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REVIEW 4 major objections 5 minor 56 references

Soft Weighted Machine Unlearning

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Replacing binary deletion with optimized continuous weights is the paper's fix for over-unlearning in fairness and robustness tasks, and it reports better target metrics with less utility loss.

desk verdict Soft weighting is a genuine advance for unlearning, but the unvalidated additivity assumption means the headline results rest on a first-order approximation the paper never checks. read the letter →

arxiv 2505.18783 v1 pith:UXKDAJRW submitted 2025-05-24 cs.LG cs.AI

Xinbao Qiao , Ningning Ding , Yushi Cheng , Meng Zhang This is my paper
classification cs.LGcs.AI
keywords machineunlearninginfluencefunctionsfairnessadversarialrobustnessover-unlearningconvexquadraticprogrammingdatareweightingmodelcorrection
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

Machine unlearning for fairness and robustness has been using a binary remove-or-keep rule inherited from privacy, and this paper argues that rule is the cause of "over-unlearning": harmless samples get erased, the most harmful samples mostly stay, and accuracy drops for no benefit. The authors propose a soft-weighted scheme in which every training sample receives a continuous weight, computed by solving a convex quadratic program over per-sample influence estimates on utility, fairness, and robustness. Across five datasets and nine unlearning algorithms, the soft-weighted versions improve the target fairness or robustness metric relative to their hard-weighted counterparts while mitigating the usual utility loss. The broader claim is that soft weighting is a general plug-in upgrade for existing unlearning algorithms, not a new standalone method.

What carries the argument

The load-bearing object is the weighted influence function: for a validation-set metric, $I_{\text{metric}}(z_j; \epsilon_j) = -\epsilon_j I_{\text{metric}}(z_j;-1)$, where $I_{\text{metric}}(z_j;-1)$ approximates the leave-one-out change from dropping sample $z_j$ via a Hessian-inverse gradient product, e.g. $\nabla_\theta f(T;\hat\theta)^\top H^{-1}_{\hat\theta} \nabla_\theta \ell(z_j;\hat\theta)$ for fairness. This identity converts unlearning from a binary decision into a linear-in-$\epsilon$ control problem. The weights come from the convex quadratic program of Eq. (6), whose objective is total metric influence plus an $\ell^2$ penalty, with a lower bound preventing over-correction and a constraint protecting utility, and the paper derives the piecewise analytical solution in Eq. (7). The final model update is the closed-form sum in Eq. (8); Eq. (9) shows the same weights can be reinterpreted as per-sample gradient scaling, which is the mechanism that lets the scheme be dropped into gradient-based unlearning algorithms.

What would settle it

On the Adult dataset, compute the quadratic-program weights from Eq. (6), then retrain the model from scratch on the dataset reweighted by those exact weights and measure the realized change in demographic parity and test loss against the influence-predicted change; if the realized gains are much smaller than predicted or utility drops, the additivity assumption underlying Eqs. (3)-(5) is the point of failure.

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Extended reading notes

Core claim

The paper's central claim is that the hard-weighted (binary) framing of machine unlearning is wrong for non-privacy tasks, and that replacing it with optimized continuous per-sample weights yields better corrections. Concretely, it defines weighted influence functions $I_{\text{metric}}(z_j; \epsilon_j) = -\epsilon_j I_{\text{metric}}(z_j;-1)$ for utility, fairness (demographic parity and equal opportunity), and adversarial robustness, then solves a convex quadratic program that minimizes the targeted influence while capping total correction (to avoid reverse bias) and requiring that the predicted utility change stay non-positive. The resulting weights are applied either in a closed-form parameter update or, equivalently, by scaling gradient-ascent and fine-tuning updates, which is why the scheme ports across gradient-ascent/fine-tuning, influence-function, Fisher, NTK, SCRUB, Bad-T, CF-k, and EU-k unlearning. The empirical claim is that soft-weighted variants outperform hard-weighted ones on the target metric and reduce accuracy decline, sometimes improving both (called "free lunch"), across Adult, Bank, CelebA, Jigsaw, and CIFAR-100.

Load-bearing premise

The scheme assumes that the total effect of reweighting many samples at once equals the sum of the individual leave-one-out influence estimates, an assumption the paper validates only for single-sample removal; if simultaneous reweighting has large interaction effects, the predicted fairness, robustness, and utility gains will not appear on the test set.

