageNetV2 more than any other currently proposed explicit robustness intervention. However, adding more data also yields only small gains: the accuracy drops of around 10% from ImageNet to ImageNetV2 shrink by 1 -2%, even when adding 1,000× more data.

Overall, our results show that current robustness gains on synthetic distribution shifts do not transfer to improved robustness on the natural distribution shifts presently available as test sets. This suggests that research on reliable machine learning may currently be focusing on interventions that do not promote robustness on natural distribution shifts. Achieving robustness on real data may instead require new methodology and more evaluations on natural distribution shifts.

To aid this development, we will release and maintain our robustness testbed as a platform for proposing and evaluating new models and datasets. In total, our testbed includes prediction data for 29,253,000 pairs of models and image inputs. We hope that a comprehensive repository for robustness evaluations will simplify the process of comparing proposed models and evaluation settings and enable further analysis of robustness questions.

In the next section, we describe our experimental setup in detail. Section 3 introduces our main measure of robustness. The following three sections then investigate our three main questions:

• Are synthetic robustness measures predictive of performance on natural distribution shifts?

• What robustness interventions are effective for natural distribution shifts?

• How does the amount of training data impact robustness?

2. EXPERIMENTAL SETUP:

We first formally define our experimental setup. In the standard classification setting, a model f is first trained on i.i.d. samples from a fixed data distribution. We then test f on another set S 1 of i.i.d.

samples from the same distribution to compute the test accuracy acc S1 ( f ) = (x,y)∈S1 I[ f (x) = y].

We refer to any deviation from this setup as a distribution shift.

More specifically, our robustness evaluation involves distribution shifts defined as follows. Instead of using the original test set S 1 , we may also evaluate the accuracy on a new test set S 2 that is collected via a similar but not identical procedure to the original test set S 1 (i.e., S 2 represents a different distribution). Moreover, we allow each data point (either from S 1 or S 2 ) to be pertubed before passing it to the classifier f . We consider a general setup where the perturbation π(x, y, f ) may depend on the model f to be evaluated. For instance, we can generate ∞ -adversarial examples by setting π(x, y, f ) = arg min x-x ∞≤ε I[ f (x ) = y]. Alternatively, we can simply perturb each data point with Gaussian noise, i.e., π(x, y, f ) = x + N (0, σ 2 ) independently of y and f .

Combining the choice of test set S and perturbation π, the test accuracy under distribution shift S, π is then defined as acc S,π ( f ) = (x,y)∈S

I[ f (π(x, y, f )) = y] .

Depending on S and π, this "shifted" test accuracy may be higher or lower than the original accuracy acc S1 . The focus of this paper is on distribution shifts where there is reasonable hope to classify the images correctly (e.g., because humans can do so), but standard models achieve only a substantially lower accuracy than on the original test set. Reducing these accuracy gaps between original and shifted accuracy is an important goal of robust machine learning.

2.1. TYPES OF DISTRIBUTION SHIFTS:

At a high level, we distinguish between two main types of distribution shift. The crucial distinction between the two is whether the distribution shift involves a synthetic intervention at the pixel level. We use the term natural distribution shift for cases that rely only on unmodified images. In contrast, we refer to distribution shifts as synthetic if they involve modifications of existing test images.

To be concrete, we now provide an overview of the various distribution shifts in our robustness evaluation.

2.1.1. NATURAL DISTRIBUTION SHIFTS:

Our testbed includes two distribution shifts that involve only unmodified natural images.

ImageNetV2.:

The first example is the new ImageNetV2 test set recently collected by Recht et al. (2019) . The goal of this test set was to closely reproduce the original ImageNet dataset creation process, e.g., by matching the data source (Flickr) and the data cleaning process (Mechanical Turk). Nevertheless, the authors found that state-of-the-art models still suffer a performance drop of at least 11% on the new test set. This makes the dataset an interesting example for studying robustness to natural distribution shifts. Testing on ImageNetV2 fits into our evaluation framework by letting S be the new ImageNetV2 test set (denoted by S 2 ) and leaving π to be the identity function.

ImageNetVidRobust. In contrast to precisely defined, synthetic notions of robustness such as padversarial examples, it is currently an open problem to characterize the distribution shift arising in ImageNetV2. To narrow this gap between the real and synthetic robustness challenges, Shankar et al. (2019) have introduced a variant of the ImageNetVid dataset (Berg et al., 2015) . The authors assembled consecutive video frames that are all highly similar to a human yet cause classifiers to make errors on some of the images. Inspired by p -adversarial examples, the authors propose the following pm k (plus-minus k) metric to evaluate the accuracy of a classifier as

pm k,S ( f ) = (x,y)∈S min x ∈B k (x) I[ f (x ) = y] ,

where B k (x) contains the 2k frames around the anchor frame x (k frames in each temporal direction). This corresponds to a perturbation function π(x, y,

f ) = arg min x ∈B k (x) I[ f (x ) = y].

Under this metric, the authors find that even the best models see an accuracy drop of at least 13%.

2.1.2. SYNTHETIC DISTRIBUTION SHIFTS:

The research community has developed a wide range of synthetic robustness notions for image classification over the past five years. In our study, we consider the following classes of synthetic distribution shifts.

Adversarial examples. One prominent example of synthetic distribution shifts are adversarial examples, which demonstrate that current image classifiers can be fooled by small image perturbations that are (almost) imperceptible to a human (Szegedy et al., 2013; Biggio & Roli, 2018) . In our robustness evaluation, we focus on untargeted adversarial perturbations bounded in ∞ -or 2 -norm.

