MALT Powers Up Adversarial Attacks

We thank the reviewer for the positive and thorough review.

"While MALT's primary innovation is rooted in its refined class selection process, which sets it apart from AutoAttack, this refinement may somewhat temper the overall novelty of this manuscript."

We acknowledge that the main contribution of MALT is the introduction of a refined class selection process and its use with existing attacks such as APGD. We believe that although APGD is already widely used, the addition of MALT significantly improves it. We are sorry if we didn’t understand this point and would be happy to elaborate further.

"The authors have chosen a specific value of c (c=100) and demonstrated empirically that this value is sufficient for the Imagenet dataset. However, the selection of an optimal value of c that generalizes well across various datasets remains unclear, leaving room for future exploration and refinement."

It is an interesting question to optimize the value of c, thus further reducing the running time of MALT. However, we believe it would be very beneficial if the value of c can be universal across all datasets and models, and thus be treated as a constant rather than a hyperparameter that needs tuning. In section 5.1, lines 314-325 we study the effect of the value of c, by choosing c=1000 (i.e. all the possible classes of Imagenet), and show that the robust accuracy doesn’t improve. This indicates that a value of c=100 is indeed a proper choice for all our experiments, at least as an upper bound, and we admittingly haven’t attempted to optimize it further.

"In line with their earlier findings, the authors have empirically demonstrated that APGD outperforms alternative strategies in the context of MALT. While this suggests a strong case for APGD as a suitable choice for MALT, it remains to be seen whether this advantage will hold across diverse settings and datasets."

This is a good point. We have tested MALT combined with the targeted FAB attack (lines 297-299), and it performed worse than with APGD with the DLR loss. We additionally conducted another experiment for the rebuttal phase, using MALT with APGD and the CE loss (instead of DLR) on the SWIN-L model. The robust accuracy against MALT with APGD and CE loss is 60.52%, for Autoattack it is 59.9% and for MALT with APGD and DLR loss it is 59.84% (lower is better). We will add this experiment in the final version. It is indeed an interesting research direction to study other targeted attacks and experiment with MALT beyond the datasets that appear in the RobusBench benchmark.

"The authors showed that MALT leans towards the top-1. Should we select a=1 in all cases then?"

Although MALT does lean towards the top-1 better than naive top-k targeting, there are still images where the attacked target is not the top-1. We used top-9 according to the MALT class selection to align with the current targeting (top-9 according to the highest model confidence). Thus a=9 seems to be a good choice, although it could possibly be further optimized to further improve the running time of MALT.

"Do the authors have any intuition behind why APGD is better than FAB for MALT?"

We think that, in general, a targeted FAB attack is less successful than a targeted APGD attack. This can be seen in the experiments done in [Croce and Heine 2020] (Table 1). Hence, this difference between APGD and FAB is probably unrelated to MALT. We believe this is also true for the additional experiment done in the rebuttal phase with APGD and CE loss, which underperforms compared to APGD with the DLR loss.

We thank the reviewer for the thorough review.

"W1: This paper seems to be behind its time."

We first emphasize that all our experiments are done against the top robust models according to Robustbench, which is the de facto standard benchmark in this field. All the models we tested on are from 2024 or 2023 and are large-scale. For example, Swin-L [Liu et al. 2023] is the current best robust model for Imagenet, it is based on transformers and contains 187 million parameters. Our experiments are done for the Imagenet and CIFAR-100 datasets, we note that Robustbench includes only those datasets as standard benchmarks. It is a legitimate criticism that other datasets should be included as standard benchmarks in the adversarial attack research field, but this is relevant to all papers published in this field and not particular to ours.

"W2: Section 4.1 seems pointless"

Our method is based on an analysis of mesoscopic linear models, as explained in Section 3. We believe it is important and interesting to study whether this analysis is valid theoretically. Two-layer neural networks are already highly non-linear, thus studying the mesoscopic linearity properties in such networks is in itself challenging and interesting. A similar result was proven before only for networks with random weights [Bubek et al. 2021], and we extend it to trained networks under certain assumptions.

We also believe that this study of mesoscopic linearity can be of independent interest beyond the scope of adversarial attacks, as it unveils a certain intriguing phenomenon about the optimization landscape of neural networks.