Editorial extensions

If this is right

  • Soft-weighted unlearning can be added to most existing unlearning pipelines as a drop-in weighting step, so improved fairness and robustness corrections do not require inventing a new unlearning algorithm.
  • Because the quadratic program explicitly constrains predicted utility, soft-weighted corrections can avoid the accuracy degradation that hard deletion causes; on smaller datasets the experiments show both target metric and accuracy improving together, which the paper calls free lunch cases.
  • The weighting step has negligible overhead (about 0.03% of the unlearning runtime in the reported influence-function experiments), making it practical in settings where repeated deletion-rate searches would be too costly.
  • The leave-one-out counterfactual analysis gives a reusable diagnostic: fairness and robustness impact are nearly uncorrelated with utility impact, which explains over-unlearning and gives future methods a way to identify which samples to reweight rather than delete.

Reading between the lines

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

  • The same continuous-reweighting recipe could apply beyond fairness and robustness to any post-hoc model correction, such as removing poisoned or outdated data, so the paper's central mechanism is a general template for influence-based editing rather than a task-specific fix.
  • The diagnosis that borderline samples flip into opposite bias suggests that a fixed deletion rate is an artifact of binary unlearning; under soft weighting, the meaningful quantity would be the total allowed influence shift, which the quadratic program already caps. The paper does not pursue this reframing.
  • A concrete untested extension is large-language-model unlearning: the paper states that its framework was not evaluated on LLMs, and since gradient-ascent LLM unlearning suffers from utility collapse, applying the same soft weights to the ascent steps is a natural experiment that would test the framework's generality.
  • Because the utility constraint only bounds predicted influence, a stress test outside the paper would be to check whether the realized utility constraint holds when soft weights are applied through multi-step gradient updates rather than the closed-form Newton step; the paper's Eq. (9) suggests it should, but interactions could break it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper proposes soft-weighted machine unlearning: rather than binarizing each sample into "forget" (remove) or "keep", it assigns a continuous weight to every training sample. The weights are obtained by solving a convex quadratic program (Eq. 6) whose objective and constraints are built from influence-function estimates of fairness/robustness and utility changes. The resulting weights are applied either through a closed-form influence-based model update (Eq. 8) or through weighted versions of gradient ascent/fine-tuning and other unlearning algorithms (Appendix A.3). The paper identifies three causes of over-unlearning, reports explanatory experiments validating single-sample influence estimates, and presents comparisons of hard- versus soft-weighted versions of nine unlearning algorithms on fairness and robustness tasks.

Significance. The idea of replacing hard removal with a soft, optimization-driven weighting is timely and, if validated, would be a useful plug-in for existing unlearning methods. Strengths include an explicit and checkable KKT derivation of the four-case QP solution, an honest limitation statement, and broad empirical coverage (five datasets, nine algorithms, LR/NN/ResNet models). The main weaknesses are that the central linear-superposition assumption of the influence estimates is not validated for simultaneous non-infinitesimal weights, and the experimental evidence is not fully reproducible. These are fixable within the scope of a revision, so the contribution is conditionally significant.

