Analyzing Physical Adversarial Example Threats to Machine Learning in Election Systems
Authors: Khaleque Md Aashiq Kamal, Surya Eada, Aayushi Verma, Subek Acharya, Adrian Yemin, Benjamin Fuller, Kaleel Mahmood
Organizations: Department of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Kingston, RI, USA · Voting Technology Center, University of Connecticut, Storrs, CT, USA · Department of Computer Science and Statistics, University of Rhode Island, Kingston, RI, USA
Developments in the machine learning voting domain have shown both promising results and risks. Trained models perform well on ballot classification tasks (> 99% accuracy) but are at risk from adversarial example attacks that cause misclassifications. In this paper, we analyze an attacker who seeks to deploy adversarial examples against machine learning ballot classifiers to compromise a U.S. election. We first derive a probabilistic framework for determining the number of adversarial example ballots that must be printed to flip an election, in terms of the probability of each candidate winning and the total number of ballots cast. Second, it is an open question as to which type of adversarial example is most effective when physically printed in the voting domain. We analyze six different types of adversarial example attacks: l_infinity-APGD, l2-APGD, l1-APGD, l0 PGD, l0 + l_infinity PGD, and l0 + sigma-map PGD. Our experiments include physical realizations of 144,000 adversarial examples through printing and scanning with four different machine learning models. We empirically demonstrate an analysis gap between the physical and digital domains, wherein attacks most effective in the digital domain (l2 and l_infinity) differ from those most effective in the physical domain (l1 and l2, depending on the model). By unifying a probabilistic election framework with digital and physical adversarial example evaluations, we move beyond prior close race analyses to explicitly quantify when and how adversarial ballot manipulation could alter outcomes.
Figures & tables
Figure 1: U.S. Election Pipeline: First officials define a ballot layout which is then sent for printing. During the printing step, an attacker could potentially compromise ballot printers and add adversarial examples to the ballots. The ballots are then distributed to voters on election day and tabulation can be done by a ballot classifier.
Model (Trained On)
Training Accuracy
Validation Accuracy
Bubbles
Combined
Bubbles
Combined
SVM-B
1.0000
.8992
1.0000
.9026
VGG-16-B
1.0000
.9205
1.0000
.9247
ResNet-20-B
1.0000
.9147
1.0000
.9155
CaiT-B
1.0000
.8955
1.0000
.8992
SVM-C
.9989
.9824
.9989
.9784
Table 1: Clean training and validation accuracies on the Bubble and Combined dataset for all models.
Figure 2: Physical Adversarial examples with varying ϵ or k for all attacks on the CaiT-C model.
Model
l∞ -APGD
l1 -APGD
l2 -APGD
l0 PGD
l0+l∞ PGD
l0+σ PGD
ϵ=16/255
ϵ=20
ϵ=2
k=1
ϵ=64/255
k=1
SVM-B
1.000
1.000
1.000
1.000
1.000
1.000
SVM-C
0.500
0.500
0.500
1.000
1.000
1.000
VGG16-B
0.000
0.498
0.000
1.000
1.000
0.774
VGG16-C
0.000
0.500
0.000
0.889
0.537
0.500
ResNet20-B
0.219
0.027
0.260
1.000
1.000
1.000
Table 2: Robust accuracy for each attack using the selected imperceptible perturbation parameters. For the ”-C” models, we bold the attack that is the most effective (lowest robustness).
Model
Clean
Clean+AE
l∞ -APGD
l1 -APGD
l2 -APGD
l0 PGD
l0+l∞ PGD
l0+σ PGD
0/255
0/255
ϵ=16/255
ϵ=20
ϵ=2
k=1
ϵ=64/255
k=1
SVM-C
0.936
0.977
0.583
0.603
0.552
1.000
0.960
1.000
VGG-16-C
0.971
0.972
1.000
0.708
0.946
1.000
1.000
0.999
ResNet20-C
0.972
0.976
1.000
0.971
0.989
1.000
1.000
0.975
CaiT-C
0.969
0.994
0.540
0.501
0.503
1.000
0.919
0.963
Table 3: Physical world robust accuracy for the Combined models for each of the six norm attacks.
