Title: SHAPE FEATURES IMPROVE GENERAL MODEL RO-BUSTNESS

Abstract: Recent studies show that convolutional neural networks (CNNs) are vulnerable under various settings, including adversarial examples, distribution shifting and backdoor attacks. Motivated by the findings that human visual system pays more attention to global structure (e.g., shape) for recognition while CNNs are biased towards local texture features in images, we propose a unified framework EdgeGANRob based on robust edge features to improve the robustness of CNNs on multiple tasks, which first explicitly extracts shape/structure features from a given image and then reconstructs a new image by refilling the texture information with a trained generative adversarial network (GAN). In addition, to reduce the sensitivity of edge detection algorithm to adversarial perturbation, we propose a robust edge detection approach Robust Canny based on the vanilla Canny algorithm. To gain more insights, we also compare EdgeGANRob with its simplified backbone procedure EdgeNetRob, which performs learning tasks directly on the extracted robust edge features. We find that EdgeNetRob can help boost model robustness significantly but at the cost of the clean model accuracy. EdgeGANRob, on the other hand, is able to improve clean model accuracy compared with EdgeNetRob and without losing the robustness benefits introduced by EdgeNetRob. Extensive experiments show that EdgeGANRob is resilient in different learning tasks under diverse settings.

1. INTRODUCTION:

Convolutional neural networks (CNNs) have been studied extensively (Goodfellow et al., 2016) , and have achieved state-of-the-art performance in many learning tasks (He et al., 2016; Zhu et al., 2017) . However, recent works have shown that CNNs are vulnerable to adversarial examples (Carlini and Wagner, 2017; Goodfellow et al., 2014b; Szegedy et al., 2013) , where imperceptible perturbation can be added to the test data to tamper the predictions. Different from adversarial examples where test data is manipulated, an orthogonal setting: data poisoning or backdoor attacks where training data is manipulated to reduce model's generalization accuracy and achieve targeted poisoning attack (Li et al., 2016; Chen et al., 2017b ). In addition, recent studies show that CNNs tend to learn surface statistical regularities instead of high level abstraction, leading it fails to generalize to the superficial pattern transformation (radial kernel, random kernel (Jo and Bengio, 2017a; Wang et al., 2019a; b) . We refer to this problem as model's robustness under distribution shifting. How to improve the general robustness of DNNs under these settings remains unsolved.

To improve the robustness of CNNs, recent studies explore the underlying cause of their vulnerability. For example, Ilyas et al. (2019) attributes the existence of adversarial examples to the existence of non-robust but highly-predictive features. They suggest to train a classifier only on "robust features" which contain the necessary information for recognition and are insensitive to small perturbations. In addition, it is shown that human recognition relies mainly on global object shapes rather than local patterns (e.t. textures), while CNNs are more biased towards the latter (Baker et al., 2018; Geirhos et al., 2019) . For instance, Geirhos et al. (2019) creates a texture-shape cue conflict, such as a cat shape with elephant texture, and feeds it to an Imagenet trained CNN and huamn respectively. While Human can still recognize it as a cat, CNN wrongly predicts it as an elephant. Therefore, the bias toward local features potentially contributes to CNN's vulnerability to adversarial examples, distribution shifting and patterns of backdoor attacks. Particularly, previous researcher also shows that the shape of objects is the most important cue for human object recognition (Landau et al., 1988) .

Given the above evidence, a natural question emerges: Can we improve the robustness of CNNs by making it rely more on global shape structure? To answer this question, we need to formalize the notion of global shape structure first. We propose to consider a specific type of shape representation: edges (image points that have sharp change in brightness). Using edges comes with two benefits: 1) it is an effective device for modelling shape; 2) edges are easy to be captured in images, with many sophisticated algorithms (Canny, 1986; Xie and Tu, 2015; Liu et al., 2017) available.