major comments (4)
  1. [§4.2–§4.3, Eqs. (6)–(8)] The optimization and update assume that the total effect of a weight vector ϵ is the sum of per-sample first-order influence terms, I_metric(z_i; ϵ_i) = −ϵ_i I_metric(z_i; −1), and Eq. (8) updates θ by −(1/n) Σ_i ϵ_i H^{-1}∇ℓ(z_i; θ). This linear-superposition assumption ignores Hessian changes and interactions among simultaneously reweighted samples. It is validated only for single-sample removal (ϵ_i = −1) in Fig. 3 and Appendix Fig. 9, while the optimized weights are not small: Fig. 4 shows weights spanning roughly −1 to 1, and Case 2 of Eq. (7) yields a λ-independent solution. The paper reports no check of predicted versus actual total change under the optimized ϵ, so the utility-preservation constraint (6c) and the target-objective gain (6a) may not hold for the actually updated model. Please add a direct validation: apply Eq. (8) with optimized weights on a validation split, measure the actual changes in utility/fairness/robustness, and compare them with the values predicted by Eq. (6), reporting correlation and constraint-satisfaction rates.
  2. [§4.4 and Appendix A.3, Eq. (29)] The soft-weighted gradient update has a sign error relative to the stated hard-weighted special cases. Eq. (29) writes θ_{t+1} = θ_t + ϵ_j η_t ∇ℓ(z_j; θ_t). For fine-tuning, §4.4 sets ϵ_r = 1, which would give θ + η∇ℓ (gradient ascent on the remaining set), but Eq. (28) correctly defines FT as θ − η∇ℓ. For gradient ascent, §4.4 sets ϵ_f = −1, which would give θ − η∇ℓ, the opposite of Eq. (27). Either the sign in Eq. (29) or the mapping in §4.4 is inconsistent; please correct and state the exact update used for SW-GAFT, SW-CF-k, and SW-EU-k. A related omission appears in Eq. (37), where the max-step for soft-weighted SCRUB does not contain ϵ_f, so the stated objective in Eq. (35) is not implemented by the update.
  3. [§5 and Appendix B] The values of the key hyperparameters are not reported: λ in Eq. (6) (it enters Cases 1 and 3 of the solution in Eq. (7)), γ in the robustness perturbation definition in §3, and σ (or the learning-rate schedule η_t) in Eq. (9). Without these values the reported numbers cannot be reproduced, and the claim of negligible overhead cannot be verified. Please report the chosen values, the tuning procedure, and a sensitivity analysis for λ and γ.
  4. [§5.2, Fig. 5; Appendix B.3.3] The main comparisons are single-run plots without error bars or seed counts, and no code is provided. The hard-weighted baseline procedure is described inconsistently: §5.2 says 'iteratively removing the most harmful samples until no further improvement is observed in fairness,' while Appendix B.3.3 says the hard-weighted framework 'consistently removes 20% of the training samples.' The claim of significant improvement needs a defined baseline protocol and variance estimates. Please report means and standard deviations over multiple seeds, specify the exact deletion/stopping rule, and release code or a detailed protocol.
minor comments (5)
  1. [Eq. (7), Condition 2] Condition 2 in Eq. (7) appears to be missing an operator; it should read |I_metric|^2 − 2λΔ ≥ 0, matching the condition in Appendix A.2.
  2. [Eqs. (3)–(5) and §5] The symbol T is used for both the validation set (Eqs. 3–5) and the test set (Section 5); please introduce distinct notation, such as T_val and T_test, to remove ambiguity.
  3. [Figure 1] Figure 1 reports Spearman correlations of −0.11 and −0.16 without confidence intervals or p-values; please report effect sizes and uncertainty, especially given the large sample size.
  4. [References] References [2] and [17] are the same paper, as are [21] and [22]; please consolidate them into single entries.
  5. [Limitation and Societal Impacts] The appended limitation statement is helpful, but it should also mention the missing hyperparameter values and the unavailability of code, in addition to the already noted gap for LLM unlearning.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the soft-weighted scheme is optimized on validation-set influence estimates and evaluated on a held-out test set; the central claim does not reduce to its inputs.

full rationale

The paper's derivation chain is not circular. The weights in Eq. (6) are obtained by solving a convex quadratic program whose objective and constraints are built from leave-one-out influence estimates computed on a validation set, and the reported fairness, robustness, and utility numbers in Figures 5, 10, and 11 are measured on a held-out test set after the weighted update. No equation in the paper defines the reported test metrics in terms of the optimized weight vector by construction: Eq. (8) is an influence-function approximation of the parameter change, and the actual post-unlearning metrics are computed from the updated model, not from the QP objective. The only self-citation is reference [37], cited in a footnote as one of three practical strategies for non-convex models; it does not carry the central claim and is not load-bearing. The main correctness risk is that the QP assumes first-order additivity of per-sample influence estimates and validates this only for single-sample leave-one-out removal, so the predicted gains could fail under simultaneously applied non-infinitesimal weights; this is an approximation-risk concern, not circularity.

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

The central method needs the standard machinery of influence functions and convex optimization, plus domain assumptions about additivity and validation-to-test transfer. The main unstated free parameters are lambda, gamma, and the Hessian damping sigma, none of which are reported with values or selection rules.

free parameters (3)
  • lambda = not reported
    Regularization coefficient in Eq. (6a); determines weight magnitudes but no value or selection method is given.
  • gamma = not reported
    Adversarial perturbation size in Section 3; only stated as gamma > 1, not tied to attack success or dataset.
  • sigma = not reported
    Damping constant for Hessian approximation in Section 4.3 when updating non-convex models with Eq. (9).
assumptions (4)
  • domain assumption Empirical risk is twice-differentiable and strictly convex for Eq. (2).
    Required for the influence function derivation; authors note non-convex models use surrogates or damping.
  • domain assumption Total effect of reweighting many samples equals the sum of individual leave-one-out influence estimates.
    Used to formulate the QP objective and constraints in Eq. (6); only single-sample removal is validated in Figure 3.
  • domain assumption Validation set is representative of the test set.
    Weights are optimized on validation-set influences but reported on test-set metrics.
  • standard math KKT conditions and strong duality hold for the convex quadratic program.
    The analytical solution in the appendix uses Lagrange multipliers and active-set cases.