Image corruptions. Since p -adversarial examples are unlikely to occur outside a truly worstcase setting, the research community has proposed various synthetic image corruptions as less adversarial distribution shifts. The goal of these corruptions is to test robustness to distribution shifts that are more realistic and hopefully predictive of performance on real data (we will investigate this assumption in Section 4). In our testbed, we include all corruptions from (Hendrycks & Dietterich, 2019) and additionally some corruptions from (Geirhos et al., 2018) . These include common examples of image noise (Gaussian, shot noise, etc.), various blurs (Gaussian, motion), simulated weather conditions (fog, snow), and "digital" corruptions such as various JPEG compression levels.

We refer the reader to Appendix A.6.3 for a full list of the 38 corruptions.

Style transfer. We also include a style transfer version of the ImageNet test set (Huang & Belongie, 2017) . This distribution shift was proposed to evaluate whether classification models are relying more on shape or texture features (Geirhos et al., 2019) .

2.2. CLASSIFICATION MODELS:

Our model testbed includes 147 ImageNet models covering a variety of different architectures and training methodologies. Our goal was to include most relevant pretrained ImageNet models available online. In multiple cases we also contacted paper authors with various degrees of success. At a high level, the models can be divided into the following three categories (see Appendix A.5.1 for a list of all models).

Standard models. We refer to models trained on the ILSVRC 2012 training set without a specific robustness focus as standard models. This category includes 74 models, ranging from the seminal AlexNet with top-1 accuracy 56.5% through widely used architectures such as VGG, ResNet, and Inception to the state-of-the-art EfficientNet with top-1 accuracy 84.4% (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014; He et al., 2016; Szegedy et al., 2015; Tan & Le, 2019) .

Robust models. This category includes models with an explicit robustness intervention. We subdivide this class further into two types of robustness interventions:

• Models with increased adversarial robustness. We include both models trained with projected gradient descent (Xie et al., 2019; Shafahi et al., 2019) and models with evaluation via randomized smoothing (Cohen et al., 2019; Salman et al., 2019) , which yields a total of 14 models. • Further robustness interventions such as data augmentation schemes (Geirhos et al., 2019; Yun et al., 2019) and anti-aliasing (Zhang, 2019) . This subset contains 51 models.

Models trained on more data. Finally, our testbed also contains three types of models that utilized substantially more training data than the aforementioned models. The ResNet152-ImageNet11k model was trained on 12.4 million images for 11,221 classes from the full ImageNet dataset (Wu, 2016) . Like all other models, we only evaluate it over the 1,000 classes from ILSVRC 2012. Facebook recently released models trained on 1 billion images from Instagram; we refer to these models as Instagram models (Mahajan et al., 2018) . We also include evaluations from the JFT-300M model trained on 300 million images at Google (Sun et al., 2017) .

3. MEASURING THE EFFECT OF ROBUSTNESS INTERVENTIONS:

When comparing interventions to increase robustness, a crucial question is how to measure their effect in a meaningful way. One approach would be to simply use the absolute accuracy numbers acc S,π under the distribution shift specified by S and π (see Section 2 above). If the goal is to select the best performing model (e.g., for a concrete deployment), this is indeed a relevant criterion.

On the other hand, relying on absolute accuracy numbers becomes less relevant when comparing various robustness interventions with different unperturbed accuracies acc S1 . As can be seen from Figure 1 , the accuracy under distribution shift varies substantially with the standard accuracy: models with higher standard accuracy already achieve higher accuracy under distribution shift. So to isolate the effect of a training intervention on the robustness to distribution shift, we would like to measure how much a robustness intervention increases the shifted accuracy beyond what is possible with standard models at the same standard accuracy.1 

To quantify this notion of robustness, we define a "baseline" function β S,π (x) to return the shifted accuracy that a standard model with test accuracy x on the standard test set S 1 is expected to achieve under the distribution shift S, π. So if f is a model without robustness intervention, β should satisfy β S,π (acc S1 ( f )) = acc S,π ( f ).

A priori, it is unclear if such a function β exists. The accuracy of a trained model f on the distribution shift (S, π) could depend on a variety of properties besides the standard accuracy of f (model architecture, data augmentation scheme used during training, etc.). However, both natural distribution shifts we study in our paper have the intriguing property that the standard test accuracy is a nearly perfect predictor of the test accuracy under distribution shift for all standard models in our testbed. In particular, fitting a simple logistic model to the (acc S1 ( f ), acc S,π ( f )) pairs yields a good linear fit in the logit domain (see Figure 1 ). This shows that we can obtain an accurate estimate β from data, which we will rely on in the remainder of the paper.

With the baseline robustness function β in place, we can now define the effective robustness ρ( f , S, π) of a trained model f to distribution shift (S, π) as

ρ( f , S, π) = acc S,π ( f ) -β S,π (acc S1 ( f )) ,

If a model f is truly more robust under distribution shift S, π (in particular, more so than standard models without a robustness intervention), f should have effective robustness ρ( f , S, π) substantially larger than 0. Graphically, ρ can be interpreted as the vertical deviation away from the linear fit in Figure 1 . In the following, we will study to what extent various synthetic robustness measures are predictive of the effective robustness on natural distribution shifts, and which models achieve the largest effective robustness on natural distribution shifts.

4. DOES SYNTHETIC ROBUSTNESS PREDICT NATURAL ROBUSTNESS?:

Given the difficulty of measuring a model's robustness to natural distribution shifts, an important question is whether there are simple synthetic proxies. We therefore study to what extent robustness to synthetic distribution shifts predicts robustness on natural distribution shift.

A simple approach would be to directly compare different models' robustness to synthetic distribution shift and their robustness to natural distribution shift. However, we run into an important confounding factor. As mentioned earlier, models that have higher accuracy have a smaller accuracy drop on the natural distribution shifts we consider. Moreover, we find that models with higher accuracy also see smaller accuracy drops under various synthetic distribution shifts. Therefore it would not be methodologically sound to directly compare synthetic robustness to natural robustness and draw any conclusions about transferability between the two. Simply the fact that a model is more accurate will simultaneously predict both that (i) the accuracy drop under natural distribution shift will be smaller, and that (ii) the model will be more robust to synthetic distribution shift.

