Rethinking the Backward Propagation for Adversarial Transferability

Transfer-based attacks generate adversarial examples on the surrogate model, which can mislead other black-box models without access, making it promising to attack real-world applications. Recently, several works have been proposed to boost adversarial transferability, in which the surrogate model is usually overlooked. In this work, we identify that non-linear layers (e.g., ReLU, max-pooling, etc.) truncate the gradient during backward propagation, making the gradient w.r.t. input image imprecise to the loss function. We hypothesize and empirically validate that such truncation undermines the transferability of adversarial examples. Based on these findings, we propose a novel method called Backward Propagation Attack (BPA) to increase the relevance between the gradient w.r.t. input image and loss function so as to generate adversarial examples with higher transferability. Specifically, BPA adopts a non-monotonic function as the derivative of ReLU and incorporates softmax with temperature to smooth the derivative of max-pooling, thereby mitigating the information loss during the backward propagation of gradients. Empirical results on the ImageNet dataset demonstrate that not only does our method substantially boost the adversarial transferability, but it is also general to existing transfer-based attacks. Code is available at https://github.com/Trustworthy-AI-Group/RPA.

Paper

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Peer review

Reviewer YaZN6/10 · confidence 4/52023-06-22

Summary

This paper presents the Backward Propagation Attack (BPA) as a solution to the issue of gradient truncation in transfer-based attacks within adversarial machine learning. Through empirical validation, the authors highlight the negative impact of gradient truncation on adversarial transferability and propose modifications to the backward propagation process. BPA effectively enhances the relevance of the gradient between the loss function and the input, resulting in significant improvements in various untargeted and targeted transfer-based attacks compared to baseline approaches. This work not only provides valuable insights for enhancing adversarial transferability but also suggests promising directions for bolstering model robustness.

Strengths

The paper demonstrates originality by identifying and addressing the issue of gradient truncation in transfer-based attacks, which has not been extensively explored before. The proposed Backward Propagation Attack (BPA) introduces modifications to the backward propagation process, mitigating the detrimental effect of gradient truncation. The empirical evaluation on the widely used ImageNet dataset showcases the high quality of the research, with rigorous experimentation and comparisons against baselines. The clarity of the paper is commendable, effectively communicating the problem, the proposed solution, and the experimental methodology. The findings are significant as they contribute to advancing transfer-based attacks, provide new insights into adversarial transferability, and have potential implications for improving model robustness.

Weaknesses

While the paper presents valuable contributions, there are a few areas that could be improved. Firstly, the theoretical underpinnings of the proposed modifications to the gradient truncation during the backward propagation process could be further elaborated to enhance the understanding of the approach. Additionally, the limitations of the proposed techniques could be further discussed to provide a comprehensive view of its effectiveness, such as the potential performance decrease caused by replacing the ReLU function. Furthermore, the paper focuses mainly on the ImageNet dataset, and it would be beneficial to explore the generalizability of the approach on other datasets or domains. Overall, addressing these weaknesses would strengthen the paper and provide further insights into the proposed approach.

Questions

1. The paper proposes modifications to the backward propagation process to mitigate gradient truncation. Could the authors provide more theoretical justification for the choice of these specific modifications? 2. The experimental evaluation is conducted on the ImageNet dataset. Have you considered testing the proposed BPA method on other datasets to assess its generalizability? It would be valuable to understand how the approach performs across different domains and datasets. 3. It would be beneficial to discuss the limitations of the proposed BPA method. Are there any specific scenarios or conditions where the effectiveness of BPA may be compromised? Besides, could the authors explain the main improvements of BPA compared with LinBP? 4. The paper primarily focuses on the enhancement of transfer-based attacks. Could you discuss potential applications or implications of the proposed BPA method in other areas of adversarial training, such as these gradient-based white-box attacks?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

N/A

Reviewer g4446/10 · confidence 3/52023-07-05

Summary

This paper have developed a new method, Backward Propagation Attack (BPA), to enhance the transferability of adversarial examples. BPA uses a non-monotonic function as the derivative of ReLU and incorporates softmax with temperature to smooth the derivative of max-pooling, reducing information loss during gradient backward propagation. The method has demonstrated significant improvements in adversarial transferability on the ImageNet dataset.

