Evaluating machine unlearning remains challenging, as existing methods typically require retraining reference models or performing membership inference attacks, both of which rely on prior access to training configuration or supervision labels, making them impractical in realistic scenarios. Motivated by the fact that most unlearning algorithms remove a small, random subset of the training data, we propose a subset-level evaluation framework based on statistical independence. Specifically, we design a tailored use of the Hilbert-Schmidt Independence Criterion to assess whether the model outputs on a given subset exhibit statistical dependence, without requiring model retraining or auxiliary classifiers. Our method provides a simple, standalone evaluation procedure that aligns with unlearning workflows. Extensive experiments demonstrate that our approach reliably distinguishes in-training from out-of-training subsets and clearly differentiates unlearning effectiveness, even when existing evaluations fall short.
Figures & tables
Figure 1
Figure 3: Effect of kernel bandwidth σ on F1 score. The solid lines show F1 score trends across different σ values. Vertical dashed lines indicate the heuristic of σ=dim , while dotted lines correspond to the median heuristic.
R
5%
10%
20%
∣S∣
400
1000
2000
400
1000
2000
400
1000
2000
SV-AllCNN
0.62±0.14
0.74±0.08
0.83±0.09
0.50±0.21
0.62±0.06
0.73±0.12
0.72±0.03
0.82±0.08
0.90±0.06
C10-AllCNN
0.69±0.07
0.79±0.05
0.81±0.14
0.61±0.05
0.66±0.12
0.82±0.09
0.45±0.00
0.71±0.18
0.79±0.09
SV-ResNet18
0.71±0.09
0.91±0.01
0.93±0.07
0.63±0.10
0.78±0.09
0.85±0.14
0.90±0.03
0.96±0.02
0.97±0.05
C10-ResNet18
0.87±0.06
0.97±0.02
0.99±0.01
0.88±0.04
0.95±0.06
0.97±0.03
0.86±0.10
0.96±0.03
1.00±0.00
C100-ResNet18
0.99±0.01
1.00±0.00
1.00±0.00
0.97±0.05
1.00±0.00
1.00±0.00
0.99±0.01
1.00±0.00
1.00±0.00
Table 1: F1 score of distinguishing in/out-of-training status of target S , across the amount of Df and the size of S .
Figure 4
R
5%
10%
20%
∣S∣
400
1000
2000
400
1000
2000
400
1000
2000
MMD
0.63±0.07
0.65±0.09
0.87±0.12
0.45±0.21
0.70±0.13
0.87±0.14
0.63±0.03
0.72±0.08
0.89±0.11
Wasserstein
0.70±0.08
0.77±0.10
0.94±0.11
0.52±0.20
0.89±0.08
0.98±0.03
0.72±0.02
0.87±0.07
0.99±0.02
SDE (OURS)
0.87±0.06
0.97±0.02
0.99±0.01
0.88±0.04
0.95±0.06
0.97±0.03
0.86±0.10
0.96±0.03
1.00±0.00
Table 3: Comparison with distribution-based metrics
Method
Accr (%)
Accf (%)
ASR
h
hp
F1
OTR (%) ↑
F1
OTR (%) ↑
Retrain
98.57 ± 0.08
93.25 ± 0.45
0.30 ± 0.09
0.94 ± 0.03
87.00 ± 10.24
0.95 ± 0.05
94.00 ± 4.94
RandLabel
98.80 ± 0.04
98.63 ± 0.13
0.29 ± 0.02
0.88 ± 0.12
84.00 ± 13.54
0.91 ± 0.09
83.20 ± 10.11
Unroll
99.36 ± 0.05
99.21 ± 0.11
0.30 ± 0.12
0.88 ± 0.04
3.00 ± 2.19
0.90 ± 0.07
4.40 ± 4.03
Sparsity
92.72 ± 0.93
90.56 ± 0.82
0.42 ± 0.09
0.62 ± 0.15
50.80 ± 22.61
0.59 ± 0.16
53.80 ± 24.19
SalUn
98.66 ± 0.03
98.53 ± 0.07
0.29 ± 0.02
0.85 ± 0.12
52.40 ± 21.86
0.86 ± 0.15
51.80 ± 23.05
Table 4: Evaluating unlearned models on CIFAR10-ResNet18 with R=10% . Accr and Accf denote unlearned models’ training accuracy on the Dr and Df , respectively. ASR refers to the success rate of MIA. For these metrics, the closer to the retrained model’s the better. For our method, the higher OTR indicates more effective unlearning.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: H(S,h) distribution changes along the training epoch. The dashed gray line is the p=0.01 baseline.
Table 8
Data-Arch
Acc
10%
20%
40%
80%
SV-AllCNN
Train
88.09
95.73
98.51
99.92
Test
88.16
92.97
92.54
94.26
C10-AllCNN
Train
92.77
99.21
100.00
100.00
Test
90.49
92.07
94.76
94.83
SV-ResNet18
Train
77.52
84.92
89.22
98.65
Test
71.42
78.12
80.06
91.49
Appendix
Table 7: Task utilities of models across training progress.
