/Contents 367 0 R In this paper, we propose composite adversarial training (CAT), a novel training method that ﬂexibly inte-grates and optimizes multiple adversarial losses, leading to signiﬁcant robustness improvement with respect to individual perturbations as well as their “compo-sitions”. Adversarial Training and Robustness for Multiple Perturbations Florian Tramèr Stanford University Dan Boneh Stanford University Abstract Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small ‘ 1-noise). /Contents 369 0 R 12 0 obj [14] formulates the defense ofmodel ro-bustness as a min-max optimization problem, in which the adversary is constructed to achieve high loss value Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small ℓ∞ ℓ ∞ -noise). /Producer (PyPDF2) Get the latest machine learning methods with code. /Resources 339 0 R << /Parent 1 0 R Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). This site uses cookies for analytics, personalized content and ads. In particular, we uncover a pernicious gradient-masking phenomenon on MNIST, which causes adversarial training with first-order $\ell_\infty, \ell_1$ and $\ell_2$ adversaries to achieve merely $50\%$ accuracy. robust optimization, which guarantees performance under adversarial input perturbations. Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small -noise). /Contents 317 0 R Using adversarial training to defend against multiple types of perturbation requires expensive adversarial examples from different perturbation types at each training step. >> /Parent 1 0 R >> /Filter /FlateDecode Adversarial training improves the model robustness by train-ing on adversarial examples generated by FGSM and PGD (Goodfellow et al.,2015;Madry et al.,2018).Tramer et al. (2018) proposed an ensemble adversarial training on ad-versarial examples generated from a number of pretrained “Exploiting Excessive Invariance caused by Norm-Bounded Adversarial Robustness” ∈0, 1784 natural. 09/09/2019 ∙ by Pratyush Maini, et al. [Download notes as jupyter notebook](adversarial_training.tar.gz) ## From adversarial examples to training robust models In the previous chapter, we focused on methods for solving the inner maximization problem over perturbations; that is, to finding the solution to the problem $$\DeclareMathOperator*{\maximize}{maximize} \maximize_{\|\delta\| \leq \epsilon} \ell(h_\theta(x + … << Notice, Smithsonian Terms of /Contents 228 0 R Adversarial training improves the model robustness by train-ing on adversarial examples generated by FGSM and PGD (Goodfellow et al.,2015;Madry et al.,2018).Tramer et al. (2018) proposed an ensemble adversarial training on ad-versarial examples generated from a number of pretrained >> /Publisher (Curran Associates\054 Inc\056) Building upon new multi-perturbation adversarial training schemes, and a novel efficient attack for finding \ell_1-bounded adversarial examples, we show that no model trained against multiple attacks achieves robustness competitive with that of models trained on each attack individually. the Lipschitz constant [9, 20, 39] or adversarial training [19, 26]. /Contents 338 0 R In this paper, we propose composite adversarial training (CAT), a novel training method that ﬂexibly inte- grates and optimizes multiple adversarial losses, leading to signiﬁcant robustness endobj Repeat until convergence Besides, a single attack algorithm could be insufﬁcient to explore the space of perturbations. /Parent 1 0 R << Building upon new multi-perturbation adversarial training schemes, and a novel efficient attack for finding \ell_1-bounded adversarial examples, we show that no model trained against multiple attacks achieves robustness competitive with that of models trained on each attack individually. xڭZK�۸�ϯ�%��b�_�!���)o�g=�� Browse our catalogue of tasks and access state-of-the-art solutions. Here, we take an orthogonal approach to the previous studies and seek to increase the lower bound of Equation 2 by exploring the joint robustness of multiple classiﬁers. /Annots [ 50 0 R 51 0 R 52 0 R 53 0 R 54 0 R 55 0 R 56 0 R 57 0 R 58 0 R 59 0 R 60 0 R 61 0 R 62 0 R 63 0 R 64 0 R 65 0 R 66 0 R 67 0 R 68 0 R 69 0 R 70 0 R ] << Adversarial training techniques for single modal tasks on images and text have been shown to make a model more robust and generalizable. endobj Adversarial Robustness Against the Union of Multiple Perturbation Models Algorithm 1 Multi steepest descent for learning classiﬁers that are simultaneously robust to ℓp attacks for p ∈ S Input: classiﬁer fθ, data x, labels y Parameters: ǫp,αp for p ∈ S, maximum iterations T, loss function ℓ /EventType (Poster) As we seek to deploy machine learning systems not only on virtual domains, but also in real systems, it becomes critical that we examine not only whether the systems don’t simply work “most of the time”, but which are truly robust and reliable. 1. Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small \ell_\infty-noise). /MediaBox [ 0 0 612 792 ] /Book (Advances in Neural Information Processing Systems 32) /MediaBox [ 0 0 612 792 ] /Editors (H\056 Wallach and H\056 Larochelle and A\056 Beygelzimer and F\056 d\047Alch\351\055Buc and E\056 Fox and R\056 Garnett) /Annots [ 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R 211 0 R 212 0 R 213 0 R 214 0 R 215 0 R 216 0 R 217 0 R 218 0 R 219 0 R 220 0 R 221 0 R 222 0 R 223 0 R 224 0 R 225 0 R 226 0 R 227 0 R ] For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. 1 0 obj /Resources 16 0 R /Annots [ 340 0 R 341 0 R 342 0 R 343 0 R 344 0 R 345 0 R 346 0 R 347 0 R 348 0 R 349 0 R ] stream /Length 3650 >> endobj Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple … << << /Parent 1 0 R /Resources 370 0 R For other perturbations, 11 0 obj >> Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. Recent works have proposed defenses to improve the robustness of a single model against the union of multiple perturbation types. /Contents 15 0 R 15 0 obj /MediaBox [ 0 0 612 792 ] /firstpage (5866) By considering a Lagrangian penalty formulation of perturbation of the underlying data distribution in a Wasserstein ball, we provide a training procedure that augments model parameter updates with worst-case perturbations of training data. endobj Szegedy et /Annots [ 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R 245 0 R 246 0 R 247 0 R ] /Count 11 Furthermore, we complement all the methods with efﬁcient training /Contents 350 0 R We propose new multi-perturbation adversarial training schemes, as well as an efficient attack for the \ell_1-norm, and use these to show that models trained against multiple attacks fail to achieve robustness competitive with that of models trained on each attack individually. [Download notes as jupyter notebook](adversarial_training.tar.gz) ## From adversarial examples to training robust models In the previous chapter, we focused on methods for solving the inner maximization problem over perturbations; that is, to finding the solution to the problem$$ \DeclareMathOperator*{\maximize}{maximize} \maximize_{\|\delta\| \leq \epsilon} \ell(h_\theta(x + … (Simple dataset, centered and scaled, non-trivial robustness is achievable) Using adversarial training, models have been trained to “extreme” levels of robustness (E.g., robust to L 1noise > 30 or L ∞noise > 0.3) 13 Jacobsen et al.“Exploiting Excessive Invariance caused by Norm-Bounded Adversarial Robustness” ∈0,1784 natural L 1perturbed L /Type /Catalog We corroborate our formal analysis by demonstrating similar robustness trade-offs on MNIST and CIFAR10. /Resources 318 0 R %aF,K�BR����� P�W�9�l ��F��d�H�If��"]l7Te�PqY���,�o�~�߽ۛ�07��H���~!�4.�l��E\�jq�]|���~Y�$2]_uu�_�d�D��\G]U7u������ˏ�z)�����{��/e������E��Zf��(�R��ǻ�~��{ó��z� �n] u��������L�q�,����-����v��2�,��~�m���.؎sb7Q��r&�;�M���JK=0� �d's��m��|���4����;D����ɡ�"���S4�4��m���ޠ>���ͅ� ��"�"���OQHw��~��E?W�%"N�x0ZYJe�*t ^̽izCʠ��zX�T�����@C�����Š��ٹ�+��nU�:֛j��2 =)�$�,.�f����"��ږ�eT�z��:N�G�������b"E�?{>�#DA �R! Adding adversarial perturbations to the embedding space (as in FreeLB). >> Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. To address this issue, we train our MNG while randomly sampling an attack at each epoch, which incurs negligible overhead over standard adversarial training. << /Type /Pages ∙ Carnegie Mellon University ∙ 0 ∙ share . 9 0 obj >> 3 Adversarial Setting The goal of an adversary is to \fool" the target model by adding human-imperceptible perturbations to its input. (Simple dataset, centered and scaled, non-trivial robustness is achievable) Using adversarial training, models have been trained to “extreme” levels of robustness (E.g., robust to L 1 noise > 30 or L ∞ noise > 0.3)Jacobsen et al. /lastpage (5876) We prove that a trade-off in robustness to different types of $\ell_p$-bounded and spatial perturbations must exist in a natural and simple statistical setting. to adversarial perturbations is still severe in deep learning. the Lipschitz constant [9, 20, 39] or adversarial training [19, 26]. /Resources 72 0 R >> /ModDate (D\07220200213002547\05508\04700\047) gradient norm and adversarial robustness. By continuing to browse this site, you agree to this use. Adversarial Training and Robustness for Multiple Perturbations Florian Tramèr Stanford University Dan Boneh Stanford University Abstract Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small ℓ∞-noise). endobj Adversarial Robustness Against the Union of Multiple Perturbation Models. Joint Robustness of Multiple Classiﬁers Let F be an ensemble of k classiﬁers, F={fi}k−1 i=0, /Type /Page >> 7 0 obj /Parent 1 0 R The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative /MediaBox [ 0 0 612 792 ] /Type /Page << Nonetheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the research of adversarial attack and defense.

## adversarial training and robustness for multiple perturbations

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