To control for the confounder standard accuracy, we rely on the effective robustness notion introduced in Section 3, i.e., the robustness increase that cannot be attributed to an increase in standard accuracy. In Figure 2 , we analyze the relationship between two synthetic robustness notions and effective robustness on ImageNetV2. The resulting plot shows that the two quantities are almost entirely uncorrelated: a model being more robust to synthetic perturbations does not imply that the model will have a smaller accuracy drop on ImageNetV2. In Appendix A.1, we repeat the above experiment for the ImageNetVidRobust distribution shift and reach similar conclusions. The left plot shows synthetic robustness as measured by an average over image corruptions from (Hendrycks & Dietterich, 2019; Geirhos et al., 2018; 2019) . The right plot shows synthetic robustness as measured by PGD attacks for 2 -and ∞ -robustness and two perturbation sizes each. In both cases, synthetic robustness is not predictive of effective robustness under the natural distribution shift. Appendices A.1 and A.2 contains similar plots for individual synthetic robustness measures and the ImageNetVidRobust distribution shift.

5. WHAT HELPS WITH NATURAL DISTRIBUTION SHIFT?:

As can be seen in Figure 1 , most models did not achieve substantial effective robustness on ImageNetV2 and ImageNetVidRobust. Nevertheless, a few model types stood out with significant effective robustness on one of the two datasets (no model in our testbed that showed non-trivial gains for both natural distrbution shifts). We now discuss the main outliers in more detail.

ResNet152-ImageNet11k and Instagram models. The left plot in Figure 3 zooms to the two model families that displayed high effective robustness on ImageNetV2. All of these models are trained on additional data beyond the standard ILSVRC 2012 training set. The models exhibited an effective robustness of 2.0 and 1.4 (median robustness for the four Instagram models), which was substantially larger than any other model with similar accuracy. However, despite their promising performance on ImageNetV2, these models show little to no effective robustness for Ima-geNetVidRobust. Moreover, the effective robustness gain is larger for the ResNet152-ImageNet11k model trained on less data than the Instagram models. To further investigate the effect of data on model robustness, we conduct a series of controlled experiments in Section 6.

p -robust models. In the right plot of Figure 1 we see a cluster of p -adversarially robust classifiers that all exhibit substantial effective robustness for ImageNetVidRobust. However, the models are also in a low accuracy regime, in particular lower than the standard classifiers they were derived from (this trade-off is discussed in (Tsipras et al., 2019; Raghunathan et al., 2019) among others). This trade-off poses a potential confounding factor: although the p -robust models show high effective robustness, it is not clear if the resulting accuracy trade-off is meaningful. To put the trade-off into context, we compare the models to a simple baseline. In particular, consider the family of classifiers given by interpolating between random guessing and the standard classifier the p -robust models are derived from. Since random guessing is not affected by the distribution shift, this interpolation can trade off standard accuracy for effective robustness. In the right plot of Figure 3 , we illustrate this family of interpolated classifiers (the dotted line) and show that a standard ResNet152 with no robustness interventions can be interpolated with a random classifier to achieve the same trade-off as an p -robust model. So for the purpose of the natural distribution shift on ImageNetVidRobust, the p -robust models offer no benefit beyond interpolating with a random classifier.

6. HOW DOES THE AMOUNT OF TRAINING DATA IMPACT ROBUSTNESS?:

In the previous section we have seen that the ResNet152-ImageNet11k and Instagram models achieve non-zero effective robustness on ImageNetV2. This is a plausible effect since larger training sets provide a more thorough sampling of real world images. However, the JFT-300M model does not display this effect despite being trained on 300× more data than standard models. ImageNet-Vid-Robust Benign Accuracy A possible explanation could be that differences in label diversity or quality play a role in promoting robustness. For example, the Instagram models are trained on a dataset collected to overlap with the ILSVRC categories, and the ResNet152-ImageNet11k model is trained on a superset of the ILSVRC data. Meanwhile, the JFT model is trained on a long-tail, weakly-labeled dataset with 18,291 categories, which, to the best of our knowledge, were not collected to align with ILSVRC categories. To investigate the role of data in more detail, we now conduct two experiments.

Varying the number of images per class. We start by subsampling the number of images per class in the ILSVRC training set by factors of {2, 4, 8, 16, 32} and show the impact on accuracy and robustness on ImageNetV2 in Figure 4 . As expected, increasing the number of images per class consistently leads to higher accuracy. However, the impact on robustness is exactly as predicted by our fit on standard ImageNet models. This indicates that varying the the size of training sets in an i.i.d. manner affects accuracy but not effective robustness, at least for ImageNetV2.

Varying the number of classes. Next, we consider the diversity of the data by varying the set of classes. In particular, we create three successive subsets of the ILSVRC training set with 500, 250, and 125 classes (see Appendix A.6.5 for the list of classes). We then evaluate all models in our testbed on the 125 classes present in all subsets. We present results in Figure 4 , which shows that varying the number of classes again affects accuracies but not effective robustness.

Our experiments suggest that neither growing the number of images per class nor the number of classes in an i.i.d. fashion are effective robustness interventions. Nevertheless, Section 5 shows that larger dataset can provide meaningful robustness improvements. This disparity may be due to limitations of emulating changes in the training set by subsampling ILSVRC. For one, our experiments consider i.i.d. subsets of the training images or classes and do not consider growing datasets in a manner that may cover different image distributions, as in the case of Instagram data. Another possibility is that increases in dataset size may only improve robustness after the dataset size is large enough such that the accuracy on the original distribution is close to saturated. Our experiments only observe dataset sizes smaller than ILSVRC, which may fall below this inflection point.

