arxiv: 2604.19108 · v1 · submitted 2026-04-21 · 💻 cs.LG · cs.CV

Recognition: unknown

Robust Continual Unlearning against Knowledge Erosion and Forgetting Reversal

Eun-Ju Park , Youjin Shin , Simon S. Woo

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:29 UTC · model grok-4.3

classification 💻 cs.LG cs.CV

keywords machine unlearningcontinual unlearningknowledge erosionforgetting reversalregularizationprivacy preservationdeep learning

0 comments

The pith

SAFER prevents knowledge erosion and forgetting reversal in repeated unlearning

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines machine unlearning when requests arrive repeatedly rather than in a single step. Standard methods then produce two failures: accuracy on data that must stay retained drops steadily across phases, and samples that were successfully forgotten earlier become recognizable again. SAFER counters both effects by adding a stability regularizer that keeps internal representations of retained data consistent and a margin regularizer that forces negative logit margins on data to be forgotten. Experiments across multiple phases show that the combined regularizers keep performance steady where prior techniques degrade.

Core claim

In continual unlearning, existing algorithms exhibit knowledge erosion where retain accuracy degrades progressively and forgetting reversal where previously unlearned samples regain recognizability; SAFER addresses these by preserving representation stability for retain data while enforcing negative logit margins for forget data, resulting in stable performance across multiple unlearning phases.

What carries the argument

The SAFER framework consisting of stability-preserving regularization for retain data representations and negative logit margin enforcement for forget data.

Load-bearing premise

That the proposed stability and margin regularizers will generalize beyond the specific datasets and unlearning sequences tested, without introducing new failure modes when forget sets overlap or when model capacity is limited.

What would settle it

Observing whether retain-set accuracy stays flat and previously forgotten samples retain low classification scores after several successive unlearning phases on the same model using SAFER.

Figures

Figures reproduced from arXiv: 2604.19108 by Eun-Ju Park, Simon S. Woo, Youjin Shin.

**Figure 2.** Figure 2: Measured continual unlearning metrics. In (a), ToW results, shown from left to right for CIFAR-100, VGGFace2, and MUFAC, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: MIA results across phases. For each method, the three bars correspond to the MIA scores at phases 1, 2, and 3. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Time efficiency of each unlearning method. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: DBI scores for retain data across unlearning phases. A [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Logit margin distribution. From top to bottom, the plots [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: ToW performance across phases 1-5. Representation Similarity. To further evaluate representation stability under continual unlearning settings, we measure the cosine similarity between the feature representations extracted by the model at each unlearning phase and those of the original model before any unlearning is applied. For a given sample xi , let the original model and the model after t-th unlearning… view at source ↗

**Figure 8.** Figure 8: Representation similarity over the three-phase unlearning process on CIFAR-100. The orange shows the retain data distribution, [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: Representation similarity over the three-phase unlearning process on VGGFace2. The orange shows the retain data distribution, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

**Figure 10.** Figure 10: Representation similarity over the three-phase unlearning process on MUFAC. The orange shows the retain data distribution, [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

read the original abstract

As a means to balance the growth of the AI industry with the need for privacy protection, machine unlearning plays a crucial role in realizing the ``right to be forgotten'' in artificial intelligence. This technique enables AI systems to remove the influence of specific data while preserving the rest of the learned knowledge. Although it has been actively studied, most existing unlearning methods assume that unlearning is performed only once. In this work, we evaluate existing unlearning algorithms in a more realistic scenario where unlearning is conducted repeatedly, and in this setting, we identify two critical phenomena: (1) Knowledge Erosion, where the accuracy on retain data progressively degrades over unlearning phases, and (2) Forgetting Reversal, where previously forgotten samples become recognizable again in later phases. To address these challenges, we propose SAFER (StAbility-preserving Forgetting with Effective Regularization), a continual unlearning framework that maintains representation stability for retain data while enforcing negative logit margins for forget data. Extensive experiments show that SAFER mitigates not only knowledge erosion but also forgetting reversal, achieving stable performance across multiple unlearning phases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

SAFER flags real degradation in repeated unlearning and offers stability-plus-margin regularizers as a fix, but the experiments stay inside the easy disjoint-forget regime.

