Authors: Zeyu Shi, Yanhui Luo, Ziming Hong, Chongyang Gao, Kezhen Chen, Shanshan Ye, Lixu Wang
Organizations: The Chinese University of Hong Kong, Shenzhen · Zhejiang University · University of Sydney · Northwestern University · Analogy AI, Inc. · Mohamed Bin Zayed University of Artificial Intelligence
Time-series forecasting is widely used in sensitive domains. Models in these settings are often trained on longitudinal user- or entity-level records, which may later require removal because they contain sensitive or proprietary information or have been corrupted by sensor failures. To address such deletion requests without costly retraining, machine unlearning has been widely studied as a practical mechanism for privacy protection and data governance. However, the application of machine unlearning to time series prediction has not yet been well realized; this is mainly due to the following unique challenges: Gradient-based unlearning can be unstable because a deleted observation participates in multiple causally connected forecasting windows, causing parameter updates to propagate beyond the requested interval and degrade retained forecasting utility. Label-guided updating offers a more controlled alternative, but continuous and context-dependent forecasts lack a suitable replacement target, while the exact-retrained output is unavailable during unlearning. Moreover, the remaining support for a deleted temporal pattern is highly non-uniform. Some affected windows retain structurally similar counterparts in the retained data, whereas others become underrepresented or isolated. We present RDTU, a Residual Diffusion framework for time-series unlearning. RDTU first uses a retained-set neural tangent kernel predictor to obtain a deletion-compatible base forecast. Then it quantifies the global and local structural support of each affected window using the volume contribution of the retained-reference data. Then a diffusion model generates a residual correction that estimates the counterfactual forecast, yielding a pseudo-label field that guides a lightweight model update. Experiments show that RDTU consistently produces unlearned models that most closely match exact retraining.
Figures & tables
Figure 1: Overview of our proposed time-series unlearning framework RDTU. (1) The retained-set NTK predictor produces a base prediction for the affected window. (2) SIS integrates global directional contribution and local retained support to quantify the structural irreplaceability. (3) Conditioned on the NTK prediction and SIS, the residual diffusion model generates a residual correction. (4) The final label guides the unlearning update.
Method
Univariate Forecasting
Multivariate Forecasting
Air Quality
Traffic
EEG
HAR70
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
Original
0.6009
6.56
0.2546
–
0.6454
15.57
0.3941
–
0.6389
5.24
0.1069
–
0.6911
11.96
0.3495
–
Retrain
0.5034
–
0.2622
26.323
0.5291
–
0.3955
12.549
0.5235
–
0.1148
8.910
0.5210
–
0.3459
32.371
SSD
0.5218
52.8954
0.6683
0.946
0.5371
72.6908
0.8928
0.395
0.5180
54.1037
0.5877
0.227
0.5204
72.0281
0.5763
0.623
NegGrad+
0.5090
162.1498
1.5902
9.871
0.5412
140.9170
1.3989
4.340
0.5261
102.1933
0.9080
2.397
0.5372
288.0736
1.6082
10.051
Table 1: Performance comparison between our method and other unlearning baselines on univariate and multivariate forecasting tasks. Unlearning effectiveness is evaluated by the two-sided U/N AUC and the F-P Gap(%), where U/N values closer to 0.5 indicate lower distinguishability between forgotten and never-seen samples, and a lower F-P Gap(%) indicates closer predictive agreement with exact retraining. Forecasting utility is evaluated by test NRMSE, with lower values indicating better predictive performance. Computational efficiency is measured by wall-clock time in seconds.
