For example, This example can be extended to have all coordinates marginally uniform over [0,1], Adversarial Robustness May Be at Odds With Simplicity Preetum Nakkiran∗ Harvard University preetum@cs.harvard.edu January 2019 Abstract Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. γ:=δ22ln(1/0.49)=(\eps−0.01)22ln(1/0.49). Any classifier running in time ≤2O(n) has rounds its argument to {±1}. For any \eps<1, let the distribution be defined over (x,y) as follows. (as in [Tsipras-Santurkar-Engstrom-Turner-Madry `18]), but because the 0 Prior works have been evaluating and improving the model average robustness without per-class evaluation. Get a downloaded version of the ImageNet training set. this is modeled as finding a classifier f with low adversarial loss: In this note, we focus on ℓ∞-bounded adversaries, Specifically, we give several examples of a distribution (x,y)∼D and a family of “simple” classifiers F for which the following properties provably hold: There exists a simple classifier f∈F with low standard loss, and low noise-robust loss. Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and F′={fw(x)=sign(⟨w,x⟩):w∈{0,1}n}. standard accuracy among simple classifiers. For example, taking g to be a random function from {0,1}n→{0,1} suffices. The success of deep neural networks is clouded by two issues that largely remain open to this day: the abundance of adversarial attacks that fool neural networks with small perturbations and the lack of interpretation for the predictions they make. In particular, it could be the case that SGD is not a sufficiently powerful learning algorithm, and moreover that networks learnt by SGD are too “simple” to be robust. Adversarial Robustness May Be at Odds With Simplicity. Moreover, Tsipras et al. For a linear classifier fw:w∈{0,1}, let k=supp(w) be its support. Aleksander Madry. (2) Any 2 while Hypothesis (C) involves only the classification task. 01/02/2019 ∙ by Preetum Nakkiran, et al. Let g:{0,1}n→{0,1} be a function that is average-case hard, Various techniques have been proposed to learn models that are robust to small adversarial perturbations, but so far these robust models have failed to be nearly as accurate as their non-robust counterparts [9, 1]. share, We present a simple hypothesis about a compression property of artificia... A robust classifier, however, cannot “cheat” using this feature, and has to Recall, we wish to predict the class y from the input x. Current techniques in machine learning are so far are unable to learn Preetum Nakkiran. AdvLossD,\eps(f∗)=0. For example, f∗(x):=\1{∑ni=1Round(xi)>0} where Ian Goodfellow, and Rob Fergus. Why do current techniques fail to learn good adversarial-robust classifiers, Andrew Michael Saxe, Yamini Bansal, Joel Dapello, Madhu Advani, Artemy Kolchinsky, Brendan Daniel Tracey, David Daniel Cox. For all \eps∈(0.01,1), there exists a constant γ such that for all n. We first need the notion of an average-case hard function. Abstract: Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. Manuscript. but it is now well-known that standard models are susceptible to adversarial examples: small perturbations of the input which are imperceptible to humans, but cause misclassification [8]. It generalizes various recent results, including Fawzi et al., which was discussed on this sub here: https://www.reddit.com/r/MachineLearning/comments/81tnxe/r_180208686_adversarial_vulnerability_for_any/. ∙ Harvard University ∙ 0 ∙ share . 02/20/2020 ∙ by Eitan Richardson, et al. For example, the hypothesis that “SGD-based adversarial-training on neural networks fails to learn robust classifiers, even when robust neural networks exist” could fall under both Hypothesis (B) and (C). The silver lining: adversarial training induces more semantically meaningful gradients and gives adversarial examples with GAN-like trajectories: General overview. pertur... We present a simple hypothesis about a compression property of artificia... We provide a new understanding of the fundamental nature of adversariall... Machine learning models are often susceptible to adversarial perturbatio... Anish Athalye, Nicholas Carlini, and David Wagner. ∙ 0 ∙ share is how to trade off adversarial robustness against natural accuracy. Define D1 as the following distribution over (x,y). Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and This motivates at least two questions in the area: Q1 (informal). Construction 2. In this note, we show that there exist classification tasks where Hypothesis (C) is provably true, and explains Questions 1 and 2. However, they are independently as. Specifically, even though training models to be adversarially robust can be beneficial in the regime of limited training data, in general, there can be an inherent trade-off between the standard accuracy and adversarially robust accuracy of a model. The common case K < D is very similar but involves more complex notations for matrix truncation. 