More specifically, this paper explores a new approach EdgeGANRob to improve the robustness of the CNNs to adversarial attacks,distribution shifting and backdoor attacks by leveraging structural information in images. The unified framework is shown in Figure 1 . As illustrated, a simplified version of EdgeGANRob is a two-stage procedure named EdgeNetRob, which extracts the structural information by detecting edges and then trains the classifier on the extracted edges. As a consequence, EdgeNetRob forces the CNNs to make prediction solely based on shape information, rather than texture/color, thus eliminating the texture bias (Geirhos et al., 2019) . Our results show that EdgeNetRob can improve CNNs' robustness. However, there are still two challenges: (i) the direct differentiable edge detection algorithms are also vulnerable to attacks, which may lead to low robustness against sophisticated adaptive attackers. To handle this problem, we propose a robust edge detection algorithm, Robust Canny. Using Robust Canny is able to EdgeNetRob dramatically improve the robustness of EdgeGANRob. As a result, this combined method outperforms the adversarial retraining based defense method (Madry et al., 2018) . (ii). Although EdgeNetRob improves the CNNs' robustness, it decreases the clean accuracy of CNNs due to the missing texture/color information. This motivates the development of EdgeGANRob, which embeds a generative model to refill the texture/colors based on the edge images before they are fed into the classifier. Please find more visualization results on the anonymous website: https://sites.google.com/view/edgenetrob.

The main contributions of this paper include: (i) We propose a unified framework EdgeGANRob to improve the robustness of CNNs against multiple tasks simultaneously, which explicitly extracts edge/structure information from input images and then reconstructs the original images by refilling the textural information with GAN. (ii) To remain robust against sophisticated adaptive evasion attacks, in which attackers have access to the defense algorithm, we propose a robust edge detection approach Robust Canny based on the vanilla Canny algorithm to reduce the sensitivity of edge detector to adversarial perturbation. (iii) To further demonstrate the effectiveness of the inpainting GAN in EdgeGANRob, we also evaluate its simplified backbone procedure EdgeNetRob by performing learning tasks directly on the extracted robust edge features. To justify the above contributions, we conduct thorough evaluation on EdgeNetRob and EdgeGANRob in three tasks: adversarial attacks, distribution shifting and backdoor attacks, where significant improvements are achieved.

2. RELATED WORK:

Adversarial robustness A wide range of defense methods against adversarial examples have been proposed, among which many (Liao et al., 2018; Song et al., 2018 ) are shown to be not robust against adaptive attacks (Athalye et al., 2018) . The state-of-the-art defense methods are based on adversarial training (Madry et al., 2018) . Athalye et al. (2018) identified gradient obfuscation as a common pitfall for defense methods, thus suggested that defense methods should be evaluated against customized white-box attacks. Carlini et al. (2019) suggested that defense methods should be evaluated against strong adaptive attacks.

Distribution shifting Compared to adversarial examples, distribution shifting (Recht et al., 2018) is more common and general in real-world applications. Jo and Bengio (2017b) shows that CNNs have a tendency to learn the superficial statistical cues. Recently, Wang et al. (2019a) proposes a method to robustify CNNs by penalizing the predictive power of the local representations and mitigating the tendency of fitting superficial statistical cues by evaluating on four patterns, including greyscale, negcolor, radial kernel and random kernel. Hendrycks and Dietterich (2019) proposes benchmark datasets for evaluating model robustness under common perturbations.

Backdoor attack Backdoor attack (Chen et al., 2017a; Gu et al., 2017 ) is a type of poisoning attack (Shafahi et al., 2018) that works by injecting a pattern into training data. As a result, the trained models will predict a specific target class when certain pattern is injected into test data. Tran et al. (2018) has proposed a procedure to detect poisoned training data by using tools from robust statistics. Liu et al. (2018) proposes an approach to protect models from backdoor attacks by using neuron pruning.

Robust visual features.:

Recent work has highlighted a connection between recognition robustness and robust features. For image recognition, Geirhos et al. ( 2019); Baker et al. (2018) shows that CNNs rely more on textures than global shape structure, while humans rely more on shape structure than detailed texture. Itazuri et al. (2019) uses visualization methods and finds that adversarially robust models tend to capture global structure of the objects. Ilyas et al. (2019) argues that there exists non-robust features in natural images which are highly predictive but not interpretable by human. They showed that CNNs can obtain robustness by learning from images which contain only robust features. However, they did not directly identify which features are robust features. In this work, we propose explicitly to use edge as a robust feature.

