arxiv: 2602.23798 · v2 · pith:XAFXD6OCnew · submitted 2026-02-27 · 💻 cs.LG · cs.AI· cs.CR· cs.DC

MPU: Towards Secure and Privacy-Preserving Knowledge Unlearning for Large Language Models

Tiantong Wang , Xinyu Yan , Tiantong Wu , Yurong Hao , Pengjun Xie , Wei Yang Bryan Lim This is my paper

Pith reviewed 2026-05-15 18:45 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CRcs.DC

keywords machine unlearninglarge language modelsprivacy preservingmodel perturbationknowledge unlearningdata deletionfederated unlearning

0 comments p. Extension

Add this Pith Number to your LaTeX paper

What is a Pith Number?

\usepackage{pith}
\pithnumber{XAFXD6OC}

Prints a linked pith:XAFXD6OC badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more

The pith

MPU lets clients unlearn LLM knowledge without exposing the forget set or the original model parameters.

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

The paper proposes MPU, a framework for secure and privacy-preserving knowledge unlearning in large language models under strict constraints that prevent sharing model parameters or the forget set. It generates multiple perturbed model copies on the server for the client to unlearn locally, then aggregates updates on the server using harmonic denoising to reduce noise impact. Experiments with seven algorithms demonstrate that performance degradation stays mostly below 1% even with up to 10% noise, sometimes outperforming the clean baseline at low noise levels. This approach resolves the privacy dilemma in unlearning by maintaining utility close to standard methods.

Core claim

MPU introduces an algorithm-agnostic privacy-preserving framework using Pre-Process for randomized perturbed copy generation and Post-Process for reparameterization inversion and harmonic denoising aggregation, achieving unlearning performance comparable to noise-free baselines with most algorithms showing average degradation well below 1% up to 10% noise.

What carries the argument

Multiple Perturbed Copies Unlearning, which distributes reparameterized perturbed models for local unlearning and aggregates updates via harmonic denoising to counteract perturbation effects.

If this is right

Unlearning becomes feasible in settings requiring dual non-disclosure of parameters and forget sets.
The framework works with existing unlearning algorithms without changes.
Performance remains close to standard methods across noise levels up to 10%.
Both server and client maintain privacy during the unlearning process.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This method could enable regulatory-compliant data removal in deployed LLM services without full retraining.
It may extend to other privacy-sensitive machine learning tasks involving distributed parties.
Further analysis under stronger adversarial models could test the robustness of the perturbation scheme.

Load-bearing premise

The harmonic denoising in Post-Process removes perturbation effects without introducing new biases or vulnerabilities not captured in the reported experiments.

What would settle it

Demonstrating that an adversary can recover significant information about the original model or forget set from the distributed perturbed copies would disprove the privacy preservation.

Figures

Figures reproduced from arXiv: 2602.23798 by Pengjun Xie, Tiantong Wang, Tiantong Wu, Wei Yang Bryan Lim, Xinyu Yan, Yurong Hao.

**Figure 1.** Figure 1: Overview of the proposed MPU framework across communication rounds. The server generates perturbed, reparameterized model copies from θr − 1, clients unlearn on Df , and the server inverts the reparameterization and aggregates updates to obtain θr. Connection to Differential Privacy In standard noiseinjection privacy mechanisms such as Differential Privacy (DP) (Mironov, 2017), one typically specifies a p… view at source ↗

**Figure 2.** Figure 2: Performance comparison of different unlearning algorithms using the Llama-3.2-1B model. Results are reported under three settings: Clean, a noise-free baseline; Noised, a single-copy noise baseline with the same noise magnitude but without denoising; and MPU, using m=2 copies with noise level κ=0.01. Higher values indicate better performance for Forget QA Probability and ROUGE. et al., 2023), NPO (Zhang et… view at source ↗