Methods
Univariate Forecasting
Multivariate Forecasting
Air Quality
Traffic
EEG
HAR70
U/N
F-P Gap
NRMSE
U/N
F-P Gap
NRMSE
U/N
F-P Gap
NRMSE
U/N
F-P Gap
NRMSE
w/o Diffusion
0.5250
5.2378
0.2685
0.5455
11.3759
0.3946
0.5297
4.2684
0.1232
0.5190
9.8371
0.3434
Residual-MLP
0.5201
5.0807
0.2632
0.5454
10.3245
0.3940
0.5341
5.5752
0.2583
0.5261
10.064
0.3398
Residual-ARIMA
0.5392
4.9284
0.2609
0.5381
10.7915
0.3968
0.5218
4.2113
0.1135
0.5175
10.8921
0.3498
w/o SIS
0.5180
5.0545
0.2610
0.5475
10.2339
0.3964
0.5226
3.9427
0.1171
0.5213
10.0836
0.3452
Table 2: Ablation study of the key components of our method on different datasets.
Figure 2: Sensitivity analysis of RDTU under different diffusion steps of Horizon Length=1.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Method
Air Quality
Traffic
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
Original
0.6082
10.91
0.4084
–
0.6716
15.57
0.4908
–
Retrain
0.5400
–
0.4131
20.480
0.5478
–
0.5063
12.640
SSD
0.5429
43.31
0.6725
0.77
0.5501
79.35
0.9927
0.450
NegGrad+
0.5356
167.58
1.6929
7.88
0.5346
79.90
0.8708
3.930
Zero-label
0.5348
50.79
0.6918
3.33
0.5507
49.89
0.7294
1.820
Appendix
Table 3: Robustness comparison on univariate datasets under a forecasting horizon of H=3 . U/N values closer to 0.5 indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.
Method
EEG
HAR70
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
Original
0.6759
5.24
0.1986
–
0.6946
12.53
0.3977
–
Retrain
0.5152
–
0.2055
8.980
0.5162
–
0.3975
30.71
SSD
0.5257
59.03
0.6593
0.230
0.5247
82.05
0.6331
0.55
NegGrad+
0.5267
95.88
0.8748
2.350
0.5314
208.95
1.1839
9.28
Zero-label
0.5244
60.22
0.6029
0.360
0.5231
58.71
0.4528
0.62
Appendix
Table 4: Robustness comparison on multivariate datasets under a forecasting horizon of H=3 . U/N values closer to 0.5 indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.
Method
Air Quality
Traffic
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
Original
0.6653
12.39
0.5379
–
0.6645
17.02
0.5821
–
Retrain
0.5330
–
0.5556
16.54
0.5698
–
0.5916
10.94
SSD
0.5312
51.25
0.7903
1.02
0.5661
78.50
0.9965
0.76
NegGrad+
0.5423
105.31
1.1596
7.48
0.5583
53.88
0.7481
3.53
Zero-label
0.5310
50.57
0.7553
4.14
0.5723
49.50
0.7698
2.84
Appendix
Table 5: Robustness comparison on univariate datasets under a forecasting horizon of H=6 . U/N values closer to 0.5 indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.
Method
EEG
HAR70
U/N
F-P Gap
NRMSE
Time
U/N
F-P Gap
NRMSE
Time
Original
0.7301
10.74
0.3678
–
0.6982
13.88
0.4393
–
Retrain
0.5210
–
0.3770
–
0.5215
–
0.4430
34.45
SSD
0.5268
58.46
0.7230
0.62
0.5187
81.82
0.6467
0.86
NegGrad+
0.5305
93.27
0.9043
2.60
0.5271
182.69
0.9548
9.91
Zero-label
0.5289
56.45
0.6505
0.79
0.5199
59.14
0.4808
1.10
Appendix
Table 6: Robustness comparison on multivariate datasets under a forecasting horizon of H=6 . U/N values closer to 0.5 indicate better unlearning effectiveness, while lower F-P Gap, NRMSE, and runtime indicate better performance.
Figure 3: Sensitivity analysis of RDTU under different diffusion steps of Horizon Length=3. The curves report the F-P Gap and the time cost of diffusion.
Figure 4: Sensitivity analysis of RDTU under different loss-weight ratios λf/λr of Horizon Length=1. The curves report the mean test NRMSE and F-P Gap, while the shaded regions indicate the corresponding standard errors over 30 runs. Lower values indicate better performance for both metrics.