3. METHODOLOGY:

We introduce a new classification pipeline based on robust edge features, which we denote as EdgeGANRob. Our method first extracts edge/structure features from a given image and then reconstructs the original images by refilling the texture information with a trained generative adversarial network (GAN). The newly generated image is then fed into a classifier. In this section, we first describe a simplified backbone procedure of EdgeGANRob named EdgeNetRob, then introduce Robust Canny and inpainting GAN. Last, we describe three settings under which robustness is evaluated.

3.1. ED G ENE TRO B : A SIMPLIFIED BACKBONE OF ED G EGANRO B:

As a simplified backbone of EdgeGANRob, EdgeNetRob consists of two stages: First, we exploit an edge detection method to extract edge maps from an image, and then a standard image classifier f θ (•) is trained on the extracted edge maps. Formally, denote the edge extractor function as e(•), the EdgeNetRob pipeline aims to solve the following problem:

EQUATION

where D represents the underlying data distribution and L denotes the loss function (e.g., crossentropy loss). EdgeNetRob forces the decision of CNN to be solely based on edges, thus making it less sensitive to local textures. Since original images are transformed into edge maps, even if a pre-trained classifier on the original training data is available, we still need to train the edge classifier.

Despite the simplicity of EdgeNetRob, it degrades the performance of CNNs over clean test data considering that the texture/color information is missing. This motivates us to develop EdgeGANRob which embeds a generative model to refill the texture/colors of the edge images.

Because EdgeGANRob fills edge maps with texture/colors, which makes it more likely to achieve higher clean accuracy.

The robustness of such classification system that builds upon edges depends highly on the used edge detector, as many existing edge detection algorithms are also vulnerable to attacks which may lead to low accuracy of the recognition task. This motivates us to propose a robust edge detection algorithm named Robust Canny in the next section.

3.2. ROBUST EDGE DETECTION:

We now describe a robust edge detection method. Note that most neural network based edge detectors are non-robust. For example, Cosgrove and Yuille (2019) finds that neural network based edge detectors like HED (Xie and Tu, 2015) can fail easily when facing adversarial perturbation. In contrast, some traditional edge detection methods like Canny (Canny, 1986 ) is intrinsically robust since they output binary edge maps. However, as illustrated in Figure 2 (first line), when adversarial perturbation is added, the output of Canny edge detector can become noisy. We propose to improve the robustness of vanilla Canny by truncating the noisy pixels in its intermediate stages. We refer to this modified version of Canny edge detector as Robust Canny. (2)Gradient computation: We apply the Sobel operator (Kanopoulos et al., 1988) to compute the gradient magnitude and direction at each pixel from the smoothed images.

(3)Noise masking: We reduce the noise in the presence of adversarial perturbations by thresholding the gradient magnitudes by a level α. (4)Non-maximum suppression (NMS): An edge thinning step is taken to deblur the output of the Sobel operator. Gradient magnitudes that are not at a maximum along the direction of the gradient are suppressed (set to zero). ( 5)Double threshold: Using a lower threshold and a higher threshold (θ l , θ h ) for the gradient magnitude after NMS, pixels are mapped to 3 levels: strong, weak, and non-edge pixels, (6)Edge tracking by hysteresis: Edge pixels are detected by finding strong pixels, or weak pixels that are connected to other strong pixels. Note that we have modified the vanilla Canny algorithm by adding a noise masking stage after computing the image gradients. Later in Figure 2 , we show that the gradient computation stage is sensitive to input perturbations. Thus, we set all gradient magnitudes lower than a threshold α to zero to mitigate the perturbation noise. By adding a truncation operation, it is expected that adversarial noise on the gradient map with small magnitude will be reduced in early stages without affecting the quality of final edge maps. In addition to the masking operation, we find that the parameters of Canny (e.g. standard deviation of gaussian filter σ, thresholds θ l , θ h ) also affect the robustness level. Specifically, we notice that larger σ and higher thresholds θ l , θ h result in better robustness due to the stronger smoothing and pruning effects. This however comes at the cost of clean accuracy as larger σ leads to blurrier images and higher θ l , θ h may eliminate useful information in the output edges.

To obtain a robust edge detector, we should carefully choose its parameters (e.g., σ, θ l , θ h ). More details are provided in the experiment section.

