Black-box adversarial attacks are widely used as tools to test the robustness of deep neural networks against malicious perturbations of input data aimed at a specific change in the output of the model. Such methods, although they remain empirically effective, usually do not guarantee that an adversarial example can be found for a particular model. In this paper, we propose Contract And Conquer (CAC), an approach to provably compute adversarial examples for neural networks in a black-box manner. The method is based on knowledge distillation of a black-box model on an expanding distillation dataset and precise contraction of the adversarial example search space. CAC is supported by the transferability guarantee: we prove that the method yields an adversarial example for the black-box model within a fixed number of algorithm iterations. Experimentally, we demonstrate that the proposed approach outperforms existing state-of-the-art black-box attack methods on ImageNet dataset for different target models, including vision transformers.
Figures & tables
Figure 1: Illustration of the contraction of the adversarial example search space. Given the number j of algorithm iteration, the adversarial example search space on iteration j , namely, Uδ(x)j, is the intersection of the ρj− vicinity of an adversarial example zj with the initial attack search space, Uδ(x). Formally, Uδ(x)j=Uδ(x)∩Uρj(zj). The quantity ρj is defined in Eq. 7 . For each algorithm iteration, the adversarial example search space is represented by the intersection of bold circles.
Figure 2: Schematic representation of the proposed method. Given alternation iteration j and the target model T , we prepare the distillation dataset D(S) and train the surrogate model Sj . Then, Sj is attacked at the target point x in the white-box setting, and an adversarial example zj is computed. If zj is transferable to T, algorithm returns zj and stops; otherwise, the adversarial example search space is contracted as shown in Fig. 1 , (zj,T(zj)) is added to the distillation dataset, and the next instance of the surrogate model, Sj+1, is obtained.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
487.95
35.074
18.833
0.153
0.080
HopSkipJump l2
1.00
500.31
48.838
29.118
0.539
0.280
HopSkipJump l∞
1.00
500.01
73.255
35.856
0.361
0.202
SignOPT
1.00
548.24
48.047
28.467
0.551
0.283
GeoDA
1.00
524.98
49.658
31.117
0.180
0.094
Table 1: Quantitative comparison of attack methods, hard-label setting, the target model is ResNet-50, the dataset is ImageNet.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
488.91
49.282
26.488
0.165
0.091
HopSkipJump l2
1.00
500.34
70.122
38.343
0.685
0.318
HopSkipJump l∞
1.00
500.01
106.142
48.455
0.563
0.292
SignOPT
1.00
557.31
74.744
44.850
0.708
0.338
GeoDA
1.00
540.21
65.471
40.497
0.190
0.124
PAR
1.00
322.38
38.751
25.745
0.889
0.233
Table 2: Quantitative comparison of attack methods, hard-label setting, the target model is ViT-B, the dataset is ImageNet.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
489.93
36.396
19.038
0.122
0.068
SquareAttack l∞
0.98
500.00
89.292
4.953
0.250
0.000
SparseRS
0.94
500.00
44.470
2.574
0.994
0.017
Table 3: Quantitative comparison of attack methods, soft-label setting, the target model is ResNet-50, the dataset is ImageNet.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
488.60
41.370
23.579
0.144
0.084
SquareAttack l∞
0.26
500.00
90.103
4.602
0.250
0.000
SparseRS
0.79
500.00
44.335
2.444
0.993
0.017
Table 4: Quantitative comparison of attack methods, soft-label setting, the target model is ViT-B, the dataset is ImageNet.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
291.0
2.675
1.091
0.061
0.025
HopSkipJump l2
1.00
300.07
2.704
2.634
0.174
0.161
HopSkipJump l∞
1.00
310.66
3.281
3.232
0.082
0.085
SignOPT
0.92
288.59
3.642
3.351
0.242
0.209
GeoDA
0.96
300.81
3.388
3.440
0.071
0.071
Table 5: Quantitative comparison of attack methods, hard-label setting, the target model is ResNet-50, the dataset is CIFAR-10.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
489.89
21.625
11.990
0.070
0.044
HopSkipJump l2
0.99
496.30
40.160
33.460
0.417
0.281
HopSkipJump l∞
1.00
500.01
60.742
40.929
0.292
0.226
SignOPT
0.96
532.76
40.653
33.664
0.426
0.265
GeoDA
0.94
604.32
25.871
23.517
0.071
0.078
PAR
1.00
281.56
20.526
17.515
0.645
0.236
Table 6: Quantitative comparison of attack methods, hard-label setting, the target model is ViT-B, the dataset is CIFAR-10.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
291.00
2.468
1.075
0.056
0.025
SquareAttack l∞
0.82
300.00
13.028
0.637
0.250
0.000
SparseRS
0.96
300.00
4.371
0.348
0.920
0.065
Table 7: Quantitative comparison of attack methods, soft-label setting, the target model is ResNet-50, the dataset is CIFAR-10.
