8 0 obj /Annots [ 292 0 R 293 0 R 294 0 R 295 0 R 296 0 R 297 0 R 298 0 R 299 0 R 300 0 R 301 0 R 302 0 R 303 0 R 304 0 R 305 0 R 306 0 R 307 0 R 308 0 R 309 0 R 310 0 R 311 0 R 312 0 R 313 0 R 314 0 R 315 0 R 316 0 R ] >> 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. For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. adversarial attacks have been proposed to increase the model’s robustness. 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). /Parent 1 0 R /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Type (Conference Proceedings) /Type /Page Nonetheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the research of adversarial attack and defense. Introduction. << /Book (Advances in Neural Information Processing Systems 32) << 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. << /Contents 248 0 R stream /MediaBox [ 0 0 612 792 ] /Annots [ 254 0 R 255 0 R 256 0 R 257 0 R 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 264 0 R 265 0 R ] /Parent 1 0 R Adversarial Interpolation Training: A Simple Approach for Improving Model Robustness Adversarial Robustness Against the Union of Multiple Perturbation Models 发布于 2019-12-20 Adversarial robustness and training. /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 ] /Contents 369 0 R gradient norm and adversarial robustness. /Resources 229 0 R 1. /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) << of multiple perturbations is still fairly under-studied. Computer Science - Cryptography and Security. endobj However, most existing AT methods adopt a speciﬁc attack to craft adversarial examples, leading to the unreliable robustness against other unseen attacks. Repeat until convergence Creating human understandable adversarial examples (as in Szegedy et al.) the Lipschitz constant [9, 20, 39] or adversarial training [19, 26]. Besides, a single attack algorithm could be insufﬁcient to explore the space of perturbations. << /firstpage (5866) /MediaBox [ 0 0 612 792 ] /Pages 1 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! Adversarial Training and Robustness for Multiple Perturbations Adversarial training Szegedy et al., 2014 Madry et al., 2017 1. /Type /Page /Parent 1 0 R /Date (2019) /MediaBox [ 0 0 612 792 ] Adversarial Robustness Against the Union of Multiple Perturbation Models. >> We study statistical properties of adversarial robustness in a natural statistical model introduced in [tsipras2019robustness], and which exhibits many phenomena observed on real data, such as trade-offs between robustness and accuracy [tsipras2019robustness] or a higher sample complexity for robust generalization [schott2018towards]. << /Length 3650 Existing defenses against adversarial attacks are typically tailored to a specific perturbation type. 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. /Resources 72 0 R 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. endobj /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) << /MediaBox [ 0 0 612 792 ] [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 + … Implemented in one code library. /Count 11 /MediaBox [ 0 0 612 792 ] /Type /Catalog /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 ] which adversarial training is the most effective. endobj 12 0 obj For each example , find an adversarial example: 3. To address this issue, we train our MNG while randomly sampling an attack at each epoch, which incurs negligible overhead over standard adversarial training. /Resources 351 0 R << (ICLR, 2019) to simultaneous robustness to multiple perturbations. We corroborate our formal analysis by demonstrating similar robustness trade-offs on MNIST and CIFAR10. 3.2. Introduction. /Author (Florian Tramer\054 Dan Boneh) /Parent 1 0 R 4 0 obj Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small ℓ∞ ℓ ∞ -noise). 15 0 obj /Parent 1 0 R /Type /Page << We performed a fairly thorough evaluation of the models we trained using a wide range of attacks. For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. /Resources 368 0 R /Resources 318 0 R Increase the model 's vulnerability is still severe in deep learning fairly thorough evaluation of the we... 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