3.3. INPAINTING GAN:

In this section, we describe how we train a Generative Adversarial Network (GAN) (Goodfellow et al., 2014a) in EdgeGANRob. Recall that the task of generating color images from edge maps is well defined under the image-to-image translation framework (pix2pix) (Isola et al., 2017) . We train our inpainting GAN with two steps: in the first stage, we follow the common setup of pix2pix (Isola et al., 2017; Wang et al., 2018) to train a conditional GAN using the following objective function:

min G max D L gan = min G λ adv max D L adv + λ F M L F M (2)

where L adv , L F M denote the adversarial loss (Goodfellow et al., 2014a) and feature matching loss (Johnson et al., 2016) with λ adv and λ F M control their relative importance. In the second stage, since we want our classifier to achieve high accuracy over the generated RGB images, we jointly fine-tune the trained GAN from first stage along with the classifier, using the following objective function: min

EQUATION

where L cls represents the classification loss of generated images by inpainting GAN. Note that in the first step we do not include classification loss because we want our GAN to generate more realistic images, based on which it would be easier to fine-tune the classifier to gain accuracy.

3.4. APPLICATIONS:

Our method simultaneously improves robustness under three different settings: (i) adversarial attack, (ii) distribution shifting, (iii) backdoor attack. In terms of adversarial attack, EdgeGANRob is expected to improve robustness as edges are invariant to small imperceptible adversarial perturbations. Intuitively, consider a ∞ threat model, it is very challenging for an attacker to make a specific edge pixel appear/disappear by reversing the magnitude of image gradient with only limited adversarial budget per pixel. When test data is under distribution shifting with well-preserved shape structure, leveraging edge features could be helpful to improve model's generalization ability.

EdgeGANRob would work in this case by focusing on shape structure which makes it less sensitive to distribution change during testing. Recall that in backdoor attack, an attacker aims to poison the training data with a specific pattern such that the trained models can be tricked into predicting a certain class when the pattern is injected at testing time. In our cases, extracting edges can be viewed as a data sanitization step to remove the malicious pattern, thus rendering potential backdoor attacks ineffective.

4. EXPERIMENTAL RESULTS:

We evaluate the robustness of the proposed method in this section. Though EdgeNetRob is just a backbone of EdgeGANRob without inpainting GAN, our experiments show that it has unique advantage in certain settings and is of independent interest as a robust recognition method. Thus we also list it as an independent method to compare with EdgeGANRob. For our methods, we first evaluate their robustness against adversarial attacks, followed by an evaluation of their performance over distribution shifting. In addition, we evaluate the robustness against backdoor attacks.

4.1. EXPERIMENTAL SETUP:

We conduct our experiments on two datasets: Fashion MNIST (Xiao et al., 2017) and CelebA (Liu et al., 2015) . On CelebA, we evaluate our method on the task of gender classification. We did not choose the more popular MNIST and CIFAR-10 datasets because MNIST is a toy dataset where strong robustness has been achieved (Madry et al., 2018; Ding et al., 2019) and CIFAR-10 is a low-resolution dataset (32 × 32) where it is hard to extract semantically meaningful edges. Thus it can not provide informative benchmarks for our study. We use the same network architecture of classification for our method and the vanilla classifier. More details are shown in Appendix A.

4.2. ROBUSTNESS AGAINST ADVERSARIAL ATTACKS:

We evaluate our methods using the commonly used ∞ adversarial perturbation constraints with input range [0, 1] ( Madry et al., 2018; Goodfellow et al., 2016; Song et al., 2018; Samangouei et al., 2018; Xie et al., 2019) . We use standard perturbation budget on these two datasets as in Song et al. (2018) ; Samangouei et al. (2018) ; Theagarajan et al. (2019) . For Fashion MNIST, we use an ∞ budget of 8/256 and 25/256. For CelebA, we use an ∞ budget of 2/256 and 8/256. We evaluate our methods against adaptive attack (i.e., the attacker is fully aware of the defense algorithm). Specifically, we measure the robustness to white-box attacks by the BPDA attack (Athalye et al., 2018) . This attack requires a differentiable version of Canny, which is provided in Appendix C. More details on the attack setting are provided in Appendix B.