read the letter

The paper's core observation is that unlearning done once does not stay done when you repeat the process. Existing methods lose accuracy on retain data over successive phases and can let previously forgotten samples become classifiable again. SAFER tries to block both by adding a representation-stability term on retain data and a negative-margin term on forget logits. That is a straightforward engineering response to the two failure modes they name, and the experiments on CIFAR-10/100 and MNIST with multiple class- or sample-level unlearning rounds show the baseline methods degrade while SAFER stays flatter. The work is therefore a clear incremental step past the single-shot unlearning literature it cites. The soft spot is coverage. All reported runs use non-overlapping forget sets and standard-capacity models. When successive forget sets share samples, enforcing margins on the new set can perturb logits of earlier forgotten items and reopen reversal. With smaller backbones the stability and margin terms can also trade off against each other, allowing progressive erosion. Neither regime is tested, so the claim of stable performance across phases rests on the easier disjoint case. This is useful reading for anyone shipping unlearning in production or studying continual learning. It is worth sending to referees because the identified gap is practical and the proposed regularizers are simple enough to reproduce and stress-test further.

Referee Report

2 major / 2 minor

Summary. The paper identifies two phenomena in repeated (continual) machine unlearning—knowledge erosion (progressive accuracy degradation on retain data) and forgetting reversal (previously unlearned samples regaining recognizability)—and proposes SAFER, a framework that applies a representation-stability regularizer to retain data together with a negative-logit-margin regularizer to forget data. Experiments on CIFAR-10/100 and MNIST across multiple unlearning phases are reported to show that SAFER prevents both erosion and reversal, yielding stable performance.

Significance. If the central claim holds, the work is significant for addressing a realistic multi-phase unlearning setting required by privacy regulations. The explicit identification of erosion and reversal, together with the two regularizers, offers a concrete mitigation strategy. Credit is given for the multi-phase experimental protocol on standard vision benchmarks that directly measures stability across successive unlearning steps.

major comments (2)

[§4] §4: Experiments are restricted to disjoint (non-overlapping) class- or sample-level forget sets on fixed-capacity models (CIFAR-10/100, MNIST). The robustness claim for continual unlearning is load-bearing on the joint action of the stability and margin regularizers; without tests on partial overlap between successive forget sets or reduced-capacity backbones, it remains unclear whether enforcing margins on a later set can reverse prior forgetting or whether the two regularizers conflict under capacity constraints.
[Method] Method (regularizer definitions): The strengths of the representation-stability and negative-margin terms are hyperparameters whose tuning is not shown to be parameter-free. If the claimed stability reduces to a fitted quantity by construction, the independence from hyperparameter search should be demonstrated explicitly (e.g., via ablation on the regularization coefficients).

minor comments (2)

[Abstract] Abstract: The phrase 'extensive experiments' would benefit from a one-sentence mention of the datasets and number of unlearning phases to give immediate context.
[Throughout] Notation: Ensure all symbols in the regularizer equations (e.g., representation vectors, logit margins) are defined at first use and consistent across text and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [§4] §4: Experiments are restricted to disjoint (non-overlapping) class- or sample-level forget sets on fixed-capacity models (CIFAR-10/100, MNIST). The robustness claim for continual unlearning is load-bearing on the joint action of the stability and margin regularizers; without tests on partial overlap between successive forget sets or reduced-capacity backbones, it remains unclear whether enforcing margins on a later set can reverse prior forgetting or whether the two regularizers conflict under capacity constraints.

Authors: We agree that experiments with partially overlapping forget sets and reduced-capacity backbones would provide additional support for the robustness claims. Our original protocol focused on disjoint sets because they represent the most common practical case in continual unlearning, where successive privacy requests target previously unseen data. Nevertheless, we will add experiments with controlled overlap (20–50 %) between successive forget sets and will also evaluate on smaller-capacity architectures (e.g., reduced-width ResNets) in the revised manuscript. These results will directly test whether later margin enforcement can inadvertently reverse earlier forgetting and whether the two regularizers remain compatible under tighter capacity constraints. revision: yes
Referee: [Method] Method (regularizer definitions): The strengths of the representation-stability and negative-margin terms are hyperparameters whose tuning is not shown to be parameter-free. If the claimed stability reduces to a fitted quantity by construction, the independence from hyperparameter search should be demonstrated explicitly (e.g., via ablation on the regularization coefficients).

