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REVIEW 3 major objections 5 minor 1 cited by

Unified Parameter-Efficient Unlearning for LLMs

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read LLMEraser shows that instance removal, query modification, and response correction for LoRA-finetuned LLMs can each be reduced to a single influence-function-induced adapter edit that tracks retraining within a few percent of performance.

desk verdict A useful influence-function framework for editing LoRA adapters, but the unlearning claim needs direct forgetting tests before it's supported. read the letter →

arxiv 2412.00383 v2 pith:R4ZACYV4 submitted 2024-11-30 cs.AI cs.LG

Chenlu Ding , Jiancan Wu , Yancheng Yuan , Jinda Lu , Kai Zhang , Alex Su , Xiang Wang , Xiangnan He This is my paper · ORCID
classification cs.AIcs.LG
keywords machineunlearninglargelanguagemodelsinfluencefunctionsparameter-efficientfine-tuningLoRAHessian-vectorproductinstance-wisedataprivacy
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

This paper proposes LLMEraser, a framework for unlearning individual training instances from a large language model that was fine-tuned with LoRA adapters. It argues that three kinds of unlearning—deleting an instance, editing its query, or correcting its response—can all be expressed as small parameter adjustments to the adapter, and that influence functions can compute those adjustments directly. On benchmark recommendation and multimodal tasks, the edited adapter performs within 0.0038 AUC of a fully retrained model for instance removal, while running about 31 times faster. If correct, this gives a practical way to honor data-deletion requests without storing and retraining on data shards.

What carries the argument

The mechanism is the influence-function parameter-change formula, Equation 8: $\Delta\Theta_\delta \approx \frac{1}{n}\big(\nabla^2_\Theta R(Z;\hat\Theta)\big)^{-1}\big(G(x,y) - G(x+\delta_x, y+\delta_y)\big)$, which converts an unlearning request into a difference of loss gradients times the inverse Hessian of the empirical risk on the training set. The paper's algorithmic contribution is to avoid forming the inverse Hessian: it solves the equivalent convex quadratic program $F(\Delta)=\frac12 \Delta^\top \nabla^2_\Theta R(Z;\hat\Theta)\Delta - \langle b,\Delta\rangle$ using SGD/Adam with Hessian-vector products, so each iteration costs $O(p)$ instead of $O(p^2)$ or $O(p^3)$.

What would settle it

Train a LoRA adapter on a standard benchmark, stop it before convergence, delete 5% of training instances, and apply LLMEraser; if the edited adapter's AUC on the held-out set differs from full retraining by substantially more than the reported 0.0038 gap (for instance, 0.02 or more), the near-retrain claim fails for non-converged adapters. A direct numerical-rank check of the LoRA Hessian at the adapter weights would also reveal whether the invertibility condition behind Equation 8 actually holds.

Watch

Extended reading notes

Core claim

The paper's central claim is that instance-wise unlearning in LoRA-tuned LLMs reduces to one operation: computing the parameter change $\Delta\Theta$ a retrained model would undergo, and adding it to the existing adapter. For instance removal, the change is $\Delta\Theta_{\mathrm{IR}} \approx \frac{1}{n}\big(\nabla^2_\Theta R(Z;\hat\Theta)\big)^{-1}\sum_{(x,y)\in S_{\mathrm{IR}}} G(x,y)$; query modification and response correction use the same inverse-Hessian-times-gradient form with the gradient of the edited instance subtracted. The paper then converts the expensive inverse-Hessian-vector product into the solution of a convex finite-sum quadratic program, solved with mini-batch Adam and Hessian-vector products, cutting per-step cost from $O(p^2)$ to $O(p)$. On LLM4Rec and MLLM benchmarks, the resulting adapter lands within 0.0038 AUC of full retraining for instance removal, within 0.024 and 0.048 average accuracy on the two response-correction benchmarks, and within 0.0079 HitRatio@1 for query modification, while taking about $1.4\times 10^3$ seconds on a query-modification task where retraining takes $5.4\times 10^4$ seconds.