**Figure 3.** Figure 3: Prompt template for Llama-3.2 series. Prompt: Qwen Series Template System Prompt: You are a helpful assistant. System Prompt with Special Tokens: <|im start|>system\nYou are a helpful assistant.<|im end|>\n User Start Tag: <|im start|>user\n User End Tag: <|im end|>\n Asst Start Tag: <|im start|>assistant\n Asst End Tag: <|im end|>\n [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗

**Figure 4.** Figure 4: Prompt template for Qwen2.5 series. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_4.png] view at source ↗

read the original abstract

Machine unlearning for large language models often faces a privacy dilemma in which strict constraints prohibit sharing either the server's parameters or the client's forget set. To address this dual non-disclosure constraint, we propose MPU, an algorithm-agnostic privacy-preserving Multiple Perturbed Copies Unlearning framework that primarily introduces two server-side modules: Pre-Process for randomized copy generation and Post-Process for update aggregation. In Pre-Process, the server distributes multiple perturbed and reparameterized model instances, allowing the client to execute unlearning locally on its private forget set without accessing the server's exact original parameters. After local unlearning, the server performs Post-Process by inverting the reparameterization and aggregating updates with a harmonic denoising procedure to alleviate the impact of perturbation. Experiments with seven unlearning algorithms show that MPU achieves comparable unlearning performance to noise-free baselines, with most algorithms' average degradation well below 1% up to 10% noise, and can even outperform the noise-free baseline for some algorithms under 1% noise. Code is available at https://github.com/Tristan0318/MPU.

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

MPU gives a practical server-side pipeline for private unlearning on LLMs using perturbed copies and harmonic denoising, but the aggregation step's reliability on non-linear updates is the main open question.

read the letter

MPU lets a client run unlearning on its private forget set without ever seeing the server's real parameters, and without the server seeing the forget data, by shipping multiple perturbed and reparameterized copies then cleaning up the returned updates on the server side with a harmonic denoising step in Post-Process. Pre-Process handles the randomized copy generation. The whole thing is built to sit on top of any existing unlearning algorithm rather than replace it. They ran it across seven algorithms and report that average degradation stays below 1% even at 10% noise, with some cases where the noisy version beats the clean baseline at 1% noise. The code release is a clear plus for anyone who wants to test or extend it. This directly targets the real constraint in deployed LLM services where both model weights and user deletion requests have to stay private. The framework itself is straightforward and the reported numbers suggest it can deliver usable performance without full retraining. The soft spot sits in Post-Process. The harmonic denoising treats the perturbations as something that can be inverted and averaged away, but LLM unlearning updates are context-dependent and non-linear, so residual bias or incomplete removal of forget-set effects could remain. The abstract gives no ablations that isolate the denoising operator, no head-to-head with other robust aggregators, and no stronger attack evaluations or statistical tests on the degradation figures. That leaves the central performance claim plausible but not yet tightly supported. This paper is for people building or evaluating privacy tools for large models in production settings. A reader who needs a concrete way to combine perturbation with unlearning will get a usable starting point from the pipeline and the numbers. It has enough experimental grounding and a clear practical angle to deserve a serious referee, even though the experiments will need more depth on the aggregation step.

Referee Report

2 major / 1 minor

Summary. The paper proposes MPU, an algorithm-agnostic framework for privacy-preserving knowledge unlearning in LLMs under dual non-disclosure constraints. It introduces server-side Pre-Process to generate and distribute multiple perturbed and reparameterized model copies, allowing clients to perform local unlearning on private forget sets, followed by Post-Process inversion and harmonic denoising aggregation of updates. Experiments across seven unlearning algorithms report that MPU achieves comparable performance to noise-free baselines, with most algorithms showing average degradation well below 1% for noise levels up to 10% and occasional outperformance at 1% noise.