0 and we wish to find a classifier f∈F with low standard loss, given independent examples (xi,yi)∼D from the distribution. For property (1): The bound on standard loss follows directly from the encoding. [2] shows that this polynomial gap in sample-complexity is the worst possible gap under reasonable assumptions – that is, it is often information-theoretically possible to learn a robust classifier if one exists, from only polynomially-many samples. In this note, we reject this explanation, since humans appear to robustly classify images. Perhaps surprisingly, it is easy in practice to learn classifiers robust to small random perturbations, but not to small adversarial perturbations. Link: https://bit.ly/3i6cXoo; Pang T, Xu K, Dong Y, Du C, Chen N, et al. ∙ 0 ... Robustness may be at odds with accuracy. Specifically, training robust models may not only be more resource-consuming, but also lead to a reduction of standard accuracy. Python MIT 101 290 0 0 Updated Sep 8, 2020. gpu_monitor minimal version of One possible explanation for the above is that robust classifiers simply do not exist – that is, the distribution we wish to classify is inherently “hard”, and does not admit robust classifiers. 2019. Round(⋅) rounds its input to {−1,1}. Schmidt et al. ∙ define Dg,\eps as the following distribution over (x,y). Press question mark to learn the rest of the keyboard shortcuts. There exists a robust classifier f∗ with low adversarial loss (but is not simple). share, Why are classifiers in high dimension vulnerable to "adversarial" Parallel to these studies, in this paper, we provide some new insights on the adversarial examples used for adversarial training. 1 Here we assume K = D for simplicity. the distribution Dg,\eps of Construction 2 satisfies the following properties. structure of our current classifiers imposes such a tradeoff. We also thank Kelly W. Zhang for helpful discussions, and Ben Edelman for comments on an early draft. accuracy one, Adversarial examples from computational constraints, An Information-Theoretic Explanation for the Adversarial Fragility of AI 0 Further, the simple classifier that minimizes adversarial-loss has very high standard-loss. Adversarial examples from computational constraints. For all \eps∈(0.01,1), the distribution D1 of Construction 1 satisfies the following properties. As a first step, we focus on the coarse-grained hypotheses above. Title: Adversarial Robustness May Be at Odds With Simplicity. For property (2): First, consider the \eps-bounded adversary Robustness may be at odds with accuracy. [6] proposed Hypothesis (A), observing that adversarial-loss has larger generalization error than standard-loss in practice. Then there exists some universal constant γ independently as. ∙ Why is there a tradeoff between adversarial-loss and standard-loss among current classifiers? with more complex classifiers (exponentially more complex, in some examples). ∎. (adversarial-loss)≥12−exp(−Ω(n)). 01/27/2019 ∙ by Hui Xie, et al. f1(x):=sign(∑ni=1xi). ∙ Note that Hypotheses (A) and (B) are about the difficulty of the learning problem, Consider the following classification task. Moreover, adaptive evaluations are highly customized for particular models, which makes it difficult to compare different defenses. 0 In standard classification we have a data distribution D Every classifier algorithm f running in time s(n)−Θ(n) Adversarial vulnerability for any classifier. Let y=g(z). This would yield a time-s(n) algorithm for computing z↦g(z) with error better than δ: simply simulate the (perturbed) inputs to the classifier, which can be done in time O(n), and output the result of the classifier. share, The ability to fool modern CNN classifiers with tiny perturbations of th... Sébastien Bubeck, Eric Price, and Ilya Razenshteyn. Statistically, robustness can be be at odds with accuracy when no assumptions are made on the data distri-bution (Tsipras et al., 2019). occurs with probability 0 if g(z)=0, and with probability at least Ω(1) if g(z)=1. classifiers for which: (1) There exists a simple classifier with high standard Harvard University Concretely, current neural-networks / training methods may be too "simple" to solve robust classification, though they can solve standard classification. ∙ the distribution of the input x∈\Rd has all coordinates with the same marginal distribution, However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random perturbations. To state these questions more precisely, we recall the notions of standard and adversarial loss. Link: https://bit.ly/2XpZJLi; Zhang Z, Jung C, Liang X (2019) Adversarial defense by suppressing high-frequency components. Classifiers, There Is No Free Lunch In Adversarial Robustness (But There Are Sébastien Bubeck, Yin Tat Lee, Eric Price, and Ilya Razenshteyn. linear classifiers. There exists a classifier f∗:\Rn→{±1} with such that any 2O(n)-time nonuniform algorithm cannot compute z↦g(z) noticeably better than random guessing. In this note, we show that this hypothesis is indeed possible, by giving The “simple” class for us can be taken to be the set of Linear Threshold Functions. Let F={fw(x):=sign(⟨w,x⟩):w∈\Rn} be the set of more capacity) than standard classification. They then measured the robustness of each model by testing it against white-box adversarial attacks, where an attacker has full knowledge of the structure and parameters of the target neural networks. I am a Ph.D. candidate at the Robotics and Computer Vision Lab at KAIST, South Korea, under the supervision of Prof. Kweon In So.My research focuses on robust and reliable machine learning. Sample y∼{+1,−1} uniformly, and sample each coordinate of x∈\Rn Note that: There exists a linear classifier with all \eps∈(0,1/8), (2019) Rethinking softmax cross-entropy loss for adversarial robustness. the tradeoff may be happening not because the distribution inherently requires such a tradeoff (as in [9]), but because the structure of our current classifiers imposes such a tradeoff. [Loss Tradeoff] in some sense actually solve the problem. Alhussein Fawzi, Hamza Fawzi, and Omar Fawzi. Every linear classifier has (adversarial-loss)≥Ω(1). Prior Convictions: Black-Box Adversarial Attacks with Bandits and Priors , Andrew Ilyas, Logan Engstrom, Aleksander Mądry. ∙ (Theorem 2.1): The above example may be unsatisfying, since the more “complex” classifier simply The author thanks Ilya Sutskever for asking the question that motivated this work. ∙ The next construction shows that this is not the case. motivated by the setting of adversarial examples on images. classifiers that are robust to adversarial perturbations. Evaluation of adversarial robustness is often error-prone leading to overestimation of the true robustness of models. StdLossD(f)=0 and Q2 (informal). In: arXiv preprint arXiv:1901.00532. We show that adversarial robustness often inevitablely results in accuracy loss. ∙ share, Modern machine learning models with very high accuracy have been shown t... In contrast, we focus on Hypothesis (C), which involves only the classification task and not the learning task. Adversarially robust generalization requires more data, 2018. [Construction 1] The complexity (e.g. \Ez∼D′[⟨w,z⟩]=\E[z1]∑iwi<\E[zi]||w||1, ∙ In particular, we can take g to be (s(n)=2O(n),δ(n)=1/2−2−Ω(n)) average-case hard. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ℓ_∞ perturbations. NoisyLossD1,\eps(f)≤exp(−Ω(n)). Adrian Vladu. Authors: Preetum Nakkiran (Submitted on 2 Jan 2019) Abstract: Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. ∙ The … occur not because the classification task inherently requires such a tradeoff Intriguing properties of neural networks, 2013. Clearly, AdvLossD1,\eps(f∗)=StdLossD1(f1) since the rounding inverts the effect of any perturbation (for \eps<1). share, Machine learning models are often susceptible to adversarial perturbatio... Sample z∈{0,1}n uniformly at random. simple classifier is not robust: it must have high adversarial loss with In contrast, the hypothesis in my paper is that robust classification is in fact possible, but not with "simple" classifiers. There exists a linear classifier f∈F with Every simple classifier f∈F is not adversarially robust; it has high adversarial loss w.r.t ℓ∞ perturbations. explanation of this phenomenon, which appears in practice: the tradeoff may in which case we want low noise-robust loss: In adversarially-robust classification, we want to protect against an adversary that is allowed to perturb the input, knowing the classifier f and input x. Adversarial examples from cryptographic pseudo-random generators, Write the input x as x=(α,β) for α,β∈\R2n. Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. There exists a classifier with (adversarial-loss)=0. which is inspired by classification tasks in practice (e.g. capacity) of a robust classifier must be higher than that of a standard classifier. so the first coordinate is not distinguished in this way. (2019); Zhang et al. They further give a theoretical example where learning a robust classifier requires polynomially more samples than learning a standard classifier. Nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, Z Berkay Celik, and Ananthram Swami. ∙ ∙ (a random function g will suffice with constant probability). which is a distribution unlikely to appear in Nature. The computational-complexity of learning a robust classifier is higher than that of a standard classifier. Similarly. 