Machine-unlearning methods remove the influence of designated training data from a trained model without retraining from scratch, but there is no agreed criterion for when such a procedure should stop: in practice a fixed number of unlearning epochs (an 'unlearning budget') is spent and loss trajectories are inspected by hand. The source paper 'Adversarial Mixup Unlearning' (ICLR 2025) states explicitly that determining the optimal strategy for terminating unlearning remains an open question in the field. The problem is to replace fixed budgets with a principled, standardized stopping rule: which observable metrics — remaining-data performance, forget-set fit, held-out utility, or privacy-attack success rate, alone or in combination — should trigger termination; how the trade-off between retaining utility and completing forgetting should be formalized without access to a retrained reference model; and whether an automated rule can generalize across datasets, label-aware versus label-agnostic regimes, and unlearning budgets. No accepted general criterion for terminating unlearning exists to date, so the question remains open.

Background

Machine unlearning is the task of removing the influence of a designated subset of training data (the 'forget set') from an already-trained model while preserving behavior on the remaining data (the 'retain set'), at a computational cost far below retraining from scratch; the retrained model is the usual gold-standard reference for what a properly unlearned model should look like, but actually producing it defeats the purpose of unlearning. Approximate ('inexact') unlearning methods therefore fine-tune the original model with an unlearning loss, and are evaluated on a small set of recurring metrics: accuracy on retain-set training data (often written Trainr_r), accuracy or fit on the forget-set training data (Trainf_f), held-out test accuracy (Test), and the success rate of an attack — typically a membership-inference adversary that tries to distinguish whether a given example was in the training data (Attack Success Rate, ASR). Unlearning methods are also divided into label-aware ones, which may use labels of the training data during unlearning, and label-agnostic ones, which cannot; and 'catastrophic unlearning' denotes the failure mode where erasing the target data also destroys essential retained knowledge. In ordinary supervised training, termination is handled by validation-based early stopping: a held-out validation loss is monitored and training stops when it starts to increase. This mechanism does not transfer to unlearning, because there is no validation signal for 'forgotten enough' — the quantity to be matched, a model retrained without the forget data, is unavailable at stopping time, and the utility metrics and privacy-attack metrics can rank intermediate checkpoints differently. Consequently, standard practice across the unlearning literature (including SCRUB, one of the widely used baselines) is to run a fixed number of unlearning epochs — the 'unlearning budget' — and to inspect loss curves or evaluate saved checkpoints after the fact. The paper 'Adversarial Mixup Unlearning' (Peng, Tang and Yang, ICLR 2025), which introduces the MixUnlearn generator–unlearner framework that regularizes unlearning with adversarially synthesized mixup samples (convex combinations of training points, a standard data-augmentation construction), adopts exactly this fixed-budget practice and states in its appendix that determining how to terminate unlearning effectively is an open question left as a promising avenue for future research. Recent adjacent work underscores but does not settle the question: stronger membership-inference evaluations show that attack-based metrics are subtler than raw ASR suggests; a 2025 survey of unlearning verification catalogs behavioral and parametric checks of whether unlearning succeeded but proposes no stopping rule; and a 2026 language-model unlearning method (MASC) builds an online stopping rule into its own loss, showing self-terminating unlearning is possible for one method family while leaving a standardized, method-agnostic criterion — and the choice among Trainr_r, Trainf_f, Test, ASR, or a combination — open.

Problem Statement

Establish a principled, standardized criterion for terminating a machine-unlearning process — an analogue of validation-based early stopping for standard training. Concretely, as posed by the source paper: (1) determine which observable metric(s) — performance on the remaining data (Trainr_r), fit to the forget set (Trainf_f), held-out test utility, the success rate of privacy attacks such as membership inference (ASR), or a weighted combination of these — should govern the decision to stop unlearning, with a justification tied to the field's reference target of matching a model retrained without the forget data; (2) formalize the inherent trade-off between remaining-data utility and forgetting completeness, i.e. define what counts as 'sufficiently forgotten' at stopping time, when the retrained reference model is unavailable and utility-based and attack-based metrics may rank intermediate models differently; and (3) determine whether an automated stopping rule built on these quantities generalizes across datasets, across label-aware and label-agnostic unlearning regimes, and across unlearning budgets, so that it can replace the current practice of a fixed unlearning-epoch budget followed by manual inspection of loss trajectories. The criterion must address the question at this generality, not merely for a single fixed method or dataset: all three parts are required, and part (3) is resolved by establishing — or by showing the failure of — generalization across the three stated axes.