First, we illustrate why a robust edge detector is needed for defending against adversarial attacks. We compare the robustness of three edge detection methods: 1) RCF (Liu et al., 2017) which uses a CNN as backbone to generate edge maps; 2) Canny (Canny, 1986) We present our results for two benchmark datasets Fashion MNIST (Xiao et al., 2017) and CelebA (Liu et al., 2015) . We compare with the state-of-the-art baseline: Adversarial training proposed in Madry et al. (2018) . Adversarial training (Madry et al., 2018) is one of the most effective defense methods, achieving strong robustness to white-box attacks. The overall results are shown in Table 2 . We notice that EdgeNetRob and EdgeGANRob leads to a small drop in clean accuracy compared to the vanilla baseline model. However, when compared with adversarial training with = 8, both EdgeNetRob and EdgeGANRob achieve higher clean accuracy. We also observe that EdgeGANRob has higher clean accuracy than EdgeNetRob on CelebA dataset, thus validating the necessity of adding GANs on more complicated dataset to close the accuracy gap resulted from directly training on binary edge images. In terms of adversarial robustness, we observe that under We test our method for the generalization ability under distribution shifting. We follow the experiment settings in HEX (Wang et al., 2019b) and PAR (Wang et al., 2019a) , where we test the models under perturbed Fashion MNIST and CelebA with four types of patterns: greyscale, negative color, random kernel and radial kernel. The random kernel and radial kernel transformations are introduced in Jo and Bengio (2017a), which use Fourier filtering to transform an image while perserving high level semantics. We compare with state-of-the-art method PAR introduced in Wang et al. (2019a) , which adds a local patchwise adversarial regularization loss. Some visualization results of perturbed images are shown in Appendix D. The overall results are shown in Table 3 . We can see that EdgeNetRob and EdgeGANRob significantly improve the accuracy on three types of patterns: negative color, radial kernel and random kernel, while outperforming PAR. When testing on greyscale images, similar to baselines, our methods remain high accuracy. The results show that edge features are helpful for CNN's generalization to test data under distribution shifting. Under review as a conference paper at ICLR 2020

4.4. ROBUSTNESS AGAINST BACKDOOR ATTACKS:

We show that our method can be used as a defense against backdoor attacks. We follow the attack setup in Tran et al. (2018) . We embed invisible watermark pattern letter "A" into the pristine image for Fashion MNIST and letters "classified" into CelebA. The qualitative results are shown in Figure 4 on CelebA and Figure D in Appendix for Fashion MNIST. For Fashion MNIST, we randomly choose four attack and target pairs (attack, target) as (t-shirt, trouser), (trouser, pullover), (dress, coat), (coat, dress). For CelebA, the pairs (attack, target) are (male, female) and (female, male). We select the poisoning ratio as 20% and 30% for Fashion MNIST and 5% and 10% for CelebA. We compare our method with the baseline method proposed in Tran et al. (2018) , denoted as Spectral Signature.

The results are presented in Table 4 and Table 5 , where we show the test accuracy over both standard test data ('Clean Acc') and poisoned data ('Pois Acc'). We observe that our embedding pattern can successfully attack the vanilla Net with high poisoning accuracy on both CelebA and Fashion MNIST under all settings. It can be seen that Spectral Signature can not always achieve good performance with such invisible watermark patterns while EdgeNetRob and EdgeGANRob consistently remain low poisoning accuracy. Figure 4 shows the qualitative results of the backdoor images after edge detection algorithm and the reconstructed images. We can observe that the effect of invisible watermark pattern can be removed by the edge detector. In addition, we find that EdgeGANRob achieves better clean accuracy compared with EdgeNetRob which also validates the benefit introduced by inserting an inpainting GAN. 

5. CONCLUSION:

We introduced a new method based on robust edge features for improving general model robustness. By combining a robust edge feature extractor with the generative adversarial network, our method simultaneously achieves competitive results in terms of both adversarial robustness and generalization under distribution shifting. Additionally, we show that it can also be used to improve robustness against backdoor attacks. Our results highlight the importance of using shape information in improving model robustness and we believe it is a promising direction for future work.

of the input: C 2 (x) = M (x) ⊗ x, where M (•) produces the mask (i.e., an array of zeros and ones) produced by steps 3-6, and ⊗ denotes element-wise multiplication. Therefore, we can write:

EQUATION

To obtain a differentiable approximation of R-Canny for BPDA, we assume the mask to be constant.

In other words, we only backpropagate gradients through C 1 (•), and not M (•).