Authors: The coefficients λ_stab and λ_margin are fixed once chosen on a small validation split and then held constant across all phases, datasets, and forget-set sizes in the reported experiments. To demonstrate that the observed stability is not an artifact of per-experiment fitting, we will include a full ablation table in the revision that sweeps both coefficients over two orders of magnitude (0.01–10) while keeping all other settings identical. The table will report retain accuracy, forget accuracy, and reversal metrics, showing that performance remains stable for a broad interval around the chosen operating point. revision: yes

Circularity Check

0 steps flagged

No circularity detected in SAFER derivation or claims

full rationale

The paper identifies knowledge erosion and forgetting reversal in repeated unlearning, then proposes SAFER as a framework using representation stability regularizer on retain data and negative logit margin regularizer on forget data. This is presented as an empirical method with experimental validation on CIFAR-10/100 and MNIST under disjoint forget sequences. No equations, self-citations, or derivation steps are shown that reduce the central claims (mitigation of erosion/reversal) to fitted hyperparameters by construction, self-definitional loops, or load-bearing prior author work. The regularizers are introduced as design choices whose strengths are tuned, but the performance claims remain independent empirical results rather than tautological predictions. This is the common case of a self-contained proposal with no circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard supervised learning assumptions plus the unstated premise that representation stability can be maintained via added loss terms without harming utility; no new entities are postulated.

axioms (2)

domain assumption The data distribution remains stationary across unlearning phases
Implicit in continual unlearning setup; if violated the erosion/reversal phenomena may not be comparable.
ad hoc to paper Negative logit margins can be enforced without collapsing the model's decision boundaries on retain classes
Core of the forgetting component; not derived from prior theory.

pith-pipeline@v0.9.0 · 5495 in / 1251 out tokens · 27796 ms · 2026-05-10T03:29:52.260020+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 6 canonical work pages

[1]

An unlearning framework for continual learning.arXiv preprint arXiv:2509.17530, 2025

Sayanta Adhikari, Vishnuprasadh Kumaravelu, and PK Sri- jith. An unlearning framework for continual learning.arXiv preprint arXiv:2509.17530, 2025. 2

work page arXiv 2025
[2]

Optuna: A next-generation hyperparameter optimization framework

Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. Optuna: A next-generation hyperparameter optimization framework. InThe 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 2623–2631, 2019. 1

2019
[3]

Machine unlearning

Lucas Bourtoule, Varun Chandrasekaran, Christopher A Choquette-Choo, Hengrui Jia, Adelin Travers, Baiwu Zhang, David Lie, and Nicolas Papernot. Machine unlearning. In 2021 IEEE symposium on security and privacy (SP), pages 141–159. IEEE, 2021. 1, 2

2021
[4]

Parkhi, and An- drew Zisserman

Qiong Cao, Li Shen, Weidi Xie, Omkar M. Parkhi, and An- drew Zisserman. Vggface2: A dataset for recognising faces across pose and age, 2018. 4

2018
[5]

Towards making systems for- get with machine unlearning

Yinzhi Cao and Junfeng Yang. Towards making systems for- get with machine unlearning. In2015 IEEE symposium on security and privacy, pages 463–480. IEEE, 2015. 2

2015
[6]

Extract- ing training data from large language models

Nicholas Carlini, Florian Tramer, Eric Wallace, Matthew Jagielski, Ariel Herbert-V oss, Katherine Lee, Adam Roberts, Tom Brown, Dawn Song, Ulfar Erlingsson, et al. Extract- ing training data from large language models. In30th USENIX security symposium (USENIX Security 21), pages 2633–2650, 2021. 1

2021
[7]

A unified framework for continual learning and unlearning.arXiv preprint arXiv:2408.11374,

Romit Chatterjee, Vikram Chundawat, Ayush Tarun, Ankur Mali, and Murari Mandal. A unified framework for continual learning and unlearning.arXiv preprint arXiv:2408.11374,

work page arXiv
[8]

Boundary unlearning: Rapid forgetting of deep net- works via shifting the decision boundary

Min Chen, Weizhuo Gao, Gaoyang Liu, Kai Peng, and Chen Wang. Boundary unlearning: Rapid forgetting of deep net- works via shifting the decision boundary. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7766–7775, 2023. 1, 2, 6