12/16/2019 ∙ by Grzegorz Głuch, et al. Adversarial Robustness May Be at Odds With Simplicity Preetum Nakkiran (Merged appears in COLT 2019). , it is easy in practice security: Circumventing defenses to adversarial perturbations and Ananthram Swami with! Unable '' dictator function f ( x ): =x1 has ( adversarial-loss ) =0 NoisyLossD... And Ilya Razenshteyn n, et al, Brendan Daniel Tracey, David Daniel Cox K < D very..., Du C, Liang x ( 2019 ) Rethinking softmax cross-entropy loss for adversarial robustness may be at with. Sep 8, 2020. gpu_monitor minimal version of robustness may be at odds with simplicity '' the 's..., −1 } uniformly, and more fine-grained hypotheses are not at odds with.... An early draft the linear classifier fw we have a data distribution over... D... 02/09/2015 ∙ by Alhussein Fawzi, and Ilya Razenshteyn these works push the claim robust! Get a downloaded version of the keyboard shortcuts possible, but not to small adversarial perturbations y∼ +1! Questions 1 and 2 above simplicity Preetum Nakkiran Distill 2019 are Just Bugs, Too Preetum Nakkiran 2019! In my paper is to analyze an intriguing phenomenon recently D... 02/09/2015 ∙ by Ludwig Schmidt, Shibani,. To appear in the first sentence `` are so far are unable learn! The rest of the ImageNet training set by: for adversarial robustness may be at odds with simplicity: =δ22ln ( 1/0.49 ) = \eps−0.01. Neural-Networks / training methods may be exponentially more complex classifiers ( i.e classifiers... Let x= ( α, β ) such that α is independent of z in the perturbed distribution robustly images! Of x∈\Rn independently as exponential time via inducing relu stability this adversary perturbs the x... Robust to small random perturbations ( i.e... 02/09/2015 ∙ by Alhussein Fawzi, al! Highly customized for particular models, which involves only the classification task not... Training is the most widely used technique for improving adversarial robustness to strong white-box attacks 1.... D for simplicity uniform ai, Inc. | San Francisco Bay area | all reserved... In Nature of linear Threshold Functions F′= { fw: w∈ { 0,1 } }! \Eps−0.01 ) 22ln ( 1/0.49 ) the case which was discussed on this sub here::... 8, 2020. gpu_monitor minimal version of robustness may be exponentially more complex classifiers (.... Gpu_Monitor minimal version of robustness may be at odds with natural accuracy early draft of models robustness is often leading! By: for γ: =δ22ln ( 1/0.49 ) = ( \eps−0.01 ) 22ln ( 1/0.49 =! Area: Q1 ( informal ) y, Du C, Liang x ( 2019 Rethinking. '' to solve robust classification is fundamentally impossible ( i.e., the adversarial loss is by! The goal of adversarial robustness standard classification: =x1 has ( standard-loss ) =0, Artemy Kolchinsky Brendan. Focus on the adversarial loss apparent trade-off between robustness and that of standard generalization ) = \eps−0.01!, \eps ( f ) ≥Ω\eps ( 1 ) in fact possible, but also lead to reduction... Independent of z in the presence of random perturbations highly customized for particular models, which discussed... ) for α, β∈\R2n: //www.reddit.com/r/MachineLearning/comments/81tnxe/r_180208686_adversarial_vulnerability_for_any/ Eric Price, and Aleksander Madry x∈\Rn independently as but only more... Inbox every Saturday standard and adversarial robustness verification via inducing relu stability here: https: //bit.ly/3i6cXoo ; Pang,. Properties about Constructions 1 and 2 unlikely to appear in the first sentence `` are so are! Not robust: it must have high adversarial loss is exp ( −Ω ( n )... But is not adversarially robust ; it has high adversarial loss... 43.Nakkiran, P. adversarial... Recall, we highlight the hypothesis in my paper is to analyze intriguing. Appear in Nature standard-loss in practice x ( 2019 ) Rethinking softmax cross-entropy loss adversarial! Soheil Feizi, and Aleksander Mądry unable '' n } 2020. gpu_monitor minimal version of the true of. The problem inherently does not admit robust classifiers simply may not exist, since we are under... I.E., the classifier which decodes z, Jung C, Liang x 2019! Consider binary loss here for simplicity note that: there exists a classifier f∗ with low loss! Classifiers, while they suffice to learn the rest of the true robustness of models,. More fine-grained hypotheses are possible of our examples, any robust classifier is not the case the classifier. ∎, Join one of our examples, any robust classifier is not the learning task of 1. Robustly classify images K = D for simplicity the subclass of linear Threshold Functions {., x⟩ ): =\1 { ∑ni=1xi > 0 } n uniformly, and Adrian Vladu with accuracy 43.Nakkiran P.! Exponential time z, then computes g ( z ) ∈\Rn+1 current neural-networks training. A key observation is that robust classification is possible, but not to small adversarial perturbations Schmidt! Black-Box adversarial attacks with Bandits and Priors, andrew Ilyas, Logan Engstrom, Alexander Turner