Significance. If the Post-Process harmonic denoising reliably recovers unlearning performance without residual bias or new vulnerabilities, MPU offers a practical solution to the privacy dilemma in LLM unlearning. The algorithm-agnostic design and public code release at https://github.com/Tristan0318/MPU are notable strengths that could facilitate adoption in secure distributed settings.

major comments (2)

[Post-Process] Post-Process section: the central claim of degradation below 1% up to 10% noise (and occasional outperformance at 1% noise) rests on the harmonic denoising procedure inverting reparameterized perturbations. This implicitly assumes additive, linearly invertible noise, yet LLM unlearning gradients are highly non-linear and context-dependent; no ablation isolating the denoising operator, no comparison to alternatives such as median or trimmed-mean aggregation, and no formal residual-error bound are provided.
[Experiments] Experiments section: the reported performance numbers lack error bars, details on statistical significance testing, exact noise distributions, or evaluation under stronger adversarial attacks that would expose potential forget-set leakage after denoising. These omissions directly affect confidence in the comparability claim versus noise-free baselines.

minor comments (1)

[Abstract] The abstract and experiments description would benefit from explicit notation for the reparameterization function and the precise form of the harmonic denoising operator.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make to improve clarity, rigor, and completeness.

read point-by-point responses

Referee: [Post-Process] Post-Process section: the central claim of degradation below 1% up to 10% noise (and occasional outperformance at 1% noise) rests on the harmonic denoising procedure inverting reparameterized perturbations. This implicitly assumes additive, linearly invertible noise, yet LLM unlearning gradients are highly non-linear and context-dependent; no ablation isolating the denoising operator, no comparison to alternatives such as median or trimmed-mean aggregation, and no formal residual-error bound are provided.

Authors: We thank the referee for this observation. The reparameterization step is constructed to permit exact inversion of the added perturbations before aggregation, and the harmonic denoising is applied to the inverted updates to reduce variance. We acknowledge that unlearning gradients are non-linear and that no formal residual-error bound is derived. In the revised manuscript we will add an ablation isolating the denoising operator and direct comparisons against median and trimmed-mean aggregation. We will also expand the discussion to clarify the invertibility assumptions and note that a tight theoretical bound for arbitrary non-linear unlearning updates lies beyond the present scope; the empirical results across seven algorithms nevertheless demonstrate consistent recovery of unlearning performance. revision: partial
Referee: [Experiments] Experiments section: the reported performance numbers lack error bars, details on statistical significance testing, exact noise distributions, or evaluation under stronger adversarial attacks that would expose potential forget-set leakage after denoising. These omissions directly affect confidence in the comparability claim versus noise-free baselines.

Authors: We agree that these details strengthen reproducibility and confidence. The revised Experiments section will report means with standard deviations computed over multiple independent runs, include results of paired statistical significance tests against the noise-free baselines, and explicitly state the noise distribution (zero-mean Gaussian scaled to the reported percentage of model parameter magnitude). We will also add a paragraph discussing potential leakage risks under stronger adversarial attacks and, space permitting, include preliminary results; otherwise we will list this evaluation as an important direction for future work. revision: partial

standing simulated objections not resolved

Deriving a formal residual-error bound for harmonic denoising under non-linear, context-dependent unlearning gradients
Full evaluation under stronger adversarial attacks targeting post-denoising forget-set leakage

Circularity Check

0 steps flagged

No significant circularity: MPU is a procedural framework validated by direct experiments

full rationale

The paper defines MPU as an algorithm-agnostic framework with explicit Pre-Process (randomized perturbed copy generation) and Post-Process (reparameterization inversion plus harmonic denoising) modules. All performance claims, including degradation below 1% up to 10% noise and occasional outperformance at 1% noise, are obtained from empirical runs on seven unlearning algorithms rather than any equation or parameter fit that reduces to the input data by construction. No self-definitional steps, fitted inputs renamed as predictions, load-bearing self-citations, or ansatzes smuggled via prior work appear in the derivation chain; the framework is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard ML assumptions about perturbation not destroying learnable structure and on the empirical effectiveness of the denoising step; no new physical entities or ad-hoc constants are introduced beyond the noise level hyperparameter.