7. RELATED WORK:

There are several related papers that study the relationship between various synthetic robustness measure, e.g., (Geirhos et al., 2018; Engstrom et al., 2019; Hendrycks & Dietterich, 2019; Kang et al., 2019; Tramer & Boneh, 2019; Maini et al., 2019) . To the best of our knowledge, our paper is the first to compare synthetic and natural distribution shifts. Since our findings show that synthetic robustness currently does not promote natural robustness, our paper offers a complementary view to the aforementioned comparisons focused on synthetic robustness.

Our work relies on two recent papers introducing datasets with natural distribution shifts (Recht et al., 2019; Shankar et al., 2019) . Recht et al. (2019) already note that there is a clear linear relationship between original and new test set accuracy but do not evaluate any models with a robustness intervention or models trained on more data. Shankar et al. (2019) compare only a small set of robust models. Due to the limited size of their test set and model testbed, their results do not conclusively show that p -robust models offer effective robustness on their dataset. In contrast, our testbed of robustness interventions is substantially larger and aims to encompass all publicly available models.

We also include models trained on more data and conduct experiments to investigate the effect of training data on robustness. While our experiments shows that p -robust models do offer effective robustness on ImageNetVidRobust, we also put this improvement in context by demonstrating that it is comparable to interpolating with a random classifier. Moreover, none of the two papers study to what extent synthetic robustness is predictive of robustness under natural distribution shifts.

8. CONCLUSION:

One aspiration of robustness interventions is to improve performance on real distribution shifts. Since this is a challenging problem, synthetic notions of robustness offer a natural starting point.

While it is expected that corresponding interventions will be less effective on real distribution shifts, the hope is that these interventions still convey at least some robustness on real data. Unfortunately, our experiments show that this is not the case for two recent examples of real distribution shifts. On both datasets, models with a robustness intervention perform no better than baselines without such interventions. The fact that progress on synthetic distribution shifts is essentially uncorrelated with progress on real distribution shifts raises the question whether further improvements for synthetic robustness will yield benefits on real data.

To deploy machine learning in safety-critical environments, it will be necessary to address this question and improve robustness under real distribution shifts. Our experiments suggests multiple directions for future work to achieve this goal.

One important direction is to assemble more examples of natural distribution shifts in order to test robustness on real data in more detail. While it is possible that other types of natural distribution shifts are more correlated with synthetic robustness, this hypothesis needs to be tested with carefully curated datasets.

Our experiments on ImageNetV2 suggest that adding training data can improve robustness. A similar phenomenon has also been demonstrated for adversarial robustness (Schmidt et al., 2018; Carmon et al., 2019; Uesato et al., 2019; Najafi et al., 2019; Zhai et al., 2019) Each row is a model, and each column is an evaluation setting. For the corruptions, we average over the five severities defined in (Hendrycks & Dietterich, 2019) . We also plot in-memory and ondisk versions of each corruption as jpeg compression was found to be a confounding factor in (Ford et al., 2019) . We leave out the class-subsampled models and evaluations described in Section 6 for brevity.

Under review as a conference paper at ICLR 2020 We have already seen that corruption robustness does not promote effective robustness, or robustness to real distribution shift. Here, we analyze whether robustness to some corruptions transfers to others, and what may contribute to corruption robustness. Figure 22 shows the result of training various resnet50s2 on a few corruptions from imagenet-c.

In line with prior work, this plot here tells us that training against one type of synthetic corruption or one set of synthetic corruption does not transfer well to other corruptions. There are cases where transfer does happen, but overall the models are only robust to the corruption they are trained on. This fact is even more prominent when looking at the difference between the instagram model and efficientnet -while both are amongst the top in terms of robust to synthetic corruptions, instagram is more robust to the on disk versions while efficientnet is more robust to the in memory versions. At first glance, this phenomenon seems strange, but in fact it could be that since the instagram model is trained on images pulled from instagram, which are jpeg compressed, it is more resistant to on disk perturbations -while the efficientnet is trained using autoaugment, which is an augmentation strategy done in memory, explaining its greater robustness to in memory perturbations.

A.5 DETAILS ON OUR MODELS:

Table 1 : Top-1 model accuracies on the original ImageNet validation set, the Imagenetv2 test set (matched-frequency), an average over all the corruptions, and an average over all the pgd attacks.

Note that since we take an average of many attacks, the PGD column can no longer be considered a worst-case attacker for the model (look to A.6.2 for specific attacks). The confidence intervals are 99.5% Clopper-Pearson intervals; they are not provided for the average columns since iid assumptions for the intervals may be violated. References for the models can be found in Appendix A.5.1. We exclude the subsampled class models for brevity. The table continues for 3 more pages. 

:

We note that this corresponds to the problem of estimating a treatment effect as studied in causal inference. We do not explicitly rely on knowledge about causal inference to make our exposition more accessible but refer the reader to textbooks on causal inference for background(Pearl et al.,

2016;Hernan & Robins, 2019).

Each resnet50 was trained with a batch size of 256 for 120 epochs, starting with a learning rate of 0.1 and decaying by a factor of 10 every

epochs. For the resnet50s trained on corruptions, we randomly sample a corruption and severity for each image. Refer to A.6.3 for details on corruptions and severities. We use our custom fast gpu implementations of these corruptions for training.

Figures and Tables:

Figure2: Robustness to synthetic distribution shift (x-axis) vs. effective robustness to the Ima-geNetV2 distribution shift (y-axis). The left plot shows synthetic robustness as measured by an average over image corruptions from(Hendrycks & Dietterich, 2019;Geirhos et al., 2018; 2019). The right plot shows synthetic robustness as measured by PGD attacks for 2 -and ∞ -robustness and two perturbation sizes each. In both cases, synthetic robustness is not predictive of effective robustness under the natural distribution shift. Appendices A.1 and A.2 contains similar plots for individual synthetic robustness measures and the ImageNetVidRobust distribution shift.