Strengths

**Originality**: To the best of my knowledge, the idea that modifying the derivative of max-pooling, Relu activation for improving adversarial transferability is new. **Clarity**: This paper is well-structured and easy to follow. **Significance**: To understand and improve the transferability of adversarial examples is important in the domain of adversarial examples

Weaknesses

- The chosen baselines are exclusively drawn from model-related attacks. It might be beneficial to include a few from input-transformation-based attacks. Furthermore, it would provide a more comprehensive evaluation to examine if your technique could potentially work in conjunction with input-transformation-based attacks such as TIM[1]/SIN[2]/DIM[3] for further enhancing the transferability. - There's a relevant piece of work that hasn't been included.[4] [1] Dong, Yinpeng, et al. "Evading defenses to transferable adversarial examples by translation-invariant attacks." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019. [2] Lin, Jiadong, et al. "Nesterov accelerated gradient and scale invariance for adversarial attacks." arXiv preprint arXiv:1908.06281 (2019). [3] Xie, Cihang, et al. "Improving transferability of adversarial examples with input diversity." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2019. [4] Huang, Tianjin, et al. "Direction-aggregated attack for transferable adversarial examples." ACM Journal on Emerging Technologies in Computing Systems (JETC) 18.3 (2022): 1-22.

Questions

- Could your technique potentially work in conjunction with input-transformation-based attacks such as TIM/SIN/DIM for further improving the transferability?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

the authors adequately addressed the limitations

Reviewer gcCC7/10 · confidence 5/52023-07-06

Summary

In this work, the authors find that non-linear layers make the gradient imprecise, leading to limited adversarial transferability. Based on this finding, they propose Backward Propagation Attack (BPA) to increase such relevance. In particular, BPA adopts a non-monotonic function as the derivative of ReLU and incorporates softmax function to smooth the derivative of max-pooling. Extensive experiments have shown the high effectiveness of the proposed BPA.

Strengths

1.The paper is well-written and easy to follow. 2.The motivation is clear and reasonable. Intuitively, the non-linear layers can indeed truncate the gradient during the backward propagation. 3.The proposed method is novel and interesting. Simply adjusting the gradient calculation of non-linear layers can significantly boost the adversarial transferability, which also validates the motivation. 4.Different from some works which is limited to some specific architectures, the proposed method is general to existing CNNs. 5.The authors have conducted experiments on both untargeted and targeted attacks, which can validate its high effectiveness and show good generality when combined with existing model-related methods.

Weaknesses

1.For ReLU activation, the authors adopt the derivative of SiLU function. As shown in Figure 3, the derivative of SiLU function is mainly different from that of ReLU function in the range of [-5, 5]. I am curious how many elements the derivative matrix are in such range so that BPA can boost the transferability. 2.Recently, transforming the input image for gradient calculation has shown great effectiveness in boosting adversarial transferability, such as DIM, Admix, SSA and so on. It is expected to see the results on such attacks to further validate the effectiveness of BPA on various transfer-based attacks.

Questions

1.What is the temperature coefficient for max-pooling?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

4 excellent

Presentation

4 excellent

Contribution

4 excellent

Limitations

N/A

Reviewer NESJ7/10 · confidence 3/52023-07-07

Summary

This paper introduces a new way to improve adversarial transferability by removing gradient truncation in the surrogate model. Specifically, the method replaces gradients of relu and maxpool with softened version to avoid gradient truncation. Experiments are conducted over many models and show gains upon existing methods.

Strengths

- The method seems well motivated, novel and straightforward. - The empirical gain is substantial and general across different settings - The paper is well written overall and easy to follow.

Weaknesses

It is not clear to me whether the improvement is caused by the extra design to align with the function better, or just simply by making the model more linear as suggested in LinBP. For the relu case, it seems that replacing gradient with 1 is the best as shown in prelimiary study. It is not clear whether this is still the case in the general experiments due to lack of ablation. For maxpool, Fig 2 also shows that the attack is best at some middle point. Does this relate to linearity too? And why does the success rate first increases then decreases?

Questions

See above

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Not addressed.

Reviewer 5iKz5/10 · confidence 4/52023-07-08

Summary

This paper introduces the Backward Propagation Attack (BPA) to improve the transferability of adversarial examples generated based on the iterative gradient ascent procedure. The paper first empirically demonstrates that the non-linear layers such as ReLU and max-pooling truncate the loss gradient, and such a truncation procedure negatively affects the transferability of adversarial perturbations. Motivated by this observation, the paper proposes to modify the gradient computation for the ReLU and max-pooling layers. Particularly, consider a trained source model from which the adversarial perturbations are generated. BPA proposes to replace the derivative of the ReLU functions in the source model with the derivative of the SiLU function. Similarly, the derivative of the max-pooling function in the source model is replaced with a softmax function with a tunable temperature coefficient. Finally, results on randomly sampled 5000 Imagenet images demonstrate the improved transferability of adversarial perturbations generated based on PGD and MI-FGSM.