Figure 3: Digital and printed physical adversarial examples for the CaiT-C model. Each attack uses the imperceivable parameters determined in Section 5 .
l∞
l1
l2
l0
l0+l∞
l0+σ -map
RMSE
0.062
0.069
0.058
0.054
0.078
0.068
KL
5.71
12.18
0.52
22.70
22.49
22.71
SSIM
0.442
0.415
0.474
0.481
0.250
0.455
Table 4: Root Mean Square Error (RMSE), Kullback–Leibler divergence (KL) and Structural Similarity Index Measure (SSIM) between the printed perturbation δprint and the digital perturbation δdigital for each norm attack.
Figure 4: Histograms for a digital clean ballot (left), its corresponding l1 digital adversarial example (center) and the physically printed and scanned adversarial example (right).
Appendix figures & tables28 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: UConn Bubbles with Marginal Marks dataset.
Model
Hyperparameters
LR
DR
Epochs
WD
BS
CaiT-B
0.00005
0.1
200
0.0
128
ResNet20-B
0.1
0.0
60
0.0001
64
VGG16-B
0.001
0.0
40
0.0
64
CaiT-C
0.00005
0.1
200
0.0
128
ResNet20-C
0.1
0.0
100
0.0001
128
Appendix
Table 5: Hyperparameter settings for the various grayscale models. Abbreviations: LR = learning rate, DR = dropout rate, WD = weight decay, and BS = batch size.
Mark Type
Total Samples
Correct Predictions
Accuracy
Empty Bubbles
5327
5327
100.00%
Filled Bubbles
1810
1810
100.00%
Penrest
703
703
100.00%
Checkmark
703
701
99.72%
Crossmark
703
675
96.02%
Left right synthetic
703
703
100.00%
Appendix
Table 6: ResNet20-C Classification results for different mark types on the dataset.
Mark Type
Total Samples
Correct Predictions
Accuracy
Empty Bubbles
5327
5327
100.00%
Filled Bubbles
1810
1810
100.00%
Penrest
703
702
99.86%
Checkmark
703
701
99.72%
Crossmark
703
664
94.45%
Left right synthetic
703
703
100.00%
Appendix
Table 7: CaiT-C classification results for different mark types on the dataset.
Mark Type
Total Samples
Correct Predictions
Accuracy
Empty Bubbles
5327
5319
99.85%
Filled Bubbles
1810
1810
100.00%
Penrest
703
690
98.15%
Checkmark
703
665
94.59%
Crossmark
703
532
75.68%
Left right synthetic
703
703
100.00%
Appendix
Table 8: SVM-C classification results for different mark types on the dataset.
Mark Type
Total Samples
Correct Predictions
Accuracy
Empty Bubbles
5327
5327
100.00%
Filled Bubbles
1810
1810
100.00%
Penrest
703
703
100.00%
Checkmark
703
701
99.72%
Crossmark
703
675
96.02%
Left right synthetic
703
703
100.00%
Appendix
Table 9: VGG16-C classification results for different mark types on the dataset
Figure 6: Physical Adversarial examples with varying ϵ or k for all attacks on the ResNet20-C model.
Figure 7: Physical Adversarial examples with varying ϵ or k for all attacks on the VGG16-C model.
Figure 8: Physical Adversarial examples with varying ϵ or k for all attacks on the SVM-C model.
Model
Expert
l∞ -APGD
l1 -APGD
l2 -APGD
l0 PGD
l0+l∞ PGD
l0+σ -map PGD
CaiT-C
Expert 1
4
4
1
1
32
1
Expert 2
8
4
3
1
64
1
Expert 3
4
4
4
1
64
1
Expert 4
8
4
3
1
64
1
Expert 5
4
4
2
1
64
10
Expert 6
8
2
1
10
64
1
Appendix
Table 10: Election security expert selected imperceptible values for each attack and model. For l∞ -APGD and l0+l∞ PGD, values denote the numerator of ϵ/255 . For l1 -APGD and l2 -APGD, values are ϵ . For l0 -based attacks, values are k .
Model
Step size init
# Steps
Random start
SVM/VGG16/ResNet20
2ϵ
500
False
CaiT
0.05ϵ
1500
False
Appendix
Table 11: l∞ -APGD hyperparameters.