When a data license expires, deleting stored records does not remove influence encoded in a trained forecaster. Machine unlearning seeks to remove this influence without retraining. We benchmark temporal unlearning with 3,200 paired references trained on all data and oracles retrained without the requested period. The grid covers five architectures, four rolling folds, five deletable years, and three experimental deletion levels on an S&P 500 volatility panel. The 2020 COVID crisis year produces the largest memorization gap for every architecture. Removing it improves all three deployable models in every fold, with the largest improvement in the 2022 bear market, while the two non-deployable models respond inconsistently. The target for approximate unlearning is the oracle, not low predictive accuracy on the deleted period. In one Transformer cell, an oracle that never trained on 2020 still predicts it at an information coefficient of 0.51, compared with 0.55 for the reference; pushing predictions toward noise reduces test skill. Across twelve deployable architecture-method pairs, only TSMixer with the hinge method remains near the oracle in every fold, closing 74-118% of the reference-to-oracle gap without a measurable loss of test skill. Method rankings vary across architectures and rolling windows. Audit separation rises with prior memorization but can remain small after exact deletion. The window-level loss comparison reaches at most 0.69, and treating stock-level windows as independent inflates the absolute t-statistic by a median factor of 1.9. These results call for an explicit deletion scope, oracle validation for the relevant architecture and window, and power-aware auditing.
Junyi Ye
School of Computing, Montclair State University Montclair, New Jersey, USA
Machine unlearning is an emerging domain that ensures the safe removal of elements (includes concepts, attributes, entity and class) from the trained model along with least drop in model performance. The domain of machine unlearning brings its own indigenous challenges since the removal of pre-trained elements from model will always degrade the model performance on remaining elements. The existing methods basically rely on retraining for removal of elements from the pre-trained model, which is compute extensive. In this work, we propose a machine unlearning method which helps to reduce the computational requirement for faster retain-dataset accuracy convergence which also does not require extensive retraining of the pre-trained model. The proposed method, Data-Frugal Machine Unlearning (DFMU) requires only a single forward and backward pass for computing the importance score of various computational blocks of a model. The importance score computation is based on knowledge preserving pruning which helps to converge faster and requires far less data as compared to the existing methods. Experimentally, it achieves 40% more retain-accuracy with just 13% of data samples in comparison with SOTA method on various public datasets and also averages 88% faster processing time for forgetting a given class.
Privacy protection laws, such as the GDPR, grant individuals the right to request the forgetting of their personal data not only from databases but also from machine learning (ML) models trained on them. Machine unlearning has emerged as a practical means to facilitate model forgetting of data instances seen during training. Although some existing machine unlearning methods guarantee exact forgetting, they are typically costly in computational terms. On the other hand, more affordable methods do not offer forgetting guarantees and are applicable only to specific ML models. In this paper, we present \emph{efficient unlearning with privacy guarantees} (EUPG), a novel machine unlearning framework that offers formal privacy guarantees to individuals whose data are being unlearned. EUPG involves pre-training ML models on data protected using privacy models, and it enables {\em efficient unlearning with the privacy guarantees offered by the privacy models in use}. Through empirical evaluation on four heterogeneous data sets protected with k-anonymity and ε-differential privacy as privacy models, our approach demonstrates utility and forgetting effectiveness comparable to those of exact unlearning methods, while significantly reducing computational and storage costs. Our code is available at https://github.com/najeebjebreel/EUPG.
Josep Domingo-Ferrer, Najeeb Jebreel, David Sánchez
1CYBERCAT (Center for Cybersecurity Research of2026 Catalonia), ComSCIAM-Center for Computational Science and Applied Mathematics, Department of Computer EngineeringJun and Mathematics, Universitat Rovira i Virgili, Av. Pa¨ısos26 Catalans 26, E-43007 Tarragona, Catalonia