D MORE FIGURES IN EXPERIMENTS:

In 

:



Figures and Tables:

Figure 1: Structure of the proposed pipeline. EdgeNetRob feeds the output of edge detection to the classifier to produce robust predictions, while EdgeGANRob refill the edge image with texture information to reconstruct a new instance for predictions.

Figure 2: Visualization of intermediate stages of Vanilla Canny (Upper) and Robust Canny (Lower) on an image randomly sampled from Fashion MNIST. Results for clean images (Left) and adversarial images (Right) are presented.The 6 stages of our proposed Robust Canny include: (1)Noise reduction: A Gaussian filter is applied to smooth the image. (2)Gradient computation: We apply the Sobel operator(Kanopoulos et al., 1988) to compute the gradient magnitude and direction at each pixel from the smoothed images.(3)Noise masking: We reduce the noise in the presence of adversarial perturbations by thresholding the gradient magnitudes by a level α. (4)Non-maximum suppression (NMS): An edge thinning step is taken to deblur the output of the Sobel operator. Gradient magnitudes that are not at a maximum along the direction of the gradient are suppressed (set to zero). (5)Double threshold: Using a lower threshold and a higher threshold (θ l , θ h ) for the gradient magnitude after NMS, pixels are mapped to 3 levels: strong, weak, and non-edge pixels, (6)Edge tracking by hysteresis: Edge pixels are detected by finding strong pixels, or weak pixels that are connected to other strong pixels. Note that we have modified the vanilla Canny algorithm by adding a noise masking stage after computing the image gradients. Later in Figure2, we show that the gradient computation stage is sensitive to input perturbations. Thus, we set all gradient magnitudes lower than a threshold α to zero to mitigate the perturbation noise. By adding a truncation operation, it is expected that adversarial noise on the gradient map with small magnitude will be reduced in early stages without affecting the quality of final edge maps. In addition to the masking operation, we find that the parameters of Canny (e.g. standard deviation of gaussian filter σ, thresholds θ l , θ h ) also affect the robustness level. Specifically, we notice that larger σ and higher thresholds θ l , θ h result in better robustness due to the stronger smoothing and pruning effects. This however comes at the cost of clean accuracy as larger σ leads to blurrier images and higher θ l , θ h may eliminate useful information in the output edges. To obtain a robust edge detector, we should carefully choose its parameters (e.g., σ, θ l , θ h ). More details are provided in the experiment section.

Figure 3: Test accuracy under different iterations in adaptive attacks. strong adaptive attacks, EdgeNetRob and EdgeGANRob still remain robustness level better than or comparable to adversarial training baselines. It is worth noting that EdgeNetRob does not use adversarial training and thus has the advantage of time efficiency. We also show the plots for test accuracy under different attack iterations in Figure 3.

Figure 4: Qualitative results of EdgeGANRob (EdgeNetRob) with different stages for backdoor attack on CelebA.

Figure A: Test accuracy under radial kernel and random kernel perturbations with different probability on CelebA.

Figure D: Qualitative results of EdgeGANRob (EdgeNetRob) for backdoor attacks on Fashion MNIST.

which is the traditonal Canny edge detection; 3) Robust Canny. For each of the edge detection method, we train a classifier on the extracted edge maps. The results for Fashion MNIST are reported in Table1. First, we can see that using edges generated by RCF is not robust, as under strong adaptive attack, the accuracy drops near to 0. This result is in accordance withCosgrove and Yuille (2019), where they show that there exists adversarial examples for neural network based edge detectors. Second, it can be noticed that adaptive attack (PGD-40) can let EdgeNetRob based on vanilla Canny drop to a low accuracy of 39.99% with perturbation = 25. This also shows that our adaptive attacks customized for Canny is a strong adversary. Despite the weakness of vanilla Canny, we find that using Robust Canny can significantly boost the robustness under strong adaptive attack: from 39.99% to 76.75%. This shows that the truncation of values in Robust Canny is effective in reducing the adversarial risk. Therefore, for the experiments below on evaluating adversarial robustness, we use Robust Canny as the default edge extractor in EdgeNetRob and EdgeGANRob. Comparison of different edge extraction methods when used together with EdgeNetRob on Fashion MNIST tested with = 8 / = 25.