Load-bearing premise

The method assumes the fine-tuned adapter sits exactly at the optimum of the training loss, with an invertible Hessian, so that a first-order Taylor expansion accurately predicts the retrained weights.

Editorial extensions

If this is right

  • Instance removal, query modification, and response correction can all be handled by one framework without retraining or altering the model architecture.
  • Adapter edits cost $O(p)$ time and space per step, scaling linearly with the number of LoRA parameters.
  • On the reported benchmarks, the unlearned model stays within 0.0038 AUC (instance removal), 0.024 and 0.048 average accuracy (response correction on two MLLM benchmarks), and 0.0079 HitRatio@1 (query modification) of full retraining.
  • Unlearning is roughly 31 times faster than retraining on the query-modification task ($1.4\times 10^3$ seconds versus $5.4\times 10^4$ seconds on a single A100 GPU).

Reading between the lines

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

  • If the influence-function estimate stays accurate for adapters trained to convergence, the framework could extend to other PEFT methods such as prefix tuning or adapters, since the derivation only requires a differentiable loss with respect to trainable parameters.
  • The assumption that the old adapter is at the empirical-risk minimizer suggests the method may degrade for early-stopped or under-converged checkpoints; a testable extension would be to measure the AUC gap as a function of training epochs or LoRA rank.
  • Because the formulas only need gradients at the removed and replacement instances, the framework points toward a lightweight audit trail: a provider could log per-instance gradients during fine-tuning and later answer ‘what would the model look like without this record?’ without keeping the full training data.
  • The unified IR/QM/RC taxonomy could be applied to safety scenarios, such as removing a harmful output while correcting the same query toward a safe response, combining two edit types in one parameter change.
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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

3 major / 5 minor

Summary. The manuscript introduces LLMEraser, an influence-function-based framework for instance-wise unlearning in parameter-efficient fine-tuned large language models (PEFT/LLMs). The approach categorizes unlearning requests into Instance Removal, Query Modification, and Response Correction, and computes adapter parameter updates by solving a finite-sum quadratic program that approximates the inverse Hessian-vector product. The authors evaluate LLMEraser on LLM-based recommendation (TallRec, LLaRA) and multimodal LLM (LLaVA 1.5) tasks, reporting utility metrics (AUC, HitRatio@1, accuracy) and runtime against Retrain, SISA, RecEraser, Gradient Ascent, and E2URec. The reported results show near-retrain utility and 31.25x speedup versus retraining.

Significance. The paper's taxonomy of instance-wise unlearning tasks and its unified influence-function treatment of removal and correction are valuable conceptual contributions. If the forgetting behavior were verified, LLMEraser would be a significant practical tool for privacy-preserving editing of deployed PEFT adapters. The method is mathematically well-grounded in standard influence-function machinery, and the reformulation of the Hessian-vector-product computation as a mini-batch convex optimization problem is a plausible scalability improvement. The authors release code, which aids reproducibility. However, the experimental validation as presented only demonstrates utility preservation and does not directly show that target instances have been forgotten, which weakens the central claim as it stands.

