Organizations: Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China. · School of Software, Tsinghua University, Beijing 100084, China. · School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China. · Department of Computer Science and Technology, Institute for AI, BNRist, IDG/McGovern Institute for Brain Research, Tsinghua University, Beijing 100084, China · Chinese Institute for Brain Research (CIBR), Beijing 100010, China.
Adversarial examples present significant challenges to the security of Deep Neural Network (DNN) applications. Specifically, there are patch-based and texture-based attacks that are usually used to craft physical-world adversarial examples, posing real threats to security-critical applications such as person detection in surveillance and autonomous systems, because those attacks are physically realizable. Existing defense mechanisms face challenges in the adaptive attack setting, i.e., the attacks are specifically designed against them. In this paper, we propose Adversarial Spectrum Defense (ASD), a defense mechanism that leverages spectral decomposition via Discrete Wavelet Transform (DWT) to analyze adversarial patterns across multiple frequency scales. The multi-resolution and localization capability of DWT enables ASD to capture both high-frequency (fine-grained) and low-frequency (spatially pervasive) perturbations. By integrating this spectral analysis with the off-the-shelf Adversarial Training (AT) model, ASD provides a comprehensive defense strategy against both patch-based and texture-based adversarial attacks. Extensive experiments demonstrate that ASD+AT achieved state-of-the-art (SOTA) performance against various attacks, outperforming the APs of previous defense methods by 21.73%, in the face of strong adaptive adversaries specifically designed against ASD. Code available at https://github.com/weiz0823/adv-spectral-defense .
Figures & tables
Fig. 1: Spectral analysis of different physically realizable adversarial attacks with Discrete Wavelet Transform (DWT). D1 to D6 represent the detail (high-frequency) sub-bands obtained from multi-level DWT, with D1 being the highest frequency. The amplitudes correspond to absolute values of the wavelet coefficient components at each decomposition level. They capture image edges, textures, and local spatial variations at different scales. The figure highlights abnormal spectral amplitudes caused by physical adversarial perturbations. Error bars: 95% confidence intervals. Upper left: An adversarial patch (AdvPatch), an adversarial texture (AdvTexture, cropped), and a benign image patch, visualized. Bottom: A sketch of DWT.
Fig. 2: Illustration of the DWT decomposition. Left: The 1D hierarchical decomposition. Right: The outputs of the decomposition on a 2D image, called the 2D DWT pyramid.
Fig. 3: Overview of the pipeline of the proposed ASD method. ASD has a masking module, called ASD Masking , to detect and mask out possible adversarial regions with n -level DWT decomposition. Then the preprocessed images are fed into the AT detector to offer robustness against low-amplitude adversarial patterns. By setting DWT level to n1,n2,n3,… , ASD level aggregation is finally used to adapt to different object sizes in the images. The block on the right shows the details of ASD Masking, which is based on spectral decomposition.
Fig. 4: Visualization of adversarial examples with patch-based or texture-based attacks, and the images processed by ASD. (a) AdvPatch [ 5 ] example. (b) AdvPatch processed by ASD. (c) AdvTexture [ 11 ] example. (d) AdvTexture processed by ASD.
Fig. 5: The DWT amplitude of different physically realizable adversarial examples against the adversarially trained Faster R-CNN. D1 to D6 correspond to different frequency levels, from higher frequency to lower frequency. Error bar: 95% confidence interval.
Fig. 6: Frequency-amplitude division of ASD and AT.
Defense
Adaptive type
AdvPatch
ASD
Direct
71.68
Loss
71.85
Range
58.78
ASD + AT
Direct
90.04
Loss
88.00
Range
92.71
TABLE I: AP 50 (%) of Faster R-CNN against different types of adaptive attacks designed for ASD.
Patch
Texture
Imperceptible
Defense
Clean
AdvPatch [ 5 ]
AdvTshirt [ 8 ]
AdvTexture [ 11 ]
AdvCaT [ 6 ]
NumbOD [ 22 ]
LGP [ 23 ]
Average
l∞ -AT [ 30 ]
95.96
55.46
9.59
29.08
39.59
93.31
94.38
53.57
FD-JPEG [ 31 ] + AT
89.92
52.59
8.04
25.98
39.17
84.44
84.22
49.07
IDBD [ 47 ] + AT
95.28
48.24
8.48
35.80
32.55
92.25
93.07
51.73
SAC [ 14 ] + AT
95.96
55.46
9.01
26.05
40.98
93.21
94.50
53.20
Jedi [ 16 ] + AT
91.16
72.04
30.17
28.59
40.65
91.62
92.40
59.25
TABLE II: AP 50 (%) of adversarially trained Faster R-CNN [ 42 ] against physically realizable (patch, texture) and imperceptible adversarial attacks in adaptive attack settings.