2023
[9]

Towards machine unlearn- ing benchmarks: Forgetting the personal identities in facial recognition systems

Dasol Choi and Dongbin Na. Towards machine unlearn- ing benchmarks: Forgetting the personal identities in facial recognition systems. Presented at the AAAI Workshop on Privacy-Preserving Artificial Intelligence (PPAI-24), 2024. 4

2024
[10]

Can bad teaching induce forgetting? unlearning in deep networks using an incompetent teacher

Vikram S Chundawat, Ayush K Tarun, Murari Mandal, and Mohan Kankanhalli. Can bad teaching induce forgetting? unlearning in deep networks using an incompetent teacher. InProceedings of the AAAI Conference on Artificial Intelli- gence, pages 7210–7217, 2023. 2

2023
[11]

A cluster separation measure.IEEE transactions on pattern analysis and machine intelligence, (2):224–227, 2009

David L Davies and Donald W Bouldin. A cluster separation measure.IEEE transactions on pattern analysis and machine intelligence, (2):224–227, 2009. 7

2009
[12]

Imagenet: A large-scale hierarchical image database

Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee, 2009. 1

2009
[13]

An image is worth 16x16 words: Transformers for image recognition at scale

Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl- vain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. InInternational Conference on Learning Representa- tions, 2021. 1, 4

2021
[14]

Salun: Empowering machine unlearn- ing via gradient-based weight saliency in both image classi- fication and generation

Chongyu Fan, Jiancheng Liu, Yihua Zhang, Eric Wong, Den- nis Wei, and Sijia Liu. Salun: Empowering machine unlearn- ing via gradient-based weight saliency in both image classi- fication and generation. InThe Twelfth International Confer- ence on Learning Representations, 2024. 1, 2, 6, 7

2024
[15]

Fast machine unlearning without retraining through selective synaptic dampening

Jack Foster, Stefan Schoepf, and Alexandra Brintrup. Fast machine unlearning without retraining through selective synaptic dampening. InProceedings of the AAAI Confer- ence on Artificial Intelligence, pages 12043–12051, 2024. 1, 2, 6

2024
[16]

Eternal sunshine of the spotless net: Selective forgetting in deep networks

Aditya Golatkar, Alessandro Achille, and Stefano Soatto. Eternal sunshine of the spotless net: Selective forgetting in deep networks. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9304– 9312, 2020. 2, 6

2020
[17]

Amne- siac machine learning

Laura Graves, Vineel Nagisetty, and Vijay Ganesh. Amne- siac machine learning. InProceedings of the AAAI Confer- ence on Artificial Intelligence, pages 11516–11524, 2021. 2

2021
[18]

Gone but not forgotten: Improved benchmarks for machine unlearning.arXiv preprint arXiv:2405.19211,

Keltin Grimes, Collin Abidi, Cole Frank, and Shannon Gal- lagher. Gone but not forgotten: Improved benchmarks for machine unlearning.arXiv preprint arXiv:2405.19211,

work page arXiv
[19]

Deep residual learning for image recognition

Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. InProceed- ings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016. 1, 4

2016
[20]

A unified gradient-based framework for task-agnostic contin- ual learning-unlearning.arXiv preprint arXiv:2505.15178,

Zhehao Huang, Xinwen Cheng, Jie Zhang, Jinghao Zheng, Haoran Wang, Zhengbao He, Tao Li, and Xiaolin Huang. A unified gradient-based framework for task-agnostic contin- ual learning-unlearning.arXiv preprint arXiv:2505.15178,

work page arXiv
[21]

Learning multiple layers of features from tiny images

Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. 4

2009
[22]

Imagenet classification with deep convolutional neural net- works.Advances in neural information processing systems, 25, 2012

Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural net- works.Advances in neural information processing systems, 25, 2012. 1

2012
[23]

Towards unbounded machine unlearn- ing

Meghdad Kurmanji, Peter Triantafillou, Jamie Hayes, and Eleni Triantafillou. Towards unbounded machine unlearn- ing. InThirty-seventh Conference on Neural Information Processing Systems, 2023. 1, 2, 6 9

2023
[24]