major comments (3)
  1. [§4.2.1, Table 2; §4.2.2, Tables 3–5; §4.3, Figure 3] The experiments measure only utility (AUC, HitRatio@1, accuracy) on retained or corrected test data; there is no direct evaluation of whether the influence of the target instances has been removed. For instance removal, a no-op 'Original' model would also attain near-Retrain utility on the test set, so the small gap between LLMEraser and Retrain (0.0038 AUC in Table 2) does not demonstrate forgetting. The same holds for QM and RC: the reported improvements over the Corrupted baseline show that test utility is restored, but not that the model no longer relies on the specific noisy or outdated tokens. Please add forgetting-specific metrics—e.g., loss or accuracy on the target instances, membership inference, or extraction tests—and report them for each task type. Without such evidence, the central claim of the paper is not supported.
  2. [§3.3, Eq. (12); Appendix D.1] The derivation of the parameter change assumes the old adapter \hat{\Theta} is the exact minimizer of the empirical risk (Eq. 3), so that \nabla R(Z;\hat{\Theta})=0, and that the Hessian \nabla^2 R(Z;\hat{\Theta}) is invertible. These assumptions are unlikely to hold for LoRA adapters trained with early-stopped SGD: the final checkpoint is not a stationary point, and the Hessian of an over-parameterized model is typically singular. The error analysis in Appendix D.1 only bounds the Taylor-expansion residual under these assumptions; it does not quantify the error introduced when the assumptions are violated. Please provide empirical checks (e.g., the gradient norm at the checkpoint, an estimate of the Hessian's smallest eigenvalue, or a small-scale experiment where the Hessian can be computed exactly) or provide a modified error bound that relaxes the assumptions.
  3. [§4.4, Table 6; Appendix C] The runtime comparison reports a single timing per method, without standard deviation or number of runs. The claimed 31.25x speedup is a point estimate, and the runtime of LLMEraser depends on the chosen optimizer hyperparameters and the convergence criterion for solving Eq. (12). Please report the mean and standard deviation of wall-clock time over several runs, state the exact settings (optimizer, learning rate, number of iterations, LoRA rank) used for the timing, and clarify whether the reported time includes data loading, gradient computation, and the optimization loop.
minor comments (5)
  1. [Appendix B, Algorithm 1, lines 6–8] The branches for RC and IM use the wrong sets: line 6 uses S_IM instead of S_RC, and line 7 uses S_RC instead of the query-modification set; please correct these labels.
  2. [§3.2, Eq. (13)] The notation S_IM (or SIM) appears in Eq. (13), but the text and Section 3.2 define the set S_QM for query modification; please align the notation.
  3. [§4.2.1] The phrase 'direct estimation of the parameter changes between the retrained model and the original model' overstates what influence functions compute; the method provides a first-order local approximation to the parameter change, not the actual difference between two separately trained models. Please rephrase.
  4. [Tables 2–5 and Figure 3] All metrics are reported as point estimates without error bars; reporting means and standard deviations over multiple random seeds (and data splits) would make the comparisons statistically meaningful.
  5. [§5, Limitations] The Limitations section acknowledges the need for training set access and gradient information, but it does not mention the absence of direct forgetting verification in the experiments; please add a sentence noting that target-instance loss or membership inference evaluations are needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the parameter-change estimates are derived from the training loss via influence functions, and the comparison to Retrain is an external benchmark, not an input to the method.

full rationale

The derivation chain in Eqs. 8-11 computes adapter parameter changes from the empirical risk (Eq. 3), the old adapter, and the target or corrected instances supplied by the unlearning request; none of the comparison values (Retrain AUC, HitRatio@1, accuracy) enter the computation of the parameter change delta. Equations 12-15 rewrite the inverse-Hessian-vector product as an equivalent finite-sum quadratic program, which is an algebraic reformulation rather than a fit to any benchmark. Appendix D bounds the error of the Taylor and optimization approximations relative to the true parameter change, not relative to the reported evaluation metrics. The only self-citation, Ding et al. (2025), is invoked as "inspired by" for the finite-sum reformulation, and the paper supplies its own derivation and convergence analysis, so the citation is not load-bearing. The absence of a direct forgetting metric (e.g., membership inference on removed instances) is a verification gap rather than circularity: even a degenerate no-op method would be distinguishable here, since LLMEraser's IR result (AUC 0.6319) moves toward Retrain (0.6357) and away from Original (0.6400), and the QM/RC results likewise move from the corrupted baseline toward the retrained model. No step in the paper reduces to its own inputs by construction, and the Limitations section honestly states the assumptions (gradient access, Taylor-expansion error) that are correctness concerns, not circular steps.