Figure 3: The left plot zooms into the range of the ResNet152-ImageNet11k and Instagram models on ImageNetV2 and shows that the models achieve significant effective robustness, i.e., they lie significantly above the linear fit. The right plot zooms into the range of the p -robust models on ImageNetVidRobust with high effective robustness. The dotted line shows the family of models achievable by interpolating between a standard ResNet-152 and a random classifier. It achieves the same robustness trade-off as the p -robust models.

Figure5: An overview of our testbed. Each row is a model, and each column is an evaluation setting. For the corruptions, we average over the five severities defined in(Hendrycks & Dietterich, 2019). We also plot in-memory and ondisk versions of each corruption as jpeg compression was found to be a confounding factor in(Ford et al., 2019). We leave out the class-subsampled models and evaluations described in Section 6 for brevity.

SYNTHETIC CORRUPTIONS VS. EFFECTIVE ROBUSTNESS (IMAGENET-VID-ROBUST)

Figure6: Robustness to synthetic distribution shift (x-axis) vs. effective robustness to the Ima-geNetVid distribution shift (y-axis). The left plot shows synthetic robustness as measured by an average over image corruptions from(Hendrycks & Dietterich, 2019;Geirhos et al., 2018; 2019). The right plot shows synthetic robustness as measured by PGD attacks for 2 -and ∞ -robustness and two perturbation sizes each. In both cases, there is almost no correlation, with the except of the lp adversarially robust models explored earlier.

Figure22: A detailed view of corruption robustness, with cells sampled from the main grid in Figure5. Here we present resnet50s trained on some of the corruptions from the imagenet-c benchmark, as well as the best model trained on more data, instagram-resnext101 32x48d, and the best model trained on just the standard training set, efficientnet-b7.

FULL LIST OF MODELS EVALUATED IN TESTBEDThe following list contains all models we evaluated on ImageNet with references and links to the corresponding source code.