Strengths

Originality: Modifying the backward propagation procedure of the non-linear layers when computing the loss gradient during the process of generating adversarial examples is an interesting approach to improve the transferability of the perturbations. Quality: The paper is well-written. The proposed BPA method is motivated using empirical observations. The evaluations include the transferability of perturbations under both targeted and untargeted settings. Clarity: The motivation behind the proposed method as well as the structure of the paper is clear. Significance: The adversarial robustness of deep learning models against transfer-based perturbations poses a practical security concern. This paper proposes a method that can be used in combination with existing gradient-based attack algorithms to improve the transferability of perturbations.

Weaknesses

The clarity of the paper can be improved. There are some terms that are key to understanding the message which the author wants to convey, but the lack of rigorous definitions makes it difficult to understand. (See Questions for a list of clarifications ) The evaluations in the paper are performed based on perturbations bounded by the L_inf norm with an $\epsilon$ of $\frac{8}{255}$. In Ln 242, it states that the choice of $\epsilon$ aligns with existing work (which one?), whereas most existing work considers $\frac{16}{255}$ (LBP, MI, VI/VMI, etc). Especially since one of the main contributions of the proposed method is the improvement of transferability over other sota methods (ie. "remarkable margin" ln284, ln296, ln 358), it is important to make sure the evaluations and the comparison with other methods are performed fairly.

Questions

Questions/clarifications: In the abstract, why does the truncation make the gradient imprecise? The ReLU and the max-pooling layers are part of the network definition, so the derivative is exactly what it is supposed to be and I do not see the lack of precision. What does it mean by the relevance between gradient wrt input and the loss function? Since the term "relevance" appears later in the paper as well (eg. ln45, 58, 148, 315), having a more rigorous definition is warranted. Figure 2 is a crucial element in motivating the proposed method. Is the success rate averaged over nine victim models? What is the variance among the results? Ln 124 of Sec. 3.1: the paper first establishes that $z_i$ is the input to the function $f_i$ which returns $z_{i+1}$. When predicting the label, why is $z_l$ used as an input to the function $f_{l+1}$, shouldn't it be $z_{l+1}$? Ln 138: Shouldnt the j-th element of $\frac{\partial z_{k+1}}{\partial z_k}$ be 1 if $f(z_{k})_j >0$? Ln 139 "As a result, the gradient is effectively limited or weakened to some extent". ReLU was designed to address the vanishing gradient problem in training deep models. By having a step function as its derivative, it allows some gradient information to pass freely while simultaneously not updating other weights. Therefore, this is exactly how the backward propagation was designed to be with ReLU-activated networks. Ln 414: Similarly, this is exactly how bp is supposed to behave with max-pooling. Ln 149: What does it mean by "decaying the relevance"? Ln 185-186: Is this a prior result? or a claim made in this paper supported by evidence? Suggestions: Could we replace the y-axis ("Attack success rate") with the adversarial loss value on the source model? That is to plot $\ell(x+\Delta x)$, where $\Delta x$ is generated using fgsm/i-fgsm/mi-fsgm on the source model modified using the various method. If we observe a higher loss value after the modification, it indeed shows that the derivative of those nonlinear layers prevents the perturbations from reaching maxima. On the other hand, if we observe a lower loss value after the modification, this means the truncation effect of the derivative of the non-linear functions leads to perturbations overfit to the source model, despite having higher losses. Other minor suggestions: Figure 1 should not come after Figure 2.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

There is no discussion of the limitation. For instance, the proposed paper is only suitable for attack algorithms that are based on gradient computations.

Reviewer g4442023-08-11

Thank you for the rebuttal. Most of my concerns have been addressed. Therefore, I increase my score to 6.

Authorsrebuttal2023-08-12

A Gentle Reminder for Score Adjustment within the System

We are grateful for your positive comments and adjustment to the score. However, it appears that the score alteration has not been implemented within the system. **As a gentle reminder, we kindly request that you make the necessary score adjustment at your earliest convenience**. Thank you very much for your attention to this matter.

Reviewer YaZN2023-08-13

Response to authors' rebuttal

Thanks for the rebuttal. The response has addressed my major concerns, and I will raise my rating to 6.

Reviewer 5iKz2023-08-18

Thank you for the response. Most of the concerns have been addressed and I will raise my score to 5.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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