NeurIPS 2020

AdvFlow: Inconspicuous Black-box Adversarial Attacks using Normalizing Flows

Review 1

Summary and Contributions: This paper proposes a new score-based black-box attack method. A flow-based generative model is used to model the probability distribution of data. The adversarial examples are searched over the latent space of the flow-based model, making them hard to detect. Experimental results on CIFAR-10 and SVHN demonstrate the effectiveness of the proposed method over two baselines.

Strengths: This paper introduces the idea of using flow-based generative models for effective black-box adversarial attacks. The method is technically sound and empirically effective.

Weaknesses: Although the idea of using a flow-based generative model for adversarial attacks is new, there already exist other works on using other types of generative models for adversarial attacks. The authors have reviewed related works in Sec. 2, and the main claim is that the proposed model can be pre-trained and adapted to any classifier. Why do other generative models (e.g., GANs) cannot be used in this way? Another concern is about the experiments of this paper. Only two baselines (Bandits and Nattack) are adopted for comparison. There are many recent works in this field. The authors are encouraged to compare with SOTA to show the effectiveness.

Correctness: The proposed method is technically correct. The experimental methodology is also correct, though it could be improved (e.g., more experiments on ImageNet are encouraged to include).

Clarity: Yes.

Relation to Prior Work: Yes

Reproducibility: Yes

Additional Feedback: Comments after rebuttal: Thanks for the efforts when preparing the rebuttal. Now it's much clearer why normalizing flows are better for black-box adversarial attacks than other generative models. The additional results on the comparison with SimBA are also promising. Although the idea of stacking a NF model before the classifier is simple and well-motivated, I found that the adversarial attack method is almost the same as Nattack (in Eq.(12)). Then the main technical contributions lie in using the NF model, which could be insufficient since a previous work also tried to use an Auto-encoder [48] before the classifier (the authors have discussed the differences between [48], but the the idea is similar). My further suggestion on this paper is to conduct experiments on large-scale datasets (e.g., ImageNet), which could better show the effectiveness of the proposed method.

Review 2

Summary and Contributions: This work generates adversarial samples that follow the structure of the original data distribution. They are the first to estimate this data distribution with a normalizing flow and then perturb the flow's latent distribution to make it represent a modified data distribution, the adversarial distribution. The induced structure in the adversarial distribution is somewhat less likely to be detected by typical defendant classifiers than previous approaches approximating the adversarial distribution. The approach to create adversarials using generative models is a promising direction that allows arguments about the structure of the samples. This method provides better adversarials than previous SOTA for defended classifiers, and performs comparably for vanilla classifiers.

Strengths: The adversarial distribution learnt by this method can represent coordinated changes across an image instead of changing pixels independently. This allows adversarials to lie closer to the original data, smeering the line between data and adversarial distribution.

Weaknesses: The performance on vanilla and defended classifiers is different: AdvFlow only outperforms for the defended case. It is unclear to me how an affine transformation of the latent space affects the distribution represented by a normalizing flow. IMO, this is out of the scope of this paper and an open problem for NFs.

Correctness: Lemma 3.1 certainly holds – but Corollary 3.1.1 does not follow without further analysis: Is the learnt delta_z in the valid limit of the Taylor expansion?

Clarity: Yes, the paper is self-contained and guides the reader well. I would like to hear the answer to one technical question: Why can sigma not be learnt jointly with mu? --> Update: Thanks for the answer that it is a hyperparameter that might be added to the list of variables.

Relation to Prior Work: Yes, this work is the first to directly learn the adversarial distribution by slightly modifying a learnt representation of the data distribution using a flow model. The empirical findings mainly compare with the approach to explicitly represent the adversarial distributino. It would be interesting to compare to state of the art adversarial samples on the same architecture. Since the general idea is very promising, I don't deem it necessary that this line of work produces SOTA in its first steps. --> Update: The comparison with recent methods indicates that the proposed method is currently the most successful against defended classifiers, less against vanilla classifiers.

Reproducibility: Yes

Additional Feedback: I sincerely like the idea to systematically shift the data distribution in the latent space to produce a meaningful adversarial distribution. The results convince me that this learnt distribution is close to the data. Large-scale experiments such as ImageNet are computationally very expensive using NFs. I don't deem it necessary to perform such experiments to publish a neat idea, which is successful on other simpler yet non-trivial datasets.