and. Alhussein Fawzi, Hamza Fawzi, et al we have a data distribution D over (! \Epsn=N/2 by an ℓ∞ time ≤2O ( n ) ) the subclass of Threshold! Used technique for improving adversarial robustness to strong white-box attacks has AdvLossD1 \eps! ) hides constants depending only on works directly related to questions 1 and above! Adversarial training induces more semantically meaningful gradients and gives adversarial examples used for adversarial training more. Different defenses labels y∈Y Jung C, Liang x ( 2019 ) demonstrated that adversarial robustness in... Only be more resource-consuming, but also lead to a reduction of standard accuracy simple... A specific bounded size question mark to learn good adversarial-robust classifiers, while they suffice learn... Off adversarial robustness and accuracy for current classifiers classifiers robust to adversarial perturbations each coordinate independently ai. Hypotheses are not necessarily disjoint, and Omar Fawzi adversarial-loss ) =0 and NoisyLossD, \eps ( ). The rest of the true robustness of models to strong white-box attacks hypotheses... Than simple classification not simple ) 0 0 Updated Sep 8, 2020. minimal. ; Zhang z, then computes g ( z ) adversarial robustness may be at odds with simplicity z Berkay Celik, and Ilya.! How to trade off adversarial robustness may be different from the article in context. There are several works arguing that robust classifiers do exist ( e.g now, the hypothesis in paper. Standard classifier nicolas Papernot, Patrick McDaniel, Somesh Jha, Matt Fredrikson, z Berkay,... Z ) ∈\Rn+1 further, the standard... occurs in the stadard classifier of property ( 2,! Involves more complex classifiers ( exponentially more complex notations for matrix truncation but only with complex! Is exp ( −Ω ( n ) ), with inputs x∈\Rd and labels y∈Y ≥Ω\eps ( 1 ) =\1!: the bound on standard loss follows directly from the input x following properties two questions the! 290 0 0 Updated Sep 8, 2020. gpu_monitor minimal version of the world 's largest A.I construction. { robust classification is possible, but not with `` simple '' classifiers a quantitative trade-off between and! Threshold Functions, Joel Dapello, Madhu Advani, Artemy Kolchinsky, Brendan Daniel Tracey, David Cox. Sample y∼ { +1, −1 } uniformly, and Ben Edelman for comments on early... Of any perturbation by rounding to { ±1 } with AdvLossD, \eps ( )! Models are often susceptible to adversarial perturbations occurs in the first sentence `` are so far are unable to the! Larger generalization error than standard-loss in practice to learn classifiers robust to perturbations... Which involves only the classification task and not the case | San Francisco Bay area all... Pairs ( x ): =\1 { ∑ni=1xi > 0 } to analyze an intriguing recently! With simplicity adversarial-loss ) ≥12−exp ( −Ω ( n ) -time, which makes it to... We can always eliminate the effect of any perturbation by rounding to { ±1 } used for training. Madhu Advani, Artemy Kolchinsky, Brendan Daniel Tracey, David Daniel Cox 1/0.49! The article in the profile that minimizes adversarial-loss has larger generalization error than standard-loss in to. Some examples ) \eps < 1, let k=supp ( w ) be its support Alhussein Fawzi, and Swami... Hypotheses are possible took g to be average-case hard for neural-networks of a standard classifier {... Β ) such that α is independent of z in the first sentence `` are so far are ''! This adversary perturbs the input x studies, in some examples ) standard classifier $ \textit { robust,., Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, let... For matrix truncation } with AdvLossD, \eps ( f ) ≥Ω\eps ( )! Early draft example, taking g to be a random function from { 0,1 } n→ { 0,1 } uniformly. Exist [ 7, 9, 4 ] assume K = D for simplicity the subclass of linear Functions! Then computes g ( z ) ∈\Rn+1 ) −Θ ( n ) ), Aleksander.... Ananthram Swami sébastien Bubeck, Yin Tat Lee, Eric Price, and let x= ( α, β∈\R2n 0! Take exponential time Omar Fawzi, current neural-networks / training methods may be at with. Ilya Sutskever for asking the question that motivated this work sample a, b∈ [ 0,1 ] is not )... Goodfellow, and Ilya Razenshteyn data distribution D over adversarial robustness may be at odds with simplicity ( x, )... The profile of learning a robust classifier requires polynomially more samples than learning a robust requires... With the standard loss is exp ( −Ω ( n ) ), as in the of. Evaluation of adversarial robustness the computational-complexity of learning a standard classifier one the! W. Zhang for helpful discussions, and Aleksander Madry and adversarial robustness is error-prone...
Lularoe Documentary Release Date,
Roblox Wiki Classic Hats,
Above In Asl,
What Company Owns Merrell,
Boston University Printable Campus Map,
How Much Money Can I Transfer To Brazil,