Patch
Texture
Defense
Clean
AdvPatch
AdvTshirt
AdvTexture
AdvCaT
Average
l∞ -AT
93.87
30.54
7.17
30.07
18.33
21.53
IDBD + AT
93.65
29.08
6.97
27.27
17.82
20.28
FD-JPEG + AT
88.64
28.62
6.16
26.55
16.28
19.40
SAC + AT
93.87
30.97
7.36
26.89
19.29
21.13
Jedi + AT
90.35
37.20
18.16
21.52
9.48
21.59
TABLE III: AP 50 (%) of adversarially trained FCOS [ 44 ] against physically realizable adversarial attacks in the adaptive attack settings. The same conventions are used as in Table II .
Patch
Texture
Defense
Clean
AdvPatch
AdvTshirt
AdvTexture
AdvCaT
Average
l∞ -AT
66.25
38.32
43.50
57.39
51.42
47.66
IDBD + AT
66.18
36.22
20.51
58.45
53.01
42.05
FD-JPEG + AT
58.73
34.13
19.97
52.06
46.13
38.07
SAC + AT
66.26
38.16
22.20
52.89
52.68
41.48
Jedi + AT
49.27
43.67
25.89
55.06
55.38
45.00
TABLE IV: AP 50 (%) of adversarially trained YOLOv8 [ 45 ] against patch-based and texture-based attacks in the adaptive attack settings. The same conventions are used as in Table II .
Defense
AdvTexture
AdvCaT
None
0.23
5.94
IDBD
6.97
7.92
FD-JPEG
0.19
18.81
SAC
60.80
5.94
Jedi
80.36
92.85
APE
0.73
9.80
TABLE V: AP 50 (%) of Faster R-CNN [ 42 ] against texture-based attacks in the physical world.
Patch
V2
V3
V4
V4t
FR
AP 50 (%)
92.67
92.07
89.62
90.33
90.56
TABLE VI: AP 50 (%) of Faster R-CNN with ASD+AT against different NatPatch patches. Patches are denoted with the names in the original paper [ 10 ] .
Configuration of ASD
AP 50 (%)
Full configuration
88.00
Without AT
58.78 ( ↓ 29.22)
Without level aggregation ( k=1 )
78.91 ( ↓ 9.09)
Single-spectral masking ( n=1,k=1 )
75.67 ( ↓ 12.33)
TABLE VII: Ablation study on ASD, evaluated against AdvPatch attack. Target model is Faster R-CNN.
θ
0.05
0.10
0.15
0.17
0.20
0.30
AP 50 (%)
71.21
81.99
86.91
88.00
87.71
80.91
TABLE VIII: AP 50 (%) of adversarially trained Faster R-CNN with ASD with different threshold θ , evaluated against AdvPatch attack.
n
1
2
3
4
5
Without level aggregation
75.67
81.46
78.91
67.30
58.99
With level aggregation
74.12
83.64
88.00
88.52
88.34
TABLE IX: AP 50 (%) of adversarially trained Faster R-CNN with ASD with different expansion levels n , evaluated against AdvPatch attack.
Transform
DWT
FFT
DCT
AP 50 (%)
88.00
55.50
55.39
TABLE X: AP 50 (%) of adversarially trained Faster R-CNN with ASD and different time-frequency transformation methods, evaluated against AdvPatch attack.
Defense
AdvPatch
AdvTexture
NumbOD
None
36.99
0.21
12.25
ASD
58.78
15.86
18.49
AT
55.46
29.08
93.31
ASD+AT
88.00
70.08
93.23
TABLE XI: AP 50 (%) of differently trained Faster R-CNN with ASD against attacks.