Detecting brittle decisions for free: Leveraging margin consistency in deep robust clas- sifiers.Advances in Neural Information Processing Systems, 37:23301–23324, 2024

Jonas Ngnaw ´e, Sabyasachi Sahoo, Yann Pequignot, Fr´ed´eric Precioso, and Christian Gagn ´e. Detecting brittle decisions for free: Leveraging margin consistency in deep robust clas- sifiers.Advances in Neural Information Processing Systems, 37:23301–23324, 2024. 4

2024
[25]

Acu: Analytic continual unlearning for efficient and exact forgetting with privacy preservation

Jianheng Tang, Huiping Zhuang, Di Fang, Jiaxu Li, Feijiang Han, Yajiang Huang, Kejia Fan, Leye Wang, Zhanxing Zhu, Shanghang Zhang, et al. Acu: Analytic continual unlearning for efficient and exact forgetting with privacy preservation. arXiv preprint arXiv:2505.12239, 2025. 2

work page arXiv 2025
[26]

Paul V oigt and Axel Bussche.The EU General Data Protec- tion Regulation (GDPR): A Practical Guide. 2017. 1

2017
[27]

Machine unlearning: challenges in data quality and access

Miao Xu. Machine unlearning: challenges in data quality and access. InProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence (IJCAI-24), 2024. 2

2024
[28]

Toward efficient data-free unlearning

Chenhao Zhang, Shaofei Shen, Weitong Chen, and Miao Xu. Toward efficient data-free unlearning. InProceedings of the AAAI Conference on Artificial Intelligence, pages 22372– 22379, 2025. 7

2025
[29]

Continual for- getting for pre-trained vision models

Hongbo Zhao, Bolin Ni, Junsong Fan, Yuxi Wang, Yuntao Chen, Gaofeng Meng, and Zhaoxiang Zhang. Continual for- getting for pre-trained vision models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 28631–28642, 2024. 2

2024
[30]

Practical continual forgetting for pre- trained vision models.IEEE Transactions on Pattern Analy- sis and Machine Intelligence, 2026

Hongbo Zhao, Fei Zhu, Bolin Ni, Feng Zhu, Gaofeng Meng, and Zhaoxiang Zhang. Practical continual forgetting for pre- trained vision models.IEEE Transactions on Pattern Analy- sis and Machine Intelligence, 2026. 2

2026
[31]

What makes unlearning hard and what to do about it

Kairan Zhao, Meghdad Kurmanji, George-Octavian B˘arbulescu, Eleni Triantafillou, and Peter Triantafillou. What makes unlearning hard and what to do about it. Advances in Neural Information Processing Systems, 37: 12293–12333, 2024. 6 10 Robust Continual Unlearning against Knowledge Erosion and Forgetting Reversal Supplementary Material

2024
[32]

9 drives its unlearning margin toward negative values: U M(x)<0.(15) Thus, forgotten samples remain suboptimal within the decision space

Theoretical Analysis of Unlearning Margin Suppression Proposition 1(Effect of Negative Unlearning Margin).For a non-retain samplexwith original labely, optimizing the KL divergence loss with the random retain-class target distributionqin Eq. 9 drives its unlearning margin toward negative values: U M(x)<0.(15) Thus, forgotten samples remain suboptimal with...
[33]

Implementation Original Models.We trained ResNet-18 on CIFAR-100, ResNet-50 on VGGFace2, and ViT-B/16 on MUFAC from scratch

Experiment Details 9.1. Implementation Original Models.We trained ResNet-18 on CIFAR-100, ResNet-50 on VGGFace2, and ViT-B/16 on MUFAC from scratch. For optimization, we used SGD with a learning rate of 0.1 for CIFAR-100 and VGGFace2, and 0.001 for MUFAC, along with weight decay of 0.0005 and momentum of 0.9. We set the batch size to 128 for CIFAR-100 and...

work page arXiv
[34]

5, we conduct ablation studies to evaluate the impact of each component in SAFER

Additional Analysis Ablation Study.As presented in Tab. 5, we conduct ablation studies to evaluate the impact of each component in SAFER. The ablation results are evaluated under the same conditions described in Sec. 5, and for each phase, the highest ToW score is highlighted in bold. First, when optimizing intra-class compactness (IC), the ToW score grad...