Table content: <table><tr><td>ImageNet Aggregated Top-1 Accuracies Validation Imagenetv2 Accuracy Accuracy 86.0 [85.6, 86.4] 77.7 [76.5, 78.9] 85.9 [85.5, 86.4] 77.6 [76.4, 78.7] 85.4 [85.0, 85.9] 77.0 [75.8, 78.1] 85.1 [84.6, 85.5] 76.8 [75.6, 77.9] 84.4 [83.9, 84.9] 74.4 [73.2, 75.6] 84.2 [83.7, 84.6] 75.5 [74.3, 76.7] 84.0 [83.6, 84.5] 74.1 [72.8, 75.3] 83.7 [83.2, 84.1] 73.3 [72.0, 74.5] 83.5 [83.0, 83.9] 73.2 [71.9, 74.4] 82.7 [82.3, 83.2] 72.3 [71.0, 73.6] 82.7 [82.2, 83.2] 73.6 [72.4, 74.9] 82.6 [82.2, 83.1] 71.5 [70.2, 72.7] 82.5 [82.0, 83.0] 72.3 [71.0, 73.5] 81.3 [80.8, 81.8] 70.2 [68.9, 71.5] 80.9 [80.4, 81.3] 70.1 [68.8, 71.3] 80.8 [80.3, 81.3] 69.7 [68.4, 71.0] 80.3 [79.8, 80.8] 69.3 [68.0, 70.6] 80.2 [79.7, 80.7] 69.4 [68.1, 70.7] 80.1 [79.6, 80.6] 69.2 [67.9, 70.5] 79.8 [79.3, 80.3] 68.0 [66.7, 69.3] 79.7 [79.2, 80.2] 67.8 [66.5, 69.2] 79.4 [78.9, 80.0] 67.0 [65.7, 68.3] 79.4 [78.9, 79.9] 67.7 [66.4, 69.0] 79.4 [78.9, 79.9] 66.8 [65.5, 68.2] 79.4 [78.9, 79.9] 67.2 [65.9, 68.6] 79.3 [78.8, 79.8] 67.4 [66.1, 68.8] 79.3 [78.8, 79.8] 67.4 [66.1, 68.7] 79.2 [78.7, 79.7] 67.8 [66.4, 69.1] 79.2 [78.7, 79.7] 67.4 [66.1, 68.7] 79.1 [78.6, 79.6] 67.8 [66.4, 69.1] 79.0 [78.4, 79.5] 67.1 [65.8, 68.5] 78.8 [78.3, 79.4] 66.4 [65.0, 67.7] 78.8 [78.3, 79.3] 67.2 [65.9, 68.6] 78.7 [78.1, 79.2] 67.4 [66.1, 68.8] 78.6 [78.1, 79.1] 65.8 [64.5, 67.1] 78.6 [78.1, 79.1] 66.5 [65.2, 67.8] 78.5 [78.0, 79.1] 66.2 [64.9, 67.6] 78.5 [77.9, 79.0] 66.2 [64.8, 67.5] 78.4 [77.9, 78.9] 67.1 [65.8, 68.4] 78.3 [77.8, 78.8] 66.8 [65.5, 68.2] 78.2 [77.7, 78.7] 66.0 [64.7, 67.4] 78.2 [77.7, 78.7] 66.3 [64.9, 67.6] 78.1 [77.6, 78.6] 66.1 [64.7, 67.4] 77.9 [77.4, 78.4] 66.2 [64.8, 67.5] 77.8 [77.3, 78.3] 66.3 [65.0, 67.7] 77.8 [77.3, 78.3] 66.3 [64.9, 67.6] 72.6 [72.0, 73.1] 59.7 [58.3, 61.1] l PGD 1step eps 512 noise 0.50 Model FixResNeXt101 32x48d v2 FixResNeXt101 32x48d instagram-resnext101 32x48d instagram-resnext101 32x32d efficientnet-b7 instagram-resnext101 32x16d efficientnet-b6 efficientnet-b5 FixPNASNet pnasnet5large instagram-resnext101 32x8d efficientnet-b4 nasnetalarge senet154 polynet efficientnet-b3 inceptionresnetv2 se resnext101 32x4d inceptionv4 resnet101 cutmix dpn107 FixResNet50CutMix v2 dpn131 FixResNet50CutMix dpn92 resnext101 32x8d efficientnet-b2 dpn98 google resnet101 jft-300M se resnext50 32x4d resnext101 64x4d wide resnet101 2 xception se resnet152 resnet50 cutmix FixResNet50 v2 FixResNet50 wide resnet50 2 se resnet101 resnet152 resnet50 feature cutmix resnext101 32x4d resnet101 lpf3 resnet101 lpf5 efficientnet-b1 resnet101 lpf2 mobilenet v2 lpf3 resnet50-smoothing adversaria 54.7 [54.0, 55.3] 41.7 [40.3, 43.1] mobilenet v2 lpf2 72.6 [72.1, 73.2] 59.4 [58.0, 60.8] alexnet 56.5 [55.9, 57.1] 43.4 [42.0, 44.8] resnet50 with jpeg compression aws 73.6 [73.1, 74.2] 60.9 [59.5, 62.3] bninception 73.5 [73.0, 74.1] 62.0 [60.6, 63.4] mnasnet1 0 73.5 [72.9, 74.0] 60.4 [59.1, 61.8] vgg16 bn 73.4 [72.8, 73.9] 60.7 [59.3, 62.1] resnet34 73.3 [72.8, 73.9] 60.9 [59.5, 62.2] resnet50 with gaussian noise aws 73.0 [72.4, 73.5] 60.6 [59.2, 61.9] resnet50 with gaussian noise contra st motion blur jpeg compression aws 72.7 [72.2, 73.3] 60.1 [58.7, 61.5] alexnet lpf5 56.6 [56.0, 57.2] 43.4 [42.0, 44.7] alexnet lpf3 56.9 [56.3, 57.5] 43.7 [42.3, 45.1] alexnet lpf2 57.2 [56.6, 57.9] 44.0 [42.6, 45.4] squeezenet1 0 58.1 [57.5, 58.7] 44.9 [43.5, 46.3] squeezenet1 1 58.2 [57.6, 58.8] 45.4 [44.0, 46.8] resnet50 trained on SIN 60.2 [59.6, 60.8] 48.6 [47.2, 50.0] l PGD 1step eps 512 noise 0.25 resnet50-smoothing adversaria 60.5 [59.9, 61.1] 47.0 [45.6, 48.4] resnet50 with frost aws 73.8 [73.2, 74.3] 61.6 [60.2, 62.9] resnet50 adv-train-free 60.5 [59.9, 61.1] 47.4 [46.0, 48.8] vgg16 bn lpf3 73.9 [73.4, 74.5] 61.9 [60.6, 63.3] shufflenet v2 x0 5 60.6 [59.9, 61.2] 47.2 [45.8, 48.6] vgg16 bn lpf2 74.0 [73.5, 74.6] 61.7 [60.3, 63.0] resnet50 with zoom blur aws 61.3 [60.6, 61.9] 49.4 [48.0, 50.8] vgg16 bn lpf5 74.0 [73.5, 74.6] 61.2 [59.8, 62.5] DNN 2steps eps 512 noise 0.50 nasnetamobile 74.1 [73.5, 74.6] 61.3 [59.9, 62.7] resnet50-smoothing adversarial 62.2 [61.6, 62.8] 49.1 [47.7, 50.5] resnet34 lpf5 74.2 [73.6, 74.7] 62.2 [60.8, 63.6] d resnet152 baseline vgg19 bn 74.2 [73.7, 74.8] 62.0 [60.6, 63.3] facebook adv traine 62.3 [61.7, 63.0] 49.8 [48.4, 51.2] resnet34 lpf3 74.3 [73.8, 74.9] 62.2 [60.8, 63.5] of 4 batch64 original images densenet121 74.4 [73.9, 75.0] 62.1 [60.8, 63.5] resnet50 imagenet subsample 1 63.2 [62.6, 63.8] 50.5 [49.1, 51.9] resnet34 lpf2 74.5 [73.9, 75.0] 62.2 [60.8, 63.6] resnet50 with greyscale aws 63.3 [62.7, 63.9] 50.7 [49.3, 52.1] resnet50 trained on SIN and IN 74.6 [74.0, 75.1] 62.8 [61.4, 64.1] smoothing noise 0.50 resnet50 with saturate aws 74.9 [74.3, 75.4] 62.3 [60.9, 63.6] resnet50-randomized 64.2 [63.6, 64.8] 51.2 [49.8, 52.6] densenet121 lpf2 75.0 [74.5, 75.6] 63.1 [61.7, 64.5] d resnet152 denoise densenet121 lpf5 75.0 [74.5, 75.6] 62.8 [61.5, 64.2] facebook adv traine 65.3 [64.7, 65.9] 52.6 [51.2, 54.0] densenet121 lpf3 75.1 [74.6, 75.7] 62.5 [61.1, 63.8] resnet50 with motion blur aws 67.5 [66.9, 68.0] 55.9 [54.5, 57.3] resnet50 with spatter aws 75.2 [74.7, 75.8] 62.6 [61.3, 64.0] mnasnet0 5 67.6 [67.0, 68.2] 54.2 [52.8, 55.6] resnet50 with brightness aws 75.3 [74.7, 75.8] 62.7 [61.3, 64.1] DNN 2steps eps 512 noise 0.25 densenet169 75.6 [75.1, 76.1] 63.5 [62.2, 64.9] resnet50-smoothing adversarial 67.9 [67.3, 68.5] 54.5 [53.1, 55.9] smoothing noise 0.00 resnext101 denoiseAll resnet50-randomized 75.7 [75.1, 76.2] 63.8 [62.4, 65.1] facebook adv trained 68.3 [67.7, 68.9] 55.2 [53.8, 56.6] efficientnet-b0 75.8 [75.3, 76.3] 63.2 [61.9, 64.6] resnet50 with pixelate aws 68.5 [67.9, 69.1] 56.7 [55.3, 58.1] dpn68 75.9 [75.3, 76.4] 63.1 [61.7, 64.5] vgg11 69.0 [68.4, 69.6] 55.7 [54.3, 57.1] nt