Model
Step size init
# Steps
Random start
ResNet20-B
1.0ϵ
500
False
ResNet20-C
0.05ϵ
500
False
CaiT-B
0.05ϵ
500
False
CaiT-C
0.10ϵ
1250
False
SVM-B
0.05ϵ
500
False
SVM-C
0.10ϵ
500
False
Appendix
Table 12: l1 -APGD hyperparameters.
Model
Step size init
# Steps
Random start
ResNet20-B
2ϵ
100
False
ResNet20-C
2ϵ
150
False
CaiT-B
2ϵ
100
False
CaiT-C
2ϵ
750
False
SVM-B
2ϵ
100
False
SVM-C
2ϵ
100
False
Appendix
Table 13: l2 -APGD hyperparameters.
Model
# Steps
# Step size
# Restarts
Random start
ResNet20-B
25
15
10
True
ResNet20-C
30
15
10
True
CaiT-B
25
15
10
True
CaiT-C
30
15
10
True
SVM-B
25
15
10
True
SVM-C
25
15
10
True
Appendix
Table 14: l0 -PGD hyperparameters.
Model
# Steps
Step size
κ
# Restarts
Random start
ResNet20-B
75
15
10
10
True
ResNet20-C
75
15
10
10
True
CaiT-B
500
15
30
1
True
CaiT-C
500
15
30
1
True
SVM-B
500
15
30
1
True
SVM-C
75
15
10
10
True
Appendix
Table 15: l0+σ -map PGD hyperparameters.
Model
Robust acc. ( ϵ=255/255 )
ResNet20-B
0.000
ResNet20-C
0.000
CaiT-B
0.000
CaiT-C
0.017
SVM-B
0.000
SVM-C
0.000
Appendix
Table 16: Digital robust accuracy at the maximum budget for l∞ -APGD using cross-entropy (CE) loss.
Model
4/255
8/255
16/255
32/255
64/255
255/255
ResNet20-B
1.000
0.493
0.219
0.000
0.000
0.000
ResNet20-C
0.404
0.002
0.000
0.000
0.000
0.000
CaiT-B
1.000
1.000
1.000
1.000
0.614
0.000
CaiT-C
0.983
0.501
0.500
0.498
0.492
0.000
SVM-B
1.000
1.000
1.000
1.000
0.113
0.000
SVM-C
0.500
0.500
0.500
0.385
0.000
0.000
Appendix
Table 17: Digital robust accuracy for l∞ -APGD (DLR loss) at different ϵ budgets.
Model
2
4
8
20
200
2000
ResNet20-B
1.000
0.516
0.497
0.027
0.000
0.000
ResNet20-C
0.499
0.454
0.088
0.000
0.000
0.000
CaiT-B
1.000
1.000
1.000
0.496
0.000
0.000
CaiT-C
1.000
0.513
0.500
0.499
0.418
0.000
SVM-B
1.000
1.000
1.000
1.000
0.000
0.000
SVM-C
1.000
0.508
0.500
0.500
0.000
0.000
Appendix
Table 18: Digital robust accuracy for l1 -APGD (DLR loss) at different ϵ budgets.
Model
ϵ=1
ϵ=2
ϵ=3
ϵ=5
ϵ=15
ϵ=45
ResNet20-B
0.475
0.260
0.000
0.000
0.000
0.000
ResNet20-C
0.000
0.000
0.000
0.000
0.000
0.000
CaiT-B
1.000
0.999
0.482
0.000
0.000
0.000
CaiT-C
0.498
0.498
0.492
0.395
0.100
0.000
SVM-B
1.000
1.000
1.000
0.991
0.000
0.000
SVM-C
0.500
0.500
0.484
0.000
0.000
0.000
Appendix
Table 19: Digital robust accuracy for l2 -APGD (DLR loss) at different ϵ budgets.
Model
k=1
k=10
k=20
k=200
k=500
k=2000
ResNet20-B
1.000
0.998
0.871
0.500
0.383
0.000
ResNet20-C
0.998
0.500
0.500
0.500
0.500
0.000
CaiT-B
1.000
1.000
1.000
1.000
0.655
0.000
CaiT-C
1.000
0.998
0.952
0.500
0.493
0.000
SVM-B
1.000
1.000
1.000
1.000
0.739
0.000
SVM-C
1.000
0.910
0.590
0.489
0.000
0.000
Appendix
Table 20: Digital robust accuracy for l0 PGD (DLR loss) at different sparsity budgets k .