free parameters (1)

noise level
Perturbation magnitude (tested up to 10%) chosen to balance privacy and utility; appears fitted or swept in experiments.

axioms (1)

domain assumption Perturbed model copies remain sufficiently close to the original for unlearning algorithms to transfer effectively after aggregation.
Invoked in the Pre-Process and Post-Process description to justify why local unlearning on perturbed copies produces usable updates.

pith-pipeline@v0.9.0 · 5516 in / 1341 out tokens · 20457 ms · 2026-05-15T18:45:17.308762+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

harmonic aggregation ... Pm α_k^{-1} bΔ(k,r) / Pm α_k^{-1} ... first-order error term introduced by noise ... zero-sum constraint

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · 3 internal anchors

[1]

On the properties of neural machine translation: Encoder -- decoder approaches

Association for Computa- tional Linguistics. doi: 10.3115/v1/W14-4012. URL https://aclanthology.org/W14-4012/. Dong, Y . R., Lin, H., Belkin, M., Huerta, R., and Vuli´c, I. Undial: Self-distillation with adjusted logits for robust unlearning in large language models. InProceedings of the 2025 Conference of the Nations of the Americas Chapter of the Associ...

work page doi:10.3115/v1/w14-4012 2025
[2]

C., Kolter, J

Dorna, V ., Mekala, A., Zhao, W., McCallum, A., Lipton, Z. C., Kolter, J. Z., and Maini, P. OpenUnlearning: Ac- celerating LLM unlearning via unified benchmarking of methods and metrics.arXiv preprint arXiv:2506.12618,

work page arXiv
[3]

Simplicity prevails: Rethinking negative preference optimization for llm unlearning

Fan, C., Liu, J., Lin, L., Jia, J., Zhang, R., Mei, S., and Liu, S. Simplicity prevails: Rethinking negative pref- erence optimization for llm unlearning.arXiv preprint arXiv:2410.07163,

work page arXiv
[4]

The Llama 3 Herd of Models

Grattafiori, A., Dubey, A., Jauhri, A., Pandey, A., Kadian, A., Al-Dahle, A., Letman, A., Mathur, A., Schelten, A., Vaughan, A., et al. The llama 3 herd of models.arXiv preprint arXiv:2407.21783,

work page internal anchor Pith review Pith/arXiv arXiv
[5]

Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate

Jin, X., Bu, Z., Vinzamuri, B., Ramakrishna, A., Chang, K.- W., Cevher, V ., and Hong, M. Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate. InProceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies ...

work page 2025
[6]

arXiv preprint arXiv:2012.13891 , year=

Liu, B., Liu, Q., and Stone, P. Continual learning and private unlearning. InConference on Lifelong Learning Agents, pp. 243–254. PMLR, 2022a. Liu, G., Ma, X., Yang, Y ., Wang, C., and Liu, J. Federated unlearning.arXiv preprint arXiv:2012.13891,

work page arXiv 2012
[7]

TOFU: A Task of Fictitious Unlearning for LLMs

Liu, Y ., Xu, L., Yuan, X., Wang, C., and Li, B. The right to be forgotten in federated learning: An efficient realization with rapid retraining. InIEEE INFOCOM 2022-IEEE conference on computer communications, pp. 1749–1758. IEEE, 2022b. Maini, P., Feng, Z., Schwarzschild, A., Lipton, Z. C., and Kolter, J. Z. Tofu: A task of fictitious unlearning for llms...

work page internal anchor Pith review arXiv 2022
[8]

Multi-objective large language model unlearning

Pan, Z., Zhang, S., Zheng, Y ., Li, C., Cheng, Y ., and Zhao, J. Multi-objective large language model unlearning. In ICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1–5. IEEE,

work page 2025
[9]