Review 3

Summary and Contributions: The paper introduces AdvFlow, the first black-box adversarial attack that leverages normalizing flows in modeling the adversarial data distribution. A lemma is proved showing that perturbations with dependent elements can be generated (unlike some pre-existing black-box attack methods). It is shown that using a normalizing flow model, adversarial examples that have a distribution similar to that of the data can be generated. This allows the black-box attack to mislead adversarial example detectors better than pre-existing work since often detectors assume adversarial examples come from a distribution dissimilar to that of clean data.

Strengths: The theoretical set-up is sound, very closely mirroring NAttack [27]. Table 1 demonstrates some promising evidence that by modeling adversarial examples as coming from a distribution that is very similar to that of the input data, an adversarial detector that assumes adversarial examples come from a significantly different distribution can be fooled. Table 2 shows promising empirical evidence that AdvFlow is more query efficient and has a higher attack success rate than several competing methods on adversarially trained models.

Weaknesses: I believe the evaluation is not very convincing as it is right now. Namely, a particularly strong (very query-efficient, high success rate) black-box method is missing: SimBA [a]. Additionally, although Table 1 is promising, I would like to see a stronger evaluation or stronger evidence of some kind that the detector is being fooled by the distributional properties of the adversarial examples. At the very least, I think Table 1 should test against several detectors and against several black-box attacks (as opposed to one detector and one baseline attack). In general, as of right now the paper is on the level of a promising novelty. It is interesting that one can generate adversarial examples with a distribution similar to that of inputs, but evaluation for its usefulness in fooling detectors is unconvincing. [a] Simple Black-box Adversarial Attacks (

Correctness: The empirical methodology appears to be correct and the tables and figures are reasonable; the claims made are correct.

Clarity: The paper is fairly well-written; explanations are clear.

Relation to Prior Work: Yes, related work is discussed to the extent that it should be and new contributions are mentioned explicitly at the end of Section 1.

Reproducibility: Yes

Additional Feedback: I believe the paper as it is lacks in proper evaluation against detectors: it would be interesting to see it fool multiple (not just one) detector against a myriad of black-box attacks such as SimBA [a] (mentioned above). [Post-rebuttal Update] I have reviewed the authors' rebuttal, and appreciate their comparison against the strong blackbox attack SimBA and the inclusion of evaluation against multiple detectors. Based on these results, it appears that the attack may indeed be the new SoTA. I strongly encourage the authors to include said results in the updated version of their paper, and potentially make them even more extensive (e.g. running on SVHN, to get a complete version of the original Table 1). Given that some of my original concerns about evaluation have been assuaged, I have updated my rating accordingly.

Review 4

Summary and Contributions: The authors proposed a novel black-box adversarial attack method. They exploit normalizing flows on some data distributions to make their adversarial examples more robust. They build their algorithm upon the natural evolution strategies (NES) and experiment on SVHN and CIFAR-10.

Strengths: - The problem they are solving (black-box adversarial attack) is a standard problem that has been studied extensively. This work provides another insight on how we should design our attack space and may help us better understand the vulnerability of the deep networks. - The idea of using normalizing flows to add reasonable perturbation is novel and interesting. - They show that their attack is stealthier against defended networks, when compared to Bandits and N attack.

Weaknesses: - The maths are not easy to understand for an average computer vision researcher. This reviewer has difficulty understanding the role of AdvFlow, NES and N attack, thus has difficulty assessing the novelty contribution of this paper. - Figure 1 is attacking VGG19 on CelebA but there is no corresponding experiment in the paper or the supplementary material. - Discussions on possible defense methods? - I am not familiar with prior black-box attacking methods, but comparing to N-attack and bandits seems limited. If the method is built upon N attack and bandits, then it could be natural to expect that it outperforms N attack and bandits.

Correctness: The author did not check maths. However, the claims and the experiment results are consistent.

Clarity: All the parts except methodology are easy to parse and comprehend. The technical details of the method may need further work if we want to convey the methodology to a broad range of readers.

Relation to Prior Work: The authors mainly talked about N attack [27] and bandits [17]. I guess this is because their method could be a direct successor of these two methods. However, it is not clear whether there are other black-box attack methods that take a much different approach and how they compare to this work in terms of performance.

Reproducibility: Yes

Additional Feedback: After reading the author feedback and other reviewers comments I decided not to change my score.