Method
ASR
AQN
Avg l2
Std l2
Avg l∞
Std l∞
CAC (ours)
1.00
489.50
15.745
9.850
0.050
0.037
SquareAttack l∞
0.85
500.00
92.182
3.57
0.250
0.000
SparseRS
0.98
500.00
43.198
1.86
0.974
0.032
Table 8: Quantitative comparison of attack methods, soft-label setting, the target model is ViT-B, the dataset is CIFAR-10.
Neural networks, both convolution or transformer based, are essential for modern computer vision systems. However, they are vulnerable to small perturbations, almost imperceptible to humans, which significantly alter the model's prediction. These adversarial attacks are often considered to be a significant threat to the implementation of neural networks in safety-critical applications. Most attacks utilize the white-box threat model and therefore require full access to the target model, making them unrealistic to use in practice. We propose a novel approach under the more realistic black-box threat model that utilizes concepts from reinforcement learning to optimize perturbations with a non-differentiable target model. Reinforcement learning algorithms have already been optimized to be query efficient, making them an ideal starting point when designing black-box adversarial attacks. We show the success of our reinforcement learning inspired black-box adversarial attack (RIBA) in generating adversarial perturbations using only a small number of queries to the target model, by comparing it to state of the art attacks on different models on the Cifar10 and ImageNet data sets. RIBA takes 25.4% fewer median queries to generate attacked images against a ResNet-18 on Cifar10 and 22.5% fewer median queries to fool a Vit-B/16 model on ImageNet. Additionally, we demonstrate that RIBA can match the performance of white-box attacks on an adversarially trained model.
Florian Krone, Elena Hoemann, Sven Hallerbach
Institute for AI Safety and Security German Aerospace Center (DLR) Sankt Augustin, Germany
Adversarial examples in machine learning are typically generated using gradients, obtained either directly through access to the model or approximated via queries to it. In this paper, we propose a much simpler approach to craft adversarial examples, drawing inspiration from insights of explainable machine learning. In particular, we design adversarial image filters that are based on classic edge detection algorithms but optimized to deceive learning models. The resulting untargeted attacks are transferable and require only a single pass over the input. Empirically, we find that 3x3 filters already enable success rates between 30% and 80% on different neural networks. Compared to related approaches using generative models for crafting adversarial examples, we reduce the number of parameters by five orders of magnitude, resulting in a very efficient attack. When investigating the parameters of the learned filters, we observe interesting properties such as a high transferability between models and structures common to classic image filters. Our results provide further insights into the vulnerability of neural networks and their fragility to malicious noise.
Deep neural networks (NNs) for computer vision are vulnerable to adversarial attacks, such that minuscule malicious changes to inputs may induce unintuitive outputs. One key approach to verify and mitigate such robustness issues is to falsify expected output behavior, which enables local robustness guarantees and adversarial training. Due to the black-box nature of NNs, current attacks only falsify a class of the final output, such as flipping from \text{stop_sign} to \neg \text{stop_sign}. In this work we argue that robustness analysis should focus more generally on logical inconsistencies in concept-level reasoning rather than solely on output misclassification. We formalize this perspective through concept-based properties, i.e., constraints over human-interpretable concepts such as \text{red} \land \text{octogonal} \implies \text{stop_sign} and study the falsification of such properties as a principled form of adversarial attack. Furthermore, an implementation of concept-based properties on already trained NNs is proposed using techniques from concept-based explainable artificial intelligence (C-XAI). For that we formally prove that attacks on concept-based properties are expected to have a reduced search space compared to simple class falsification, whilst arguably be more aligned with intuitive robustness targets. The practical effectiveness of our approach for logically informed adversarial training is shown in an empirical study across multiple models and datasets, including both vision and a security-relevant code processing task. Our results demonstrate that concept-level falsification generalizes classical adversarial attacks: Retraining on our novel attacks maintains robustness gains as compared to classical adversarial retraining whilst better eliminating semantic biases.
Raik Dankworth, Felix Mächtle, Thomas Eisenbarth +1
Institute of Software Engineering and Programming Languages University of Luebeck · Institute of IT Security University of Luebeck