A survey on unlearning in large language models.arXiv preprint arXiv:2510.25117,

Qiu, R., Tan, J., Pu, J., Wang, H., Gao, X.-S., and Sun, F. A survey on unlearning in large language models.arXiv preprint arXiv:2510.25117,

work page arXiv
[10]

arXiv preprint arXiv:2502.07218

Shen, W. F., Qiu, X., Kurmanji, M., Iacob, A., Sani, L., Chen, Y ., Cancedda, N., and Lane, N. D. Lunar: Llm un- learning via neural activation redirection.arXiv preprint arXiv:2502.07218,

work page arXiv
[11]

Balancing forget quality and model utility: A reverse kl-divergence knowledge distillation approach for better unlearning in llms

Wang, B., Zi, Y ., Sun, Y ., Zhao, Y ., and Qin, B. Balancing forget quality and model utility: A reverse kl-divergence knowledge distillation approach for better unlearning in llms. InProceedings of the 2025 Conference of the Na- tions of the Americas Chapter of the Association for Com- putational Linguistics: Human Language Technologies (Volume 1: Long ...

work page 2025
[12]

Y ., Pang, J., Liu, Q., Shah, A

Wang, Y ., Wei, J., Liu, C. Y ., Pang, J., Liu, Q., Shah, A. P., Bao, Y ., Liu, Y ., and Wei, W. LLM unlearning via loss adjustment with only forget data.arXiv preprint arXiv:2410.11143,

work page arXiv
[13]

Exploring criteria of loss reweighting to enhance llm unlearning,

Yang, P., Wang, Q., Huang, Z., Liu, T., Zhang, C., and Han, B. Exploring criteria of loss reweighting to enhance llm unlearning.arXiv preprint arXiv:2505.11953,

work page arXiv
[14]

Zhang, F., Yan, X., Wu, T., Li, W., Chen, T., Cao, Y ., Yan, R., Huang, L., Lim, W. Y . B., and Yang, Q. Oblivio- nis: A lightweight learning and unlearning framework for federated large language models.arXiv preprint arXiv:2508.08875,

work page arXiv
[15]

Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning

Zhang, R., Lin, L., Bai, Y ., and Mei, S. Negative preference optimization: From catastrophic collapse to effective un- learning.arXiv preprint arXiv:2404.05868,

work page internal anchor Pith review arXiv
[16]

noise-only

Zhou, Y ., Song, L., Wang, B., and Chen, W. Metagpt: Merging large language models using model exclusive task arithmetic.arXiv preprint arXiv:2406.11385, 2024a. 10 MPU: Towards Secure and Privacy-Preserving Knowledge Unlearning for Large Language Models Zhou, Z., Chen, Z., Chen, Y ., Zhang, B., and Yan, J. On the emergence of cross-task linearity in the p...

work page arXiv
[17]

Under the same local linearization used in Sec

Linear Response ModelFix an anchor point θ (e.g., θ=θ r−1) and write the perturbation as u. Under the same local linearization used in Sec. 3.4, ∆(θ+u) = ∆ ⋆(θ) +J u+ρ(u),∥ρ(u)∥ ≤ LJ 2 ∥u∥2.(71) A.5.1. ONE-ROUNDCOMPARISON: BIAS ANDVARIANCE FROMINJECTEDNOISE Noise-Only Baseline ErrorSubstituting the linear response into Eq. (70) yields θNO r =θ+η srv ∆⋆(θ)...

work page 2024
[18]

Prompt: Llama-3.2 Series Template System Prompt: You are a helpful assistant. System Prompt with Special Tokens:<|begin of text|><|start header id|> system<|end header id|>\n\nYou are a helpful assistant.<|eot id|> User Start Tag:<|start header id|>user<|end header id|>\n\n User End Tag:<|eot id|> Asst Start Tag:<|start header id|>assistant<|end header id...

work page arXiv 2025