batch64 original images shufflenet v2 x1 0 69.4 [68.8, 69.9] 56.0 [54.5, 57.3] resnet50 imagenet 100perce 76.0 [75.4, 76.5] 63.2 [61.9, 64.6] resnet18 69.8 [69.2, 70.3] 57.3 [55.9, 58.7] resnet50 76.1 [75.6, 76.7] 63.2 [61.8, 64.6] googlenet/inceptionv1 69.8 [69.2, 70.4] 57.9 [56.5, 59.3] resnet50 aws baseline 76.1 [75.6, 76.7] 63.6 [62.3, 65.0] vgg13 69.9 [69.3, 70.5] 56.8 [55.4, 58.2] resnet152-imagenet11k 76.2 [75.6, 76.7] 66.1 [64.8, 67.5] smoothing noise 0.25 ImageNet Aggregated Top-1 Accuracies Validation Imagenetv2 Model Accuracy Accuracy se resnet50 77.6 [77.1, 78.2] 65.8 [64.5, 67.2] resnext50 32x4d 77.6 [77.1, 78.1] 65.8 [64.5, 67.2] resnet50 mixup 77.5 [76.9, 78.0] 65.0 [63.7, 66.4] fbresnet152 77.4 [76.9, 77.9] 65.5 [64.1, 66.8] resnet101 77.4 [76.8, 77.9] 65.5 [64.1, 66.8] FixResNet50 no adaptation 77.3 [76.8, 77.9] 65.4 [64.1, 66.8] inceptionv3 77.3 [76.8, 77.8] 65.7 [64.3, 67.0] densenet161 77.1 [76.6, 77.7] 65.3 [63.9, 66.6] resnet50 cutout 77.1 [76.5, 77.6] 64.4 [63.1, 65.8] dpn68b 77.0 [76.5, 77.6] 64.8 [63.4, 66.1] resnet50 lpf5 77.0 [76.5, 77.6] 64.5 [63.1, 65.8] densenet201 76.9 [76.4, 77.4] 64.8 [63.4, 66.1] resnet50 lpf3 76.8 [76.3, 77.3] 64.7 [63.3, 66.0] resnet50 lpf2 76.8 [76.3, 77.3] 64.5 [63.2, 65.8] resnet50 trained on SIN a nd IN then finetuned on IN 76.7 [76.2, 77.2] 64.6 [63.3, 66.0] cafferesnet101 76.2 [75.7, 76.7] 64.1 [62.8, 65.5] ImageNet Aggregated Top-1 Accuracies Validation Imagenetv2 Model Accuracy Accuracy mobilenet v2 lpf5 72.5 [71.9, 73.1] 59.8 [58.4, 61.1] vgg19 72.4 [71.8, 72.9] 59.7 [58.3, 61.1] vgg16 lpf5 72.3 [71.8, 72.9] 59.8 [58.4, 61.2] vgg16 lpf3 72.2 [71.6, 72.7] 59.3 [57.9, 60.7] vgg16 lpf2 72.2 [71.6, 72.7] 59.3 [57.9, 60.6] resnet50 with contrast aws 72.0 [71.4, 72.6] 58.9 [57.5, 60.3] mobilenet v2 71.9 [71.3, 72.4] 59.0 [57.6, 60.4] resnet50 with fog aws 71.8 [71.2, 72.3] 58.2 [56.8, 59.6] resnet18 lpf3 71.7 [71.1, 72.2] 58.5 [57.1, 59.9] vgg16 71.6 [71.0, 72.2] 58.5 [57.1, 59.9] vgg13 bn 71.6 [71.0, 72.2] 58.8 [57.4, 60.2] resnet18 lpf2 71.4 [70.8, 72.0] 58.5 [57.1, 59.9] resnet18 lpf5 71.4 [70.8, 72.0] 58.1 [56.7, 59.5] resnet50 imagenet subsample 1 of 2 batch64 original images 70.5 [69.9, 71.1] 58.0 [56.6, 59.3] vgg11 bn 70.4 [69.8, 70.9] 57.4 [56.0, 58.8] resnet50-randomized 70.3 [69.7, 70.9] 57.7 [56.3, 59.1] ImageNet Aggregated Top-1 Accuracies Validation Imagenetv2 Model Accuracy Accuracy resnet50-randomized smoothing noise 1.00 53.1 [52.5, 53.7] 40.7 [39.4, 42.1] resnet50-smoothing adversarial DNN 2steps eps 512 noise 1.00 51.9 [51.2, 52.5] 39.8 [38.4, 41.1] resnet50 imagenet subsample 1 of 8 batch64 original images 51.7 [51.1, 52.3] 39.3 [38.0, 40.7] resnet50-smoothing adversaria l PGD 1step eps 512 noise 1.00 44.3 [43.7, 44.9] 33.2 [31.9, 34.6] resnet50 imagenet subsample 1 of 16 batch64 original images 36.7 [36.1, 37.3] 27.0 [25.8, 28.3] resnet50 with defocus blur aws 31.9 [31.3, 32.5] 24.6 [23.4, 25.8] resnet50 imagenet subsample 1 of 32 batch64 original images 21.4 [20.9, 21.9] 15.6 [14.5, 16.6] n02033041 n02037110 n02056570 n02071294 n02085936 n02086079 Avg. Corr. Avg. PGD Accuracy Accuracy 65.1 19.9 65.4 20.3 65.5 24.1 64.8 24.4 63.1 30.9 63.2 29.2 63.7 33.4 62.5 31.1 61.3 61.8 60.8 60.0 61.7 54.1 54.0 55.9 56.9 52.3 55.5 50.1 52.4 43.5 52.1 43.4 49.3 49.7 53.6 51.8 53.5 50.6 52.1 48.2 51.7 50.9 44.7 43.3 43.2 15.1 46.2 26.1 50.1 28.2 47.8 22.5 44.3 25.1 51.0 22.4 46.5 22.5 46.5 51.2 46.1 22.0 34.8 17.6 35.7 53.8 29.0 34.5 17.4 21.6 24.1 23.1 41.8 40.6 36.4 35.7 40.5 45.6 51.8 22.8 32.0 24.0 22.8 30.6 45.5 22.5 29.3 21.2 20.2 18.1 16.1 20.2 16.1 18.8 39.4 19.0 21.3 39.5 37.2 58.8 15.3 42.4 21.5 29.4 57.4 26.4 36.3 18.3 23.6 16.1 28.4 36.1 17.5 33.3 12.4 26.3 36.2 19.0 25.2 44.8 22.8 39.1 59.2 23.6 41.2 20.9 24.7 37.9 16.5 35.8 37.6 26.8 42.2 20.7 30.2 43.5 20.0 27.4 21.4 29.3 41.5 21.0 28.3 18.7 25.4 47.9 22.9 25.7 42.4 20.6 39.8 61.4 18.2 41.2 20.8 30.4 41.8 21.1 38.0 39.5 18.4 40.5 20.0 38.7 15.9 30.8 42.8 22.8 27.9 17.4 25.6 43.9 22.2 27.9 46.7 21.8 40.6 61.8 28.8 34.8 41.8 20.9 40.9 41.4 30.2 45.9 29.5 39.6 19.6 23.0 45.5 17.7 28.6 22.4 30.6 30.9 16.4 36.8 41.6 21.3 35.0 19.5 33.5 41.6 21.4 38.8 21.8 30.1 42.1 21.3 28.5 19.3 29.5 47.3 30.7 22.5 Avg. Corr. Avg. PGD Accuracy Accuracy 48.1 27.4 45.6 22.5 48.2 22.2 50.0 23.5 46.1 21.8 45.2 20.5 49.8 25.7 49.4 22.2 43.8 19.9 45.7 18.7 43.5 21.7 47.6 23.9 43.3 21.8 42.2 20.8 44.0 22.6 44.8 25.5 Avg. Corr. Avg. PGD Accuracy Accuracy 34.9 17.8 32.4 20.6 31.9 19.7 32.2 19.1 32.0 19.2 40.8 17.0 34.0 17.8 37.9 16.8 36.8 20.1 31.3 20.1 31.8 15.2 36.9 19.6 36.9 19.9 35.4 21.8 31.7 18.0 40.7 63.2 Avg. Corr. Avg. PGD Accuracy Accuracy 34.9 52.1 34.4 51.6 19.8 19.7 29.8 43.7 12.7 16.0 18.2 9.6 7.2 11.1 n02093428 n02093991 n02095314 n02095570 n02096294 n02096437 n02097474 n02100236 n02100583 n02102318 n02105056 n02107574 n02112706 n02113023 n02114855 n02128925 n02134418 n02138441 n02165105 n02219486 n02226429 n02264363 n02280649 n02441942 n02483708 n02486261 n02488291 n02492035 n02641379 n02730930 n02777292 n02790996 n02795169 n02808440 n02814533 n02814860 n02837789 n02859443 n02892201 n02895154 n02948072 n02951585 n02977058 n03000247 n03110669 n03201208 n03208938 n03216828 n03240683 n03250847 n03272562 n03297495 n03337140 n03376595 n03379051 n03447721 n03492542 n03527444 n03535780 n03642806 n03670208 n03673027 n03692522 n03710193 n03775071 n03832673 n03838899 n03840681 n03868242 n03873416 n03877845 n03884397 n03908714 n03920288 n03933933 n04004767 n04009552 n04037443 n04041544 n04067472 n04074963 n04099969 n04125021 n04141975 n04149813 n04204238 n04208210 n04229816 n04266014 n04310018 n04330267 n04335435 n04336792 n04355338 n04417672 n04479046 A.5.1 n01944390 n01978287 n01980166 n02007558 n02009229 n02017213 n04505470 n07715103 n07875152 n09256479 n12620546</td></tr></table>