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Cite this review

Pith. "Pith review of Soft Weighted Machine Unlearning." pith.science (2026). https://pith.science/paper/UXKDAJRW

@misc{pith2026250518783,
  author       = {Pith},
  title        = {Pith review of: Soft Weighted Machine Unlearning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXKDAJRW}},
  note         = {Machine review of arXiv:2505.18783}
}
read the original abstract

Machine unlearning, as a post-hoc processing technique, has gained widespread adoption in addressing challenges like bias mitigation and robustness enhancement, colloquially, machine unlearning for fairness and robustness. However, existing non-privacy unlearning-based solutions persist in using binary data removal framework designed for privacy-driven motivation, leading to significant information loss, a phenomenon known as over-unlearning. While over-unlearning has been largely described in many studies as primarily causing utility degradation, we investigate its fundamental causes and provide deeper insights in this work through counterfactual leave-one-out analysis. In this paper, we introduce a weighted influence function that assigns tailored weights to each sample by solving a convex quadratic programming problem analytically. Building on this, we propose a soft-weighted framework enabling fine-grained model adjustments to address the over-unlearning challenge. We demonstrate that the proposed soft-weighted scheme is versatile and can be seamlessly integrated into most existing unlearning algorithms. Extensive experiments show that in fairness- and robustness-driven tasks, the soft-weighted scheme significantly outperforms hard-weighted schemes in fairness/robustness metrics and alleviates the decline in utility metric, thereby enhancing machine unlearning algorithm as an effective correction solution.

Figures

Figures reproduced from arXiv: 2505.18783 by the authors.

Figure 1
Figure 1. Actual Changes in Utility and Fair￾ness/Robustness on Adult dataset for each sample’s leave-one-out model. The X-axis represents the sample indices. The Y-axis for Fairness (Robustness) displays changes in demographic parity (adversarial loss) on the test set, with negative values indicating im￾proved fairness (robustness) and positive values indicating reduced fairness (robustness). The Y-axis for Utility shows cha… view at source ↗
Figure 3
Figure 3. Actual Changes vs. Approximate Changes. We evaluated the leave-one-out influence for all samples, with the First Row for LR and Second Row for the last layer of NN, on different performance metrics as follows: (Left) Model utility (loss on test set), (Middle) fairness (DP loss on test set), (Right) robustness (loss on adversarial sample). Q1: How accurate is the influence evaluation in Step 1? Note that while the va… view at source ↗
Figure 4
Figure 4. Hard Weighted Scheme vs. Soft Weighted Scheme. We use IF as the unlearning method to update model. The First Row for Fairness compares the hard- and soft-weighted schemes: A compares the weighting schemes with corresponding fairness influence values, B presents fairness and utility before and after applying hard-weighted IF, and C shows the same for soft-weighted IF. The Second Row for Robustness follows a similar s… view at source ↗
Figures from the paper (10 more)
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Time cost in each step. We use IF as the unlearning method to up￾date the model. Step 1 (evaluation) and Step 3 (removal) are common to both hard and soft weighting. Therefore, soft weighting requires only minimal addi￾tional time in Step 2. First, [PITH_FULL_IMAGE:fi…
Figure 7
Figure 7. Figure 7: Effect of the proportion of forgetting samples removed on fairness and robustness under the [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: Utility Changes vs. Fairness/Robustness Changes. We evaluated the impact of all training data on different performance metrics as follows: (Left) The model’s generalization ability, evaluated as the loss on the test dataset. (Right) The model’s robustness, evaluated as…
Figure 9
Figure 9. Figure 9: Actual EOP Change vs. Influence EOP Change. The leave-one-out influence of all training [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]
Figure 12
Figure 12. Figure 12: Actual Changes in Utility and Fairness/Robustness on Bank dataset for each sample’s leave-one-out model. The X-axis represents the sample indices. The Y-axis for Fairness (Robust￾ness) displays changes in demographic parity (adversarial loss) on the test set, with neg…
Figure 13
Figure 13. Figure 13: Actual Changes in Utility and Fairness/Robustness on Jigsaw dataset for each sample’s leave-one-out model. The X-axis represents the sample indices. The Y-axis for Fairness (Robustness) displays changes in demographic parity (adversarial loss) on the test set, with ne…
Figure 14
Figure 14. Figure 14: Actual Changes in Utility and Fairness/Robustness on CelebA dataset for each sample’s leave-one-out model. The X-axis represents the sample indices. The Y-axis for Fairness (Robustness) displays changes in demographic parity (adversarial loss) on the test set, with ne…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.