Model
4/255
8/255
16/255
32/255
64/255
255/255
ResNet20-B
1.000
1.000
1.000
1.000
1.000
0.871
ResNet20-C
1.000
0.955
0.527
0.501
0.500
0.500
CaiT-B
1.000
1.000
1.000
1.000
1.000
1.000
CaiT-C
1.000
1.000
1.000
1.000
0.997
0.952
SVM-B
1.000
1.000
1.000
1.000
1.000
1.000
SVM-C
1.000
1.000
1.000
1.000
1.000
0.590
Appendix
Table 21: Digital robust accuracy for l0+l∞ PGD (DLR loss) with fixed sparsity k=20 at different ϵ budgets.
Model
k=1
k=10
k=20
k=200
k=500
k=2000
ResNet20-B
1.000
1.000
1.000
0.500
0.456
0.000
ResNet20-C
0.558
0.500
0.500
0.500
0.500
0.000
CaiT-B
1.000
1.000
1.000
1.000
0.901
0.477
CaiT-C
0.930
0.624
0.535
0.507
0.425
0.000
SVM-B
1.000
1.000
1.000
0.999
0.505
0.372
SVM-C
1.000
0.999
0.990
0.496
0.352
0.000
Appendix
Table 22: Digital robust accuracy for l0+σ -map PGD (DLR loss) at different sparsity budgets k .
Model
4/255
8/255
16/255
32/255
64/255
255/255
ResNet20-C
1.000
1.000
1.000
0.988
0.556
0.500
CaiT-C
0.999
0.970
0.540
0.500
0.500
0.500
SVM-C
1.000
1.000
0.583
0.500
0.121
0.000
VGG16-C
1.000
1.000
1.000
0.960
0.607
0.500
Appendix
Table 23: Physical robust accuracy for l∞ -APGD on Combined-trained models at different ϵ budgets.
Model
ϵ=2
ϵ=4
ϵ=8
ϵ=20
ϵ=200
ϵ=2000
ResNet20-C
1.000
1.000
1.000
0.971
0.500
0.500
CaiT-C
1.000
0.746
0.540
0.501
0.500
0.500
SVM-C
1.000
1.000
0.963
0.603
0.005
0.003
VGG16-C
0.999
0.993
0.944
0.708
0.500
0.500
Appendix
Table 24: Physical robust accuracy for l1 -APGD on Combined-trained models at different ϵ budgets.
Model
ϵ=1
ϵ=2
ϵ=3
ϵ=5
ϵ=15
ϵ=45
ResNet20-C
1.000
0.989
0.816
0.510
0.500
0.500
CaiT-C
0.813
0.503
0.500
0.466
0.317
0.198
SVM-C
1.000
0.552
0.500
0.466
0.001
0.000
VGG16-C
1.000
0.946
0.626
0.511
0.500
0.500
Appendix
Table 25: Physical robust accuracy for l2 -APGD on Combined-trained models at different ϵ budgets.
Model
k=1
k=10
k=20
k=200
k=500
k=2000
ResNet20-C
1.000
0.899
0.644
0.500
0.500
0.500
CaiT-C
1.000
0.995
0.938
0.501
0.500
0.500
SVM-C
1.000
0.927
0.764
0.502
0.412
0.000
VGG16-C
1.000
0.901
0.594
0.500
0.500
0.500
Appendix
Table 26: Physical robust accuracy for l0 PGD on Combined-trained models at different sparsity budgets k . We use ϵ=1 for the per-pixel bound.
Model
4/255
8/255
16/255
32/255
64/255
255/255
ResNet20-C
1.000
1.000
1.000
1.000
1.000
0.742
CaiT-C
0.907
0.907
0.899
0.909
0.919
0.877
SVM-C
0.992
0.988
0.967
0.960
0.960
0.833
VGG16-C
1.000
1.000
1.000
1.000
1.000
0.645
Appendix
Table 27: Physical robust accuracy for l0+l∞ PGD on Combined-trained models at different ϵ budgets (with fixed sparsity k=20 ).
