A hybrid framework for effective and efficient machine unlearning

Haipeng Qu; Jia Xu; Mingxin Li; Ning Wang; Shen Su; Xiaodong Wang; Yizhen Yu; Zhichao Yin; Zhigang Wang

REVIEW 4 major objections 4 minor 29 references

A hybrid framework for effective and efficient machine unlearning

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper proposes a hybrid machine-unlearning strategy that chooses between partial retraining and direct parameter subtraction based on estimated retraining cost, achieving 1.5x-8x faster unlearning than SISA with comparable accuracy.

desk verdict A sensible hybrid unlearning recipe whose 100-request experiments are undermined by stale checkpoints that resurrect previously deleted samples; fixable, but as is it shouldn't be the basis for the headline claims. read the letter →

arxiv 2412.14505 v1 pith:TX2SW4AS submitted 2024-12-19 cs.LG

Mingxin Li , Yizhen Yu , Ning Wang , Zhigang Wang , Xiaodong Wang , Haipeng Qu , Jia Xu , Shen Su

show 1 more author

Zhichao Yin

This is my paper · ORCID

classification cs.LG

keywords machineunlearningexactapproximateSISAdirectparameterupdatehybridstrategyrighttobeforgottenmodelaccuracy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to show that machine unlearning need not choose between exact but expensive retraining and fast but inaccurate parameter subtraction. It proposes a hybrid strategy (HS) that estimates the retraining workload caused by a revocation and, depending on where the revoked sample sits in the training schedule, either retrains the affected slices from a saved checkpoint or subtracts the batch's parameter increment directly. A second strategy (OHS) subtracts the increment at an earlier checkpoint and then retrains a fixed number of slices to recover accuracy. The authors claim this yields 1.5x to 8x faster unlearning than SISA while keeping accuracy close to SISA on Adult, Purchase, Census, and Olympics. If true, service providers could honor many right-to-be-forgotten requests at a fraction of the retraining cost.

What carries the argument

The load-bearing object is the slice threshold $l$, derived from the acceptable retraining overhead $\varphi$ in Eq. (1), together with the saved checkpoint parameters $\theta_i$ and saved batch increments $\Delta_j$. The threshold turns the hybrid into a decision rule: if the revoked sample lies before position $l$, retraining the remainder would exceed the acceptable data-read budget, so the method uses the cheap DPUS subtraction; if it lies at or after $l$, it retrains from the nearest checkpoint. OHS modifies the subtraction path by rewinding to $\theta_{S-l}$, subtracting there, and retraining $l$ slices, which corrects the accumulated error that repeated DPUS calls would otherwise build up.

What would settle it

Run HS and OHS on Adult with $S=10$ while setting $l$ strictly from a pre-specified $\varphi$ (for example, retraining at most 20% of the data is acceptable), without tuning $l$ after seeing unlearning time or accuracy; if the 1.5x-8x speedup over SISA does not appear, or the accuracy gap to SISA exceeds the reported 0.5%, the boundary-selection claim fails.

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Extended reading notes

Core claim

The central claim is that the exact/approximate split in machine unlearning is a false choice: an acceptable-retraining budget can divide the training run into a cheap zone and an expensive zone, and the unlearning procedure can pick per request. Concretely, given S slices, saved checkpoints $\theta_i$, and saved per-batch increments $\Delta_j$, the threshold $l = \lfloor S - m \rfloor$ is computed from the largest $i$ whose cumulative data reads $i \cdot n/S + (i+1) \cdot n/S + \dots + S \cdot n/S$ fit within the tolerable overhead $\varphi$. Revocations in slices $i < l$ take the approximate path—subtract $\Delta_j$ from $\theta_S$ for HS, or subtract from $\theta_{S-l}$ and retrain $l$ slices for OHS—while revocations in $i \geq l$ take the exact path of deleting the sample and retraining from $\theta_{i-1}$. The experiments on four real datasets with MLP classifiers report that HS is 6x to 8x faster than SISA and OHS is 1.5x to 6x faster, with OHS accuracy close to SISA.

Load-bearing premise

The framework assumes the threshold $l$ (equivalently the acceptable retraining overhead $\varphi$) can be fixed in advance and accurately separates cheap from expensive retraining, but the paper never reports the $l$ or $\varphi$ values used, so the claimed speedups may depend on hindsight selection of that threshold.