Table content: <table><tr><td>Method</td><td>Clean Accuracy</td><td>FGSM</td><td>PGD-10</td><td>PGD-40</td></tr><tr><td>RCF</td><td>90.15</td><td colspan="2">65.79/50.07 43.68/3.37</td><td>33.84/0.18</td></tr><tr><td>Canny</td><td>88.32</td><td colspan="3">83.45/66.98 81.24/54.07 79.76/39.99</td></tr><tr><td>Robust Canny</td><td>87.00</td><td colspan="3">84.07/79.03 83.88/78.53 83.57/76.75</td></tr></table>

Evalution of adversarial robustness on Fashion MNIST ( = 8 / = 25) and CelebA ( = 2 / = 8).

Table content: <table><tr><td>Dataset</td><td>Method</td><td>Clean Accuracy</td><td>FGSM</td><td>PGD-10</td><td>PGD-40</td><td>CW∞</td></tr><tr><td/><td>Vanilla Net</td><td>92.88</td><td colspan="2">59.50/27.82 41.55/1.76</td><td>33.35/0.48</td><td>41.82/2.00</td></tr><tr><td>Fashion</td><td>M-PGD</td><td>88.64/86.99</td><td colspan="4">85.34/78.99 83.24/74.79 83.01/72.62 84.53/73.85</td></tr><tr><td>MNIST</td><td>EdgeNetRob</td><td>87.00</td><td colspan="4">84.07/79.03 83.88/78.53 83.57/76.75 85.53/73.43</td></tr><tr><td/><td>EdgeGANRob</td><td>87.14</td><td colspan="4">85.30/78.67 84.54/76.82 84.07/72.69 86.03/75.01</td></tr><tr><td/><td>Vanilla Net</td><td>98.30</td><td>50.04/18.67</td><td>5.92/0.00</td><td>3.98/0.00</td><td>4.39/0.00</td></tr><tr><td>CelebA</td><td>M-PGD EdgeNetRob</td><td>96.51/92.75 94.51</td><td colspan="4">91.73/84.67 89.01/82.55 89.01/81.31 92.46/83.45 93.50/87.97 93.00/84.36 92.89/82.81 93.70/83.87</td></tr><tr><td/><td>EdgeGANRob</td><td>95.88</td><td colspan="4">94.78/91.06 94.48/88.12 94.52/84.60 95.91/88.46</td></tr><tr><td colspan="3">4.2.2 COMPARISON WITH BASELINES</td><td/><td/><td/><td/></tr></table>

Test accuracy of EdgeNetRob and EdgeGANRob on Fashion MNIST and CelebA datasets with perturbed color and texture.

Table content: <table><tr><td>Dataset</td><td>Method</td><td colspan="5">Accuracy Greyscale NegColor RadialKernel RandKernel</td></tr><tr><td/><td>Vanilla Net</td><td>92.07</td><td>-</td><td>25.52</td><td>37.01</td><td>46.92</td></tr><tr><td>Fashion</td><td>PAR</td><td>92.18</td><td>-</td><td>24.20</td><td>38.67</td><td>47.94</td></tr><tr><td>MNIST</td><td>EdgeNetRob</td><td>88.00</td><td>-</td><td>88.00</td><td>57.64</td><td>51.59</td></tr><tr><td/><td>EdgeGANRob</td><td>88.57</td><td>-</td><td>88.54</td><td>47.77</td><td>49.87</td></tr><tr><td/><td>Vanilla Net</td><td>97.77</td><td>96.75</td><td>43.33</td><td>69.30</td><td>61.78</td></tr><tr><td>CelebA</td><td>PAR EdgeNetRob</td><td>98.40 95.02</td><td>98.40 95.02</td><td>59.61 95.02</td><td>73.86 79.40</td><td>61.74 74.91</td></tr><tr><td/><td>EdgeGANRob</td><td>96.28</td><td>96.28</td><td>95.51</td><td>77.08</td><td>80.48</td></tr><tr><td colspan="4">4.3 ROBUSTNESS UNDER DISTRIBUTION SHIFTING</td><td/><td/><td/></tr></table>

Results of EdgeNetRob (EdgeGANRob) against backdoor attack on CelebA. Clean Acc Pois Acc Clean Acc Pois Acc Clean Acc Pois Acc Clean Acc Pois Acc