Model
k=1
k=10
k=20
k=200
k=500
k=2000
ResNet20-C
0.975
0.975
0.875
0.500
0.500
0.500
CaiT-C
0.963
0.650
0.559
0.523
0.519
0.297
SVM-C
1.000
1.000
1.000
0.664
0.506
0.188
VGG16-C
0.999
0.999
0.952
0.504
0.500
0.500
Appendix
Table 28: Physical robust accuracy for l0+σ -map PGD on Combined-trained models at different sparsity budgets k .
Machine learning systems deployed in distributed or federated environments are highly susceptible to adversarial manipulations, particularly availability attacks -- rendering the trained model unavailable. Prior research in distributed ML has demonstrated such adversarial effects through the injection of gradients or data poisoning. In this work, we ask whether comparable degradation is still possible under a substantially more constrained action space: the adversary may only flip a limited number of labels of existing training examples, without modifying features, injecting samples, or directly controlling gradients. We analyze the extent of damage caused by constrained label flipping attacks against distributed learning under mean aggregation -- the dominant baseline in research and production. Focusing on classification problems, (1) we propose a novel formalization of label flipping attacks as a per-round constrained optimization problem, derive a greedy label-selection rule for logistic regression, and empirically evaluate it beyond its derivation setting, including on MLPs and robust aggregators. The rule is provably per-epoch optimal for the attacker under the mean aggregator. (2) Empirically, we show that optimized label flipping can cause substantial accuracy degradation while outperforming random label flipping under similar budgets. (3) We shed light on an interesting interplay between what the attacker gains from more write-access versus what they gain from more flipping budget. (4) Finally, although the attack is derived for mean aggregation, we find that it can transfer empirically to the coordinate-wise median and trimmed mean aggregators, where its effectiveness approaches that of the Little-is-Enough gradient attack. This demonstrates that even highly constrained label-flipping adversaries can pose a significant availability threat to distributed learning.
When used in automated decision-making systems, machine learning (ML) models are vulnerable to data-manipulation attacks. Some defense mechanisms (e.g., adversarial regularization) directly affect the ML models while others (e.g., anomaly detection) act within the broader system. In this paper we consider a different task for defending the adversary, focusing on the attacker, rather than the attack. We present and demonstrate a framework for identifying characteristics about the attacker from an observed attack. We prove that, without additional knowledge, the attacker is non-identifiable (multiple potential attackers would perform the same observed attack). To address this challenge, we propose a domain-agnostic framework to identify the most probable attacker. This framework aids the defender in two ways. First, knowledge about the attacker can be leveraged for exogenous mitigation (i.e., addressing the vulnerability by altering the decision-making system outside the learning algorithm and/or limiting the attacker's capability). Second, when implementing defense methods that directly affect the learning process (e.g., adversarial regularization), knowledge of the specific attacker improves performance. We present the details of our framework and illustrate its applicability through specific instantiations on a variety of learners.
Soyon Choi, Scott Alfeld, Meiyi Ma
Vanderbilt University Nashville, TN 37240 · Amherst College Amherst, MA 01002
Almost all adversarial attacks add an imperceptible perturbation to fool a model. We instead study the opposite: a large, clearly visible perturbation that causes the model to keep its original, correct prediction, even though a human would no longer recognize the image. Prior work showed such examples can be generated at scale but left three questions untested: whether humans really perform worse than the model, whether standard out-of-distribution (OOD) detection and calibration tools catch it, and whether existing defenses mitigate it. We answer all three on MNIST, CIFAR-10, and ImageNet. (i) An independent recognizer proxy drops to ~49% on CIFAR-10 while the model stays at 100% -- a gap a small human pilot (N=5) corroborates directly and that is not explained by signal loss (a matched-magnitude Gaussian control degrades recognizability faster); a CLIP zero-shot proxy confirms the gap at ImageNet scale too. (ii) Confidence- and energy-based OOD detectors and calibration are structurally blind (0% detection, ECE ~= 0), while a feature-space Mahalanobis detector flags 100% -- but is evaded by an adaptive attacker at no cost to success. (iii) No classical defense, including adversarial training (45% robust accuracy), reduces attack success (correlation with large-epsilon_l resistance r ~= 0). A mechanistic analysis further shows the attack destroys low-level texture far faster than edge/shape structure.