Editorial extensions

If this is right

A provider can answer a stream of unlearning requests at a fraction of SISA's retraining cost while keeping the delivered model nearly as accurate as an exactly unlearned one.
Models trained with saved checkpoints and batch increments, as in SISA-style pipelines, can be retrofitted with HS or OHS without changing the training architecture or hyperparameters.
OHS provides a concrete accuracy-for-time knob: retraining $l$ slices after subtraction bounds the accuracy loss from repeated approximate unlearning, so the operator can trade a little speed for near-exact accuracy.
Because only the affected slice position matters, the method's benefit grows as the number of slices $S$ increases, since more checkpoints mean shorter retraining spans when the exact path is taken.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the same threshold logic could become adaptive, raising or lowering $l$ as the distribution of incoming revocation requests shifts.
Editorial inference: the paper's timing numbers do not count the memory overhead of storing every batch increment $\Delta_j$; a deployment-level comparison would include that storage cost.
Editorial inference: the subtract-then-retrain correction in OHS is a template that could be applied to influence-function-based certified removal, where the analogous accuracy loss is also corrected by local retraining.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper's core idea is simple and plausible: train on slices, keep checkpoints and per-batch increments, use partial retraining when the deleted sample is in a late slice, and use increment subtraction otherwise. The OHS variant—subtract an increment from an earlier checkpoint and retrain the last slices—is a reasonable way to recover accuracy after subtraction. For a single unlearning request, the algorithms are coherent. The empirical trends across four datasets and several slice counts are internally consistent, and the authors are honest that DPUS degrades accuracy.

The soft spots are serious. The stress-test concern about sequential requests holds up. Algorithms 2 and 3 define unlearning for one request and never update the saved checkpoints or slice contents after a DPUS removal. The experiments run 100 sequential requests. So a later request in a late slice triggers partial retraining from a checkpoint that still contains earlier DPUS-removed samples. Those samples come back. The reported accuracy and MIA results after 100 requests are therefore not measuring what the text claims. This is a load-bearing flaw, not a missing error bar.

The unreported threshold l/phi is a real second problem. Eq. (1) is ambiguous, and no values of l or phi are given for any dataset. The 1.5x–8x speedups are controlled by that unstated choice, so they cannot be independently reproduced. There are also no error bars, no code, and the MIA validation is a hand-wave with no numbers.

The paper would be salvageable: report single-request results or fix the sequential protocol (e.g., update all checkpoints after every request, or restrict sequential requests to slices whose checkpoints are clean), and release code with l/phi values. As it stands, the central empirical claim is not well-defined.

For practitioners who need cheap approximate deletion in tabular MLPs, the single-request idea is worth looking at, but I wouldn't build on the paper's current sequential results. Yes, send it to serious peer review—a good referee could force the fixes—but the current version should not be accepted as is.

Referee Report

4 major / 4 minor

Summary. This paper proposes two hybrid machine-unlearning methods, HS and OHS, that combine SISA-style partial retraining (PRS) with Amnesiac-style direct parameter update (DPUS). A threshold l, supposedly derived from an acceptable retraining overhead φ via Eq. (1), decides per request whether to retrain from a saved checkpoint or subtract a saved parameter increment. OHS subtracts from an intermediate checkpoint and retrains the remaining slices to recover accuracy. Experiments on Adult, Purchase, Census, and Olympics with a two-hidden-layer MLP, varying the number of slices S from 5 to 30, report accuracy and unlearning time over 100 sequential requests and claim 1.5×–8× speedups over SISA with comparable accuracy, plus a qualitative membership-inference validation.

Significance. If substantiated, the framework offers a practical accuracy/efficiency trade-off in unlearning, and OHS's subtract-then-fine-tune idea is a reasonable repair for accumulated DPUS error. The paper's strengths are the simplicity of the hybrid selection rule and the breadth of datasets; however, the central quantitative claims are not yet reproducible or fully supported: the threshold values are not reported, Eq. (1) is inconsistent, the sequential protocol is not well-defined under the given algorithms, and the MIA validation is only qualitative. The claimed speedups are plausible but currently a function of unstated choices.

major comments (4)