Figure 6: F1 score across σ on the diffusion model.
R
Method
Accr (%)
Accf (%)
ASR
h
hp
F1
OTR (%) ↑
F1
OTR (%) ↑
5%
Retrain
98.70 ± 0.03
93.66 ± 0.10
0.32 ± 0.12
0.85 ± 0.10
90.60 ± 10.84
0.92 ± 0.06
93.20 ± 7.57
RandLabel
98.86 ± 0.03
98.64 ± 0.13
0.25 ± 0.03
0.88 ± 0.09
79.00 ± 26.26
0.90 ± 0.09
76.40 ± 28.08
Unroll
99.38 ± 0.03
99.24 ± 0.22
0.28 ± 0.10
0.88 ± 0.08
0.80 ± 0.75
0.88 ± 0.09
1.00 ± 2.00
Sparsity
93.75 ± 0.54
91.52 ± 0.38
0.44 ± 0.08
0.66 ± 0.29
62.00 ± 31.12
0.66 ± 0.31
62.20 ± 33.07
SalUn
98.73 ± 0.02
98.54 ± 0.14
0.23 ± 0.02
0.84 ± 0.11
38.80 ± 21.31
0.87 ± 0.11
37.20 ± 26.61
Appendix
Table 8: Unlearned models’ results on CIFAR10-ResNet18 with R∈{5%,10%,20%} . Accr and Accf denote unlearned models’ training accuracy on the Dr and Df , respectively. ASR refers to the success rate of membership inference attacks. For these metrics, the closer to the retrained model’s the better. For our method, the higher OTR means that more forgetting data has been identified as out-of-training data, indicating more effective unlearning.
Inference Time
m=50
m=100
m=200
∣S∣=400
0.29+
9.51
18.76
37.76
∣S∣=1000
0.72+
11.06
21.92
45.85
∣S∣=2000
1.43+
29.02
57.70
116.04
Appendix
Table 9: Wall-clock time cost (seconds) with different m and ∣S∣ when d=512 .
Inference Time
m=50
m=100
m=200
∣S∣=400
0.29+
13.46
26.55
52.35
∣S∣=1000
0.72+
27.15
54.18
107.99
∣S∣=2000
1.43+
84.84
168.30
335.67
Appendix
Table 10: Wall-clock time cost (seconds) with different m and ∣S∣ when d=8192 .
Evaluating whether unlearning algorithms truly remove training data influence remains an open challenge. We propose a practical auditor that computes data-dependent lower bounds on the unlearning parameter ε using membership inference attacks. Evaluating multiple unlearning algorithms, we find a sharp separation: algorithms with rigorous guarantees, such as model clipping and rewind-to-delete, achieve very small ε bounds that do not falsify their unlearning guarantees, whereas empirical methods such as Hessian-based unlearning, interleaved ascent-descent, ascent on the forget set, and fine-tuning on the retain set exhibit large bounds, indicating poor unlearning. Our auditor provides a practical tool for empirically falsifying unlearning claims through a hypothesis-testing framework, and we validate it on CIFAR-100 and Shakespeare text.
Machine unlearning has been extensively studied in response to growing privacy concerns and regulatory requirements. However, auditing whether unlearning algorithms have truly erased the influence of specific data remains an open challenge. The lack of reliable and practical auditing mechanisms can lead to critical privacy risks, such as residual information leakage. This paper initiates a systematic investigation into whether existing unlearning algorithms can truly forget the designated data. We propose the first practical and general-purpose auditing framework for machine unlearning, inspired by the concept of proof of ignorance. Our framework addresses the key practicality limitations of existing methods by eliminating the need for retraining-from-scratch baselines, avoiding the training of large numbers of shadow models, and requiring no intrusive intervention in the original training process. To evaluate the effectiveness of our framework, we first conduct validation experiments to verify its soundness and completeness. We then perform comprehensive experiments across six datasets and ten representative unlearning methods. The results demonstrate that our framework reliably distinguishes between successful and failed unlearning. In particular, we observe that retraining-based and fine-tuning-based methods can achieve effective unlearning, even when the target data remain in the original dataset. In contrast, de-optimization-based methods fail to achieve true unlearning and instead degrade the model's performance. Fisher/Hessian-based methods also fail to unlearn requested data, even formal certification is provided. Moreover, we show that our framework is robust against fake unlearning attempts and generalizes well to large language models.
Evaluating machine unlearning methods remains technically challenging, with recent benchmarks requiring complex setups and significant engineering overhead. We introduce a unified and extensible benchmarking suite that simplifies the evaluation of unlearning algorithms using the KLoM (KL divergence of Margins) metric. Our framework provides precomputed model ensembles, oracle outputs, and streamlined infrastructure for running evaluations out of the box. By standardizing setup and metrics, it enables reproducible, scalable, and fair comparison across unlearning methods. We aim for this benchmark to serve as a practical foundation for accelerating research and promoting best practices in machine unlearning. Our code and data are publicly available.
Roy Rinberg, Pol Puigdemont, Martin Pawelczyk +1
Harvard University · LIONS, EPFL, Lausanne, Switzerland.