"Q1: Why are these types of targeted attacks needed?"

In earlier days of studying adversarial attacks, this was a very important question. Indeed, targeted attacks have been shown to be more effective than untargeted attacks, for a great study on this subject we refer to [Croce and Heine 2020]. Also, note that in AutoAttack , which is a composition of four different attacks, two are targeted and two are untargeted (lines 153-159). Since our attack performs better than Autoattack, in particular, it performs better than the current top untargeted attacks.

We also emphasize that MALT runs in an untargeted fashion, just like APGD-T with top-k classes runs in an untargeted fashion. Namely, given an image to attack, the attack itself does not target some predetermined class but rather automatically choses the classes that are easiest to attack according to the score given by MALT.

"Q2: What does "interval" mean in table 1?"

In Figure 1 we divide the adversarial perturbation into 100 intervals and present the change over time in the output’s confidence for each class. We will add this explanation in the final version.

"Q3: In what sense is AutoAttack the SOTA?"

AutoAttack is widely considered to be the state-of-the-art adversarial attack, which in itself is an ensemble of four different attacks. It is the standard benchmark to test against robust models in the official RobustBench benchmark.

"L1: Model size & scale"

Please see our answer to W1.

W1 -- I think that my main issue is with models, not datasets. I still wouldn't predict much practical value for the aforementioned reasons.

W2 -- I still think that 4.1 contributes no marginal value. But I see where you're coming from. Honestly, my issue here isn't really with this paper so much as the field in general.

Qs -- thanks

Overall, I think I would stick at a 3. I understand that I'm the cranky reviewer this time, and I respect the other reviews, but I think it's important to emphasize that I just don't see the practical value of this work in 2024. Good luck. I'm open to replies.

We thank the reviewer for the thorough review.

"Some aspects of the attack evaluation should be clarified or integrated with additional assessments. As the improvements provided by MALT with respect to AutoAttack are quite marginal, the experiments should clearly show that these improvements are exclusively due to the applied method."

We emphasize that we haven’t altered any properties or any hyperparameters of APGD-T other than improved targeting. Compared to AutoAttack, we used just one out of the four attacks included in its ensemble (namely, APGD-T), and changed only its targeting method. Therefore, the time gain and the attack improvements are all due to MALT.

We acknowledge that the additional attacked images are not numerous, resulting in a marginal improvement in terms of successful attacks over AutoAttack. First, we note that the dramatic running time improvement, while also improving the attack success rate, is in itself a notable contribution. In addition, this attack success rate improvement is due to an inherent weakness of the existing widely used targeting methods and is neither dataset\model-specific nor depends on some fine-tuned hyperparameters. Using nothing but better targeting, not only do we gain the improvement over APGD-T gained by AutoAttack, but also add additional improvement by attacking images that were previously out of reach for both naively targeted APGD-T and AutoAttack.

"Even if comparing MALT with the entire AutoAttack suite is very important, it is interesting here to provide insights on how much MALT improves the standard APGD-T algorithm."

We made this comparison as the reviewer suggested. This experiment is done on the Swin-L model [Liu et al. 2023] and Imagenet dataset, this is the top robust model for Imagenet according to Robustbench. APGD-T with standard targeting achieves 59.94% robust accuracy, Autoattack achieves 59.9% robust accuracy and APGD-T with MALT targeting achieves 59.84% robust accuracy (lower is better). There is a strict inclusion between the attacks, namely every image that APGD-T with standard targeting successfully attacks, Autoattack also attacks, and similar for Autoattack and APGD-T with MALT. We acknowledge that at today’s level of adversarial attack, it is very difficult to significantly improve over current attacks. However, we believe the main advantage of our method is to outperform the current state-of-the-art on every tested model, while also significantly improving its running time. If the reviewer thinks this is an important comparison, we can add it also to the other models in our paper in the final version.

"The authors claim multiple times that their method is five times faster than AutoAttack. This value is estimated by comparing the total number of forward and backward passes required by MALT and AutoAttack and then empirically computed by measuring the runtime. However, the empirical measurements are unreliable as they are highly influenced by several factors."