[§3.1, Eq. (1)] Equation (1) does not describe a retraining workload: it sums slice indices times n/S rather than the number of affected slices times n/S. Additionally, the definition l=⌊S−m⌋ is inconsistent with the algorithm and the example: for S=4 and m=3 it gives l=1, so Alg. 2 would apply PRS to every slice and DPUS would never be used, whereas Fig. 2 states l=3. The paper never reports the φ or l values used for any dataset or S, so the 1.5×–8× speedup and the accuracy trade-off are controlled by an unstated, hand-chosen threshold. Please correct the workload formula, reconcile l with m, and report l/φ for every experimental configuration.
[§3.1–3.2 and §4.4] The algorithms do not maintain a consistent unlearning state across sequential requests. When Alg. 2 uses DPUS for d1 in an early slice, it updates only θ'S and does not delete d1 from D_i or refresh the saved checkpoints θ_k and increments Δ_j. If a later request d2 falls in a later slice, the PRS branch reloads the original θ_{i−1}, which was trained on data including d1, and retrains to θ'S, thereby reintroducing d1's influence. The same flaw appears in Alg. 3's line 7. Consequently, the 100-request experiments reported in §4.4 are not well-defined under the published algorithms. Please specify how checkpoints, slice membership, and increments are updated after every request, or use a protocol that avoids stale checkpoints.
[§4.4 (MIA)] The membership-inference validation is entirely qualitative. The text says 'through validation, we find that our methods achieve effective unlearning' but reports no attack success rate, AUC, membership advantage, or comparison with SISA/DPUS. Without quantitative MIA results, the claim that revocation data is 'thoroughly erased' is unsupported. Please report attack metrics for all methods and the revoked-data set, ideally with confidence intervals.
[§4.4, Figs. 4–5] All accuracy and timing comparisons are shown as single curves with no error bars, no number of independent runs, and no seeds. In this setting, an accuracy gap of 0.5% (HS vs SISA) or 5% (DPUS vs HS) cannot be assessed without variance information. Please provide means and standard deviations over multiple runs, or at a minimum the number of seeds and a significance test for the main accuracy comparisons.

minor comments (4)

[§2] The phrase 'extract MU' appears to be a typo for 'exact MU'.
[References] Reference entries [18] and [19] are duplicates of the same Koh and Liang paper; please consolidate them.
[Figs. 4–5] The axis label 'Number of slice' should be pluralized to 'Number of slices'.
[§4.4] The shadow-model MIA description omits the number of shadow models, the attack model architecture, and the dataset split used to train the attack model; these details are needed for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the efficiency and accuracy claims are empirical comparisons against SISA and DPUS, not quantities forced by the construction.

full rationale

The paper's contribution is a hybrid (HS) and optimized hybrid (OHS) procedure that selects between partial retraining (PRS) and direct parameter subtraction (DPUS) using a threshold l derived from an accepted retraining overhead phi in Eq. (1). The central claim of 1.5x to 8x efficiency improvement over SISA is an empirical result from measured unlearning times (Fig. 5), not a quantity defined into existence by the algorithms: HS and OHS execute genuine retraining or subtraction operations whose runtime is measured, and SISA is an independent baseline. The unstated l/phi values are an experimental reproducibility and selection-sensitivity concern, but they do not make the derivation circular, because nothing in Alg. 1-3 defines the reported accuracy or time as equal to the input threshold. Self-citations in the reference list ([27], [28], [29]) are background systems and differential-privacy work by the authors and are not load-bearing for the unlearning claim. No step was found where a prediction reduces by construction to a fitted parameter, a self-citation, or the paper's own assumptions.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims rest on two hand-picked hyperparameters, S and l (via phi), both unreported for the reported figures, plus DPUS's increment-subtraction assumption. No new entities are introduced.

free parameters (3)

l (slice threshold) = not reported
Determines whether a revocation is handled by DPUS or PRS in Algorithms 2 and 3; derived from the unspecified phi in Eq. (1), and never disclosed for the four datasets across S=5..30.
phi (acceptable retraining overhead) = not reported
Input to Eq. (1); controls l and therefore the speed-accuracy trade-off, but no value is given in the paper.
S (number of slices) = 5, 10, 15, 20, 25, 30
Experimentally swept; the method's efficiency and accuracy strongly depend on it, but no selection rule is provided.

assumptions (4)

domain assumption Saved batch increment delta_j approximates the contribution of that batch to the final parameters.
Used in Algorithm 2 line 4 and Algorithm 3 line 4; inherited from DPUS/Amnesiac, not re-validated in this paper.
domain assumption Retraining from a saved checkpoint theta_(i-1) after deleting d yields the same model as retraining from scratch on the remaining data.
Exactness of SISA-style partial retraining, invoked in Algorithm 2 line 6 and Algorithm 3 line 7.
domain assumption Computational cost of retraining is proportional to the data read from the revoked slice onward.
Modeled by Eq. (1) in Section 3.1; ignores optimizer iterations and data-dependent costs.
domain assumption A membership-inference attack predicting '0' indicates successful unlearning.
Final paragraph of Section 4.4 treats MIA predictions as ground truth for unlearning effectiveness without reporting quantitative attack results.