Peer review (iclr2020):
This paper studied an interesting question, whether the gain of robustness from synthetic distribution shifts can be transferred/generalized to the robustness under natural distribution shifts. It was shown that in the context of natural distribution shifts, no current robustness intervention can really outperform standard models without a robustness intervention. The main strength of this paper is its extensive experimental study. However, I still have concerns on this work. 1) The authors mentioned *an implicit assumption underlying this research direction is that robustness to such synthetic distribution shifts will lead to models that also perform more reliably on natural distribution shifts.* However, I am uncertain about this point. Let us take adversarial robustness as an example, I am NOT surprising that the robustness on crafted adversarial examples cannot be generalized to the robustness over natural distribution shifts. Thus, I do not think that adversarial robustness obeys the *implicit assumption*. In other words, the studied problem should be better connected to adversarial robustness. 2) The significance of *effective robustness* is not clear. It seems that most of insights were learnt from Figure 1, 3 and 4. Do they rely on the metric *effective robustness*? 3) In Figure 1, *Trained with more* -> *Trained with more data* ############# Post-feedback ################ Thanks for the response. I am still not fully convinced by the significance of the findings in this work. In the paper, the authors highlighted that *our results show that current robustness gains on synthetic distribution shifts do not transfer to improved robustness on the natural distribution shifts presently available as test sets.* I am not surprising at this point, since the synthetic shift, e.g., introduced from adversarial examples, may only characterize the short-cut shift for misclassification. Thus, robustness learnt from this synthetic distribution shift might not transfer to the natural distribution shift. I decide to keep my original score.