For the empirical measurements of the running time of AutoAttack and MALT, we used 5 different batches while performing the experiments on the exact same GPU. All the details are in lines 288-295. We agree that this empirical measurement might not be precisely exact, but since it is consistent across 9 different models, and for five different batches for each model (while having relatively small variance) we believe this is a reasonable conclusion. We acknowledge that the analysis in Section 3.3 is for a worst-case scenario, and we’ll emphasize it in the final version.

"Can you compare the MALT performance to APGD-T with random restarts and APGD-T with 9 randomly chosen target classes? How does MALT perform using APGD with targeted CE loss? (If you perform these experiments, it would also be interesting to see APGD with random restarts and randomly chosen target classes.)"

We thank the reviewer for these helpful questions. We performed these experiments for the rebuttal as the reviewer suggested, and will add them in the final version. Here are the details:

(1) We performed an APGD-T attack with 9 random targets on the Swin-L model [Liu et al. 2023] (which is the top robust model for Imagenet according to Robustbench). This attack was significantly less successful, achieving a robust accuracy of 78.54%, compared to 59.9% with Autoattack and 59.84% with MALT and APGD-T with a DLR loss (lower is better).

(2) We performed an APGD-T attack with CE loss combined with the targeting of MALT. Again, the attacked model is Swin-L, and the dataset is Imagenet. This resulted in a robust accuracy of 60.52%, which is close to APGD-T with the DLR loss and MALT (59.84%), but still underperforms.

(3) Regarding random restarts, all our experiments that include APGD have a random restart which is the default setting of APGD. According to [Croce and Heine, 2020], which introduced the APGD attack, additional random restarts do not improve the success rate.

"These two papers also provide improvements with respect to AutoAttack (in both performance and efficiency). Can you compare MALT with them?"

Thank you for the suggestion. Due to time constraints in the rebuttal phase, we did not run those experiments, but we will consider adding these comparisons in the final version. Both papers include also targeted attacks, thus MALT can also be used as an off-the-shelf targeting method to improve these methods. We also note that both papers consider only the CIFAR dataset and not Imagenet. The reason may be because these are adaptive methods, which adapt to the model and dataset and require a very long precalculation to allow this adaptivity. These precalculations may be too long to run for Imagenet and for the current state-of-the-art robust models which are significantly larger than the models that are used in those papers.

We thank the reviewer for the thorough review.

"The proposed MALT's performance advantage over AutoAttack is not obvious."

We acknowledge that the additional attacked images are not numerous, resulting in a marginal improvement in terms of successful attacks over Autoattack. However, this is a very different concept from an improvement in other metrics in machine learning where indeed marginal improvement may not be significant. The reason is that for every image that AutoAttack successfully attacks, MALTs also successfully attack, while also attacking additional images that are out of reach for AutoAttack. Hence, there is a strict inclusion in the successful attacks. This is while improving running time by a factor of 5 on the entire imagenet attack test set. Also, this improvement is consistent across all the 9 tested models, and two benchmark datasets.

Also, note that we haven’t altered any other properties or any hyperparameters other than improved targeting. Compared to AutoAttack, we used just one out of the four attacks included in its ensemble (namely, APGD-T), and changed its targeting method. Therefore, the time gain and the attack improvements are all due to MALT.

"Does the proposed method be effective for untargeted method?"

Yes, actually MALT is a method to choose the top-k targets. Thus, by choosing k targets MALT runs as an untargeted method, just like APGD with top-k classes runs in an untargeted fashion, meaning that choosing the targets is not part of the attacker's input but rather a part of the algorithm. We note that APGD can run completely untargeted, i.e. doing gradient steps that are not targeting any target class. MALT is a method to improve the choice of easier targets to attack, thus it is inherently different from APGD in this sense. Also, targeted attacks have been shown to perform better than untargeted attacks (see for example [Croce and Heine 2020]), thus we focus in this paper on the targeted version of APGD.

"The proposed MALT's performance advantage over AutoAttack is not obvious as shown in Table 1 and Table 2"

Please see our answer to the first comment.

"Deepfool is also the minimal distance attack method"

Deepfool can be compared to APGD as an attack that performs gradient steps. However, MALT is a method to improve the targeting in targeted attacks. Thus, MALT may also improve the performance of Deepfool. We focused on APGD since this is a widely used standard attack, which is part of AutoAttack, the current state-of-the-art adversarial attack.

We will fix the typos in the final version