Table content: <table><tr><td/><td/><td/><td/><td/><td colspan="2">Method</td><td/><td/><td/></tr><tr><td colspan="2">Source Target Ratio</td><td colspan="2">Vanilla Net</td><td colspan="2">Spectral Signature</td><td colspan="2">EdgeNetRob</td><td colspan="2">EdgeGANRob</td></tr><tr><td>Man</td><td>5 10</td><td>98.3 98.2</td><td>97.4 99.0</td><td>98.35 98.03</td><td>52.89 76.14</td><td>92.3 92.2</td><td>13.80 12.10</td><td>94.53 93.84</td><td>3.66 5.46</td></tr><tr><td>Woman</td><td>5 10</td><td>98.2 98.2</td><td>99.0 96.9</td><td>98.28 98.00</td><td>93.68 22.41</td><td>94.3 93.9</td><td>8.80 7.70</td><td>93.91 94.10</td><td>11.73 9.68</td></tr></table>

Results of EdgeNetRob (EdgeGANRob) against backdoor attack on Fashion MNIST.

Table content: <table><tr><td/><td/><td/><td/><td/><td/><td colspan="2">Method</td><td/><td/></tr><tr><td>Source</td><td>Target</td><td>Ratio</td><td colspan="2">Vanilla Net</td><td colspan="2">Spectral Signature</td><td colspan="2">EdgeNetRob</td><td colspan="2">EdgeGANRob</td></tr><tr><td/><td/><td/><td colspan="8">Clean Acc Pois Acc Clean Acc Pois Acc Clean Acc Pois Acc Clean Acc Pois Acc</td></tr><tr><td/><td>T-shirt/top</td><td>20 30</td><td>87.17 87.03</td><td>95.80 97.49</td><td>86.32 84.79</td><td>96.30 98.00</td><td>83.10 82.44</td><td>1.00 2.00</td><td>88.91 88.71</td><td>0.30 0.30</td></tr><tr><td/><td>Trouser/pants</td><td>20 30</td><td>86.98 87.12</td><td>93.19 95.80</td><td>87.23 86.78</td><td>93.40 94.50</td><td>82.60 82.22</td><td>0.10 3.90</td><td>88.62 88.73</td><td>1.70 6.10</td></tr><tr><td/><td>Coat</td><td>20 30</td><td>87.55 86.83</td><td>95.59 95.80</td><td>84.88 83.18</td><td>94.80 95.20</td><td>82.90 82.71</td><td>9.2 11.80</td><td>88.98 88.82</td><td>3.20 2.92</td></tr><tr><td/><td>Dress</td><td>20 30</td><td>86.95 86.80</td><td>90.79 96.90</td><td>87.29 87.01</td><td>10.30 8.60</td><td>82.90 82.53</td><td>9.20 9.50</td><td>88.85 88.38</td><td>3.45 3.85</td></tr></table>

Peer review (iclr2020):
The paper proposes to train a classifier on top of edge detection (and, optionally, GAN-based texture filling-in) and claims to achieve robustness to adversarial examples, domain shifts and backdoor attacks using this approach. Strengths: + The rationale to make nets rely more on shape features is justified + The approach is relatively straightforward and easy to follow Weaknesses: - Solid tests for adversarial robustness are missing - Thresholding in the *robust* Canny seems to perform gradient masking - Use of GAN after edge detection is questionable (data processing inequality) Detailed comments: 1.) My main concern with the paper is that – like many other papers claiming adversarial robustness – it does not perform a solid evaluation using a range of strong attacks. Specifically, the thresholding procedure in the *robust* Canny algorithm effectively performs gradient masking, as it sets the gradient to zero wherever the Canny operator is below threshold on the unperturbed image. Thus, gradient-based attacks like the ones used by the authors are not effective. Such manipulation, however, does not imply robustness! At the very least, the authors have to apply decision-based attacks like the boundary attack [1], which is trivial to apply [2]. 2.) It*s not clear to me what purpose the GAN-based texture inpainting is meant to serve. If the GAN can learn to fill in textures that help discriminating classes, then the classifier should be able to use the same features in the edge image that the GAN uses (this statement follows from the data processing inequality). [1] Brendel, Rauber, Bethge, ICLR 2018: https://arxiv.org/abs/1712.04248 [2] https://github.com/bethgelab/foolbox