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Title: Defending Against Physically Realizable Attacks on Image Classification

Paper content:
We study the problem of defending deep neural network approaches for image classification from physically realizable attacks.
First, we demonstrate that the two most scalable and effective methods for learning robust models, adversarial training with PGD attacks and randomized smoothing, exhibit very limited effectiveness against three of the highest profile physical attacks.
Next, we propose a new abstract adversarial model, rectangular occlusion attacks, in which an adversary places a small adversarially crafted rectangle in an image, and develop two approaches for efficiently computing the resulting adversarial examples.
Finally, we demonstrate that adversarial training using our new attack yields image classification models that exhibit high robustness against the physically realizable attacks we study, offering the first effective generic defense against such attacks.
State-of-the-art effectiveness of deep neural networks has made it the technique of choice in a variety of fields, including computer vision (He et al., 2016) , natural language processing (Sutskever et al., 2014) , and speech recognition (Hinton et al., 2012) .
However, there have been a myriad of demonstrations showing that deep neural networks can be easily fooled by carefully perturbing pixels in an image through what have become known as adversarial example attacks (Szegedy et al., 2014; Goodfellow et al., 2015; Carlini & Wagner, 2017b; Vorobeychik & Kantarcioglu, 2018) .
In response, a large literature has emerged on defending deep neural networks against adversarial examples, typically either proposing techniques for learning more robust neural network models (Wong & Kolter, 2018; Wong et al., 2018; Raghunathan et al., 2018b; Cohen et al., 2019; Madry et al., 2018) , or by detecting adversarial inputs (Metzen et al., 2017; Xu et al., 2018) .
Particularly concerning, however, have been a number of demonstrations that implement adversarial perturbations directly in physical objects that are subsequently captured by a camera, and then fed through the deep neural network classifier (Boloor et al., 2019; Eykholt et al., 2018; Athalye et al., 2018b; Brown et al., 2018) .
Among the most significant of such physical attacks on deep neural networks are three that we specifically consider here: 1) the attack which fools face recognition by using adversarially designed eyeglass frames (Sharif et al., 2016) , 2) the attack which fools stop sign classification by adding adversarially crafted stickers (Eykholt et al., 2018) , and 3) the universal adversarial patch attack, which causes targeted misclassification of any object with the adversarially designed sticker (patch) (Brown et al., 2018) .
Oddly, while considerable attention has been devoted to defending against adversarial perturbation attacks in the digital space, there are no effective methods specifically to defend against such physical attacks.
Our first contribution is an empirical evaluation of the effectiveness of conventional approaches to robust ML against two physically realizable attacks: the eyeglass frame attack on face recognition (Sharif et al., 2016) and the sticker attack on stop signs (Eykholt et al., 2018) .
Specifically, we study the performance on adversarial training and randomized smoothing against these attacks, and show that both have limited effectiveness in this context (quite ineffective in some settings, and somewhat more effective, but still not highly robust, in others), despite showing moderate effectiveness against l ∞ and l 2 attacks, respectively.
Our second contribution is a novel abstract attack model which more directly captures the nature of common physically realizable attacks than the conventional l p -based models.
Specifically, we consider a simple class of rectangular occlusion attacks in which the attacker places a rectangular sticker onto an image, with both the location and the content of the sticker adversarially chosen.
We develop several algorithms for computing such adversarial occlusions, and use adversarial training to obtain neural network models that are robust to these.
We then experimentally demonstrate that our proposed approach is significantly more robust against physical attacks on deep neural networks than adversarial training and randomized smoothing methods that leverage l p -based attack models.
Related Work While many approaches for defending deep learning in vision applications have been proposed, robust learning methods have been particularly promising, since alternatives are often defeated soon after being proposed (Madry et al., 2018; Raghunathan et al., 2018a; Wong & Kolter, 2018; Vorobeychik & Kantarcioglu, 2018) .
The standard solution approach for this problem is an adaptation of Stochastic Gradient Descent (SGD) where gradients are either with respect to the loss at the optimal adversarial perturbation for each i (or approximation thereof, such as using heuristic local search (Goodfellow et al., 2015; Madry et al., 2018) or a convex over-approximation (Raghunathan et al., 2018b; Wang et al., 2018) ), or with respect to the dual of the convex relaxation of the attacker maximization problem (Raghunathan et al., 2018a; Wong & Kolter, 2018; Wong et al., 2018) .