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

The method introduces no new entities or forces. It relies on standard influence-function mathematics plus three domain assumptions: optimality of the old adapter, invertible Hessian, and availability of the training data. The main hand-chosen values are the optimizer settings for solving the quadratic program, which are not fully specified.

free parameters (3)
  • Adam learning rate for solving Eq. 12 = not reported precisely
    The optimization of the quadratic program uses Adam with a learning rate delta_lr; the value is not given in the main text, and the quality of the estimated parameter change depends on it.
  • Number of optimization iterations = not reported
    The loop in Algorithm 1 runs until convergence; no tolerance or iteration cap is specified, affecting accuracy and runtime.
  • LoRA rank = 8, 16, 32
    The memory and quality results depend on the rank of the adapter; it is an architecture choice rather than a fitted parameter.
assumptions (4)
  • standard math Taylor expansion of the perturbed risk around the old optimum (Koh and Liang 2017)
    Used to derive Equations 6-8 in Section 3.2.
  • domain assumption The old adapter is the exact empirical risk minimizer of Eq. 3
    Influence-function derivation assumes optimality; SGD-trained adapters are not at the exact optimum.
  • domain assumption The Hessian H_hat is positive definite and invertible
    Assumed in Appendix D.1 to justify the Taylor expansion error bound; likely violated for over-parameterized LoRA.
  • domain assumption The full training set Z is available at unlearning time
    Stated in Section 5 Limitations; the method needs the training data and target gradients.

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Cite this review

Pith. "Pith review of Unified Parameter-Efficient Unlearning for LLMs." pith.science (2026). https://pith.science/paper/R4ZACYV4

@misc{pith2026241200383,
  author       = {Pith},
  title        = {Pith review of: Unified Parameter-Efficient Unlearning for LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R4ZACYV4}},
  note         = {Machine review of arXiv:2412.00383}
}
read the original abstract

The advent of Large Language Models (LLMs) has revolutionized natural language processing, enabling advanced understanding and reasoning capabilities across a variety of tasks. Fine-tuning these models for specific domains, particularly through Parameter-Efficient Fine-Tuning (PEFT) strategies like LoRA, has become a prevalent practice due to its efficiency. However, this raises significant privacy and security concerns, as models may inadvertently retain and disseminate sensitive or undesirable information. To address these issues, we introduce a novel instance-wise unlearning framework, LLMEraser, which systematically categorizes unlearning tasks and applies precise parameter adjustments using influence functions. Unlike traditional unlearning techniques that are often limited in scope and require extensive retraining, LLMEraser is designed to handle a broad spectrum of unlearning tasks without compromising model performance. Extensive experiments on benchmark datasets demonstrate that LLMEraser excels in efficiently managing various unlearning scenarios while maintaining the overall integrity and efficacy of the models.

Figures

Figures reproduced from arXiv: 2412.00383 by the authors.

Figure 1
Figure 1. 1a: A brief description of the different types of LLM unlearning tasks. 1b: The framework of exact LLM unlearning method, approximate unlearning method. tion (LLM4Rec) as well as MLLM relation mining tasks to validate the effectiveness of LLMEraser. Our extensive evaluations across these diverse scenarios demonstrate that LLMEraser consistently outperforms the state-of-the-art unlearning methods. 2 PRELIMINARY This … view at source ↗
Figure 2
Figure 2. The framework of LLMEraser. The old adapter is obtained through PEFT on domain [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. 3a: Experimental results of the instance removal task using TallRec as the LLM4Rec model on the BookCrossing dataset, where 5% and 10% of the training data were randomly deleted. 3b: Experimental results of the query modification task using LLaRA as the LLM4Rec model on the MovieLens dataset, where interactions were randomly removed from 5% and 10% of users. parameter changes. Additional experimental results and rel… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Instance Removal Case Study & Query Modification Case Study. [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]
Figure 5
Figure 5. Figure 5: Response Correction Case Study. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]

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Forward citations

Cited by 1 Pith paper

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.