Patch
Texture
Defense
Clean
AdvPatch
AdvTshirt
AdvTexture
AdvCaT
Average
None
96.21
36.99
8.93
0.21
0.32
11.61
IDBD
95.09
42.99
8.28
2.13
0.34
13.44
FD-JPEG
90.34
30.84
6.66
0.15
0.38
9.51
SAC
96.21
57.72
35.53
0.25
0.67
23.54
Jedi
92.67
64.40
27.36
2.30
0.70
23.69
TABLE XII: AP 50 (%) of standardly trained Faster R-CNN against patch-based and texture-based attacks in the adaptive attack settings. The same conventions are used as in Table II .
Defense
Tench
Balloon
Umbrella
Throne
Teddy bear
AT
56.22
32.84
31.54
75.80
16.30
AT+ASD
99.42
78.74
87.50
99.86
99.96
TABLE XIII: Accuracy (%) of ResNet-50 [ 48 ] with defenses against Adversarial Patch [ 3 ] targeting different ImageNet [ 49 ] classes.
Defense
Latency ( ms/im )
AP 50 (%)
None
22.5
55.46
FD-JPEG
28.2
52.59
ASD (without level agg.)
23.3
78.91
ASD (full)
56.8
88.00
TABLE XIV: Inference latency per image of Faster R-CNN with different frequency-based defense methods applied.
Audio deepfake detectors remain vulnerable to adversarial perturbations that suppress the acoustic cues used for detection, allowing manipulated utterances to evade the detector. Although existing defenses can improve robustness, they require retraining the detector or introduce additional distortion. Diffusion-based purification instead leaves the pretrained detector unchanged, but existing methods use the same purification strength for all inputs, creating a trade-off between removing adversarial perturbations and preserving the subtle spoofing cues needed for detection. In this paper, we propose Detection-Guided Adaptive Purification (DGAP), a diffusion-based defense that adjusts purification strength per input. Building on the observation that a light purification perturbs the detector score of an adversarial input far more than that of a benign one, the framework uses the resulting score shift as a reference-free indicator of adversarial manipulation. Inputs with small shifts are passed unchanged, whereas flagged inputs undergo stronger purification before final detection. We evaluate the framework against three adversarial attack settings across three deepfake detectors, and compare it with nine existing defenses. Our results show that DGAP achieves the best defense performance across all detectors while leaving benign inputs nearly unaffected, and remains effective under the defense-aware adaptive attack.
The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this work, we study this phenomenon in detail and present a formal adversarial noise amplification theorem. We specify a set of sufficient conditions under which the adversarial noise amplification is mathematically guaranteed. Based on theoretical observations, we propose a novel training methodology with a custom spectral loss function and a specific architectural design to enhance the amplification signal for detecting adversarial data. Finally, we introduce a new, lightweight detection mechanism that leverages the enhanced amplification signal and operates entirely at inference time. To validate our approach, we demonstrate the detector's efficacy against both state-of-the-art attacks and a purpose-built adaptive attack, confirming that enhanced amplification can serve as a robust and reliable signal for adversarial defense.
Adversarial attacks can readily compromise deep neural networks (DNNs). In particular, transferable attacks (TAs) exploit the shared vulnerabilities among DNNs, enabling perturbations crafted on surrogates to transfer to unseen models. Training-time and post-attack defenses have been extensively studied for combating TAs. Orthogonal to these approaches, preemptive robustification (PR) has emerged as a pre-attack defense that enhances the robustness of benign samples by superimposing protective variations before attacks. Despite its promise, PR remains underexplored and faces several important limitations. First, dependence on well-trained surrogate classifiers limits applicability, as surrogates are task-specific and may even be unavailable in some practical settings. Second, the required iterative optimization or dedicated PR generator training incurs substantial costs. Third, the generated variations are opaque to humans. To address these, we seek an efficient PR that is surrogate-free, optimization-free, training-free, and human-interpretable. Intriguingly, we discover a numerical correlation between the shared vulnerabilities of DNNs and Laplacian responses, with their cosine similarity being significantly negative. This indicates that negated high-frequency response constitutes an important component of shared vulnerabilities. Consequently, strengthening Laplacian responses counteracts this component, improving resistance to TAs. Building upon this insight, we propose Fast Preemptive Robustification (FPR), which performs Laplacian sharpening via a single channel-wise convolution with a 3\times3 kernel. FPR is simple yet effective, as demonstrated by extensive experiments. Specifically, FPR reduces the attack success rate (ASR) of untargeted TAs by 12.7% and that of targeted TAs from 10.7% to 4.1%. Code will be released publicly.