Despite these advances, adversarial training a la Madry et al. (2018) remains the most practically effective method for hardening neural networks against adversarial examples with l ∞ -norm perturbation constraints.
Recently, randomized smoothing emerged as another class of techniques for obtaining robustness (Lecuyer et al., 2019; Cohen et al., 2019) , with the strongest results in the context of l 2 -norm attacks.
In addition to training neural networks that are robust by construction, a number of methods study the problem of detecting adversarial examples (Metzen et al., 2017; Xu et al., 2018) , with mixed results (Carlini & Wagner, 2017a) .
Of particular interest is recent work on detecting physical adversarial examples (Chou et al., 2018) .
However, detection is inherently weaker than robustness, which is our goal, as even perfect detection does not resolve the question of how to make decisions on adversarial examples.
Finally, our work is in the spirit of other recent efforts that characterize robustness of neural networks to physically realistic perturbations, such as translations, rotations, blurring, and contrast (Engstrom et al., 2019; Hendrycks & Dietterich, 2019) .
There are two possible reasons why conventional robust ML perform poorly against physical attacks:
1) adversarial models involving l p -bounded perturbations are too hard to enable effective robust learning, and
2) the conventional attack model is too much of a mismatch for realistic physical attacks.
In Appendix B, we present evidence supporting the latter.
Specifically, we find that conventional robust ML models exhibit much higher robustness when faced with the l p -bounded attacks they are trained to be robust to.
As we have shown, conventional methods for making deep learning approaches for image classification robust to physically realizable attacks tend to be relatively ineffective.
In contrast, a new threat model we proposed, rectangular occlusion attacks (ROA), coupled with adversarial training, achieves high robustness against several prominent examples of physical attacks.
While we explored a number of variations of ROA attacks as a means to achieve robustness against physical attacks, numerous questions remain.
For example, can we develop effective methods to certify robustness against ROA, and are the resulting approaches as effective in practice as our method based on a combination of heuristically computed attacks and adversarial training?
Are there other types of occlusions that are more effective?
Answers to these and related questions may prove a promising path towards practical robustness of deep learning when deployed for downstream applications of computer vision such as autonomous driving and face recognition.
(Parkhi et al., 2015 ) is a benchmark for face recognition, containing 2622 subjusts with 2.6 million images in total.
We chose ten subjects: A. J. Buckley, A. R. Rahman, Aamir Khan, Aaron Staton, Aaron Tveit, Aaron Yoo, Abbie Cornish, Abel Ferrara, Abigail Breslin, and Abigail Spencer, and subselected face images pertaining only to these individuals.
Since approximately half of the images cannot be downloaded, our final dataset contains 300-500 images for each subject.
We used the standard corp-and-resize method to process the data to be 224 × 224 pixels, and split the dataset into training, validation, and test according to a 7:2:1 ratio for each subject.
In total, the data set has 3178 images in the training set, 922 images in the validation set, and 470 images in the test set.
We use the VGGFace convolutional neural network (Parkhi et al., 2015) model, a variant of the VGG16 model containing 5 convolutional layer blocks and 3 fully connected layers.
We make use of standard transfer learning as we only classify 10 subjects, keeping the convolutional layers as same as VGGFace structure, 3 but changing the fully connected layer to be 1024 → 1024 →10 instead of 4096 → 4096 →2622.
Specifically, in our Pytorch implementation, we convert the images from RGB to BGR channel orders and subtract the mean value [129.1863, 104.7624, 93 .5940] in order to use the pretrained weights from VGG-Face on convolutional layers.
We set the batch size to be 64 and use Pytorch built-in Adam Optimizer with an initial learning rate of 10 −4 and default parameters in Pytorch.
4 We drop the learning rate by 0.1 every 10 epochs.
Additionally, we used validation set accuracy to keep track of model performance and choose a model in case of overfitting.
After 30 epochs of training, the model successfully obtains 98.94 % on test data.

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