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Cite this review

Pith. "Pith review of A hybrid framework for effective and efficient machine unlearning." pith.science (2026). https://pith.science/paper/TX2SW4AS

@misc{pith2026241214505,
  author       = {Pith},
  title        = {Pith review of: A hybrid framework for effective and efficient machine unlearning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TX2SW4AS}},
  note         = {Machine review of arXiv:2412.14505}
}

abstract

Recently machine unlearning (MU) is proposed to remove the imprints of revoked samples from the already trained model parameters, to solve users' privacy concern. Different from the runtime expensive retraining from scratch, there exist two research lines, exact MU and approximate MU with different favorites in terms of accuracy and efficiency. In this paper, we present a novel hybrid strategy on top of them to achieve an overall success. It implements the unlearning operation with an acceptable computation cost, while simultaneously improving the accuracy as much as possible. Specifically, it runs reasonable unlearning techniques by estimating the retraining workloads caused by revocations. If the workload is lightweight, it performs retraining to derive the model parameters consistent with the accurate ones retrained from scratch. Otherwise, it outputs the unlearned model by directly modifying the current parameters, for better efficiency. In particular, to improve the accuracy in the latter case, we propose an optimized version to amend the output model with lightweight runtime penalty. We particularly study the boundary of two approaches in our frameworks to adaptively make the smart selection. Extensive experiments on real datasets validate that our proposals can improve the unlearning efficiency by 1.5$\times$ to 8$\times$ while achieving comparable accuracy.

Figures

Figures reproduced from arXiv: 2412.14505 by the authors.

**Figure 1.** An example of SISA. in approximate unlearning, although it may have some impact on the model performance. After considering the advantages and disadvantages of these two methods, we propose a hybrid strategy and optimized hybrid strategy that aim to fully utilize their advantages. 3 Proposed Methods In this paper, we first propose a novel machine unlearning method called hybrid strategy (HS), to improve the efficien… view at source ↗

**Figure 2.** An example of hybrid strategy. retraining from Di is acceptable), the parameters trained from the previous slice are directly loaded. Subsequently, d is deleted, and the final model parameters θ ′ S are obtained by retraining based on θ(i−1) (Lines 3-6). Finally, the model is updated with the θ ′ S to obtain the model M ′ [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** An example of optimized hybrid strategy from θ3 to obtain θ ′ 3 and then retrain the last slice based on θ ′ 3 to obtain the unlearning model. When the retraining overhead is acceptable, the optimized hybrid strategy behaves the same as the hybrid strategy, directly adopting the PRS. The optimization aims to ensure the usability of the model regardless of the chosen strategy while maintaining unlearning efficiency. … view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The comparison of accuracy among direct parameters update strategy(DPUS), hybrid strategy(HS), partial retraining(SISA) and optimized hybrid strategy(OHS) across the four datasets. increments means that the model loses not only the specific unlearned data’s contributi…

**Figure 5.** Figure 5: The comparison of unlearning time among direct parameters update(DPUS) , partial retraining(SISA), hybrid strategy(HS) and optimized hybrid strategy(OHS) across the four datasets. efficiency gain arises because our methods do not always trigger the retraining of affect…

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Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

State of Califor nia Oﬃce of the Attorney General (2024), https://oag.ca.gov/privacy/ccpa

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Bourtoule, L., Chandrasekaran, V., Choquette-Choo, C.A ., Jia, H., Travers, A., Zhang, B., Lie, D., Papernot, N.: Machine unlearning. In: 20 21 IEEE Symposium on Security and Privacy (SP). pp. 141–159. IEEE (2021)

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In: International Conference on Machine Learning

Brophy, J., Lowd, D.: Machine unlearning for random fores ts. In: International Conference on Machine Learning. pp. 1092–1104. PMLR (2021)

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In: 2015 IEEE symposium on security and privacy

Cao, Y., Yang, J.: Towards making systems forget with mach ine unlearning. In: 2015 IEEE symposium on security and privacy. pp. 463–480. IE EE (2015)

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In : 28th USENIX security symposium (USENIX security 19)

Carlini, N., Liu, C., Erlingsson, Ú., Kos, J., Song, D.: Th e secret sharer: Evaluating and testing unintended memorization in neural networks. In : 28th USENIX security symposium (USENIX security 19). pp. 267–284 (2019)

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In: Proceedings of the 2022 ACM SIGSAC conferen ce on computer and communications security

Chen, M., Zhang, Z., Wang, T., Backes, M., Humbert, M., Zha ng, Y.: Graph unlearning. In: Proceedings of the 2022 ACM SIGSAC conferen ce on computer and communications security. pp. 499–513 (2022)

work page 2022