References

  1. Peng, Zhuoyi; Tang, Yixuan; Yang, Yi (2025). 'Adversarial Mixup Unlearning.' arXiv:2502.10288, ICLR 2025 Poster. DOI: 10.48550/arXiv.2502.10288. https://arxiv.org/abs/2502.10288
  2. Kurmanji, Meghdad; Triantafillou, Peter; Hayes, Jamie; Triantafillou, Eleni (2023). 'Towards Unbounded Machine Unlearning' (SCRUB). arXiv:2302.09880. DOI: 10.48550/arXiv.2302.09880. https://arxiv.org/abs/2302.09880
  3. Hayes, Jamie; Shumailov, Ilia; Triantafillou, Eleni; Khalifa, Amr; Papernot, Nicolas (2024). 'Inexact Unlearning Needs More Careful Evaluations to Avoid a False Sense of Privacy.' arXiv:2403.01218. DOI: 10.48550/arXiv.2403.01218. https://arxiv.org/abs/2403.01218
  4. Wang, Cheng-Long; Li, Qi; Xiang, Zihang; Cao, Yinzhi; Wang, Di (2025). 'Towards Lifecycle Unlearning Commitment Management: Measuring Sample-level Unlearning Completeness.' arXiv:2506.06112. DOI: 10.48550/arXiv.2506.06112. https://arxiv.org/abs/2506.06112
  5. Zhang, Xiang; Wei, Kun; Yang, Xu; Li, Jiahua; Yan, Su; Deng, Cheng (2025). 'Rotation Control Unlearning: Quantifying and Controlling Continuous Unlearning for LLM with The Cognitive Rotation Space.' arXiv:2509.25743. DOI: 10.48550/arXiv.2509.25743. https://arxiv.org/abs/2509.25743
  6. Di Gennaro, Federico; Shevchenko, Alexander; Yang, Fanny (2026). 'Fast Unlearning at Scale via Margin Self-Correction' (MASC). arXiv:2606.02920. DOI: 10.48550/arXiv.2606.02920. https://arxiv.org/abs/2606.02920
  7. Xue, Lulu; Hu, Shengshan; Lu, Wei; Shen, Yan; Li, Dongxu; Guo, Peijin; Zhou, Ziqi; Li, Minghui; Zhang, Yanjun; Zhang, Leo Yu (2025). 'Towards Reliable Forgetting: A Survey on Machine Unlearning Verification.' arXiv:2506.15115. DOI: 10.48550/arXiv.2506.15115. https://arxiv.org/abs/2506.15115
  8. Duan, Hanyu; Yang, Yi; Abbasi, Ahmed; Tam, Kar Yan (2025). 'Ready2Unlearn: A Learning-Time Approach for Preparing Models with Future Unlearning Readiness.' arXiv:2505.10845. DOI: 10.48550/arXiv.2505.10845. https://arxiv.org/abs/2505.10845
  9. Xie, Linxi; Teng, Xin; Ke, Shichang; Wen, Hongyi; Wang, Shengjie (2025). 'Reveal and Release: Iterative LLM Unlearning with Self-generated Data.' arXiv:2509.14624. DOI: 10.48550/arXiv.2509.14624. https://arxiv.org/abs/2509.14624
  10. Alkhatib, Yahya; Jamal, Muhammad Ahmar; Tay, Wee Peng (2025). 'Conformal Unlearning: A New Paradigm for Unlearning in Conformal Predictors.' arXiv:2508.03245. DOI: 10.48550/arXiv.2508.03245. https://arxiv.org/abs/2508.03245
  11. Shen, Hangyi; Pan, Yizhi; Li, Tiansuo; Jiang, Weiqi; Sun, Guanqun (2026). 'Image Feature Fusion-based Federated Client Unlearning (FCU).' arXiv:2605.26715. DOI: 10.48550/arXiv.2605.26715. https://arxiv.org/abs/2605.26715
  12. Li, Xujia; Li, Dan; Lou, Jian; Feng, Wenjie (2026). 'Signal-Guided Optimization for Machine Unlearning' (GSUO). arXiv:2607.11975. DOI: 10.48550/arXiv.2607.11975. https://arxiv.org/abs/2607.11975
  13. Batorski, Pawel; Swoboda, Paul (2026). 'EvoMU: Evolutionary Machine Unlearning.' arXiv:2602.02139. DOI: 10.48550/arXiv.2602.02139. https://arxiv.org/abs/2602.02139
  14. Wang, Haoyu; Huang, Zhuo; Wang, Xiaolong; Han, Bo; Lin, Zhiwei; Liu, Tongliang (2026). 'MeGU: Machine-Guided Unlearning with Target Feature Disentanglement.' arXiv:2602.17088. DOI: 10.48550/arXiv.2602.17088. https://arxiv.org/abs/2602.17088