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arxiv: 2607.02513 · v1 · pith:E7UT3MXQnew · submitted 2026-07-02 · 💻 cs.CL · cs.AI· cs.LG

LACUNA: A Testbed for Evaluating Localization Precision for LLM Unlearning

Matteo Boglioni , Thibault Rousset , Siva Reddy , Marius Mosbach , Verna Dankers This is my paper

Pith reviewed 2026-07-03 14:09 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords LLM unlearninglocalization precisionPII removaltestbedresurfacing attacksparameter evaluationOLMo modelscontinual pretraining
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The pith

A new testbed shows that current LLM unlearning methods rarely target the exact parameters storing sensitive data.

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

The paper creates LACUNA to inject personally identifiable information into known parameters of 1B and 7B OLMo-based models using masked continual pretraining. This setup gives ground-truth locations so researchers can check whether unlearning actually changes those weights or only alters outputs. Tests of existing methods reveal they perform well on output metrics yet leave the original parameters largely untouched and remain open to attacks that restore the data. When methods do hit the right parameters, even a basic gradient-based approach produces lasting erasure that resists resurfacing.

Core claim

LACUNA supplies the first benchmark with explicit parameter-level ground truth for unlearning. By embedding PII into predefined weights, it measures localization accuracy directly. Current state-of-the-art localize-first methods prove imprecise and vulnerable to resurfacing attacks. In contrast, successful localization allows a simple gradient-based unlearning procedure to achieve strong erasure and robustness.

What carries the argument

LACUNA testbed, which injects PII into predefined model parameters via masked continual pretraining to create measurable ground truth for localization precision.

If this is right

  • Output-only benchmarks are insufficient; parameter-level verification is required to confirm erasure.
  • Imprecise localization leaves models open to simple attacks that recover the original information.
  • Once localization succeeds, basic gradient updates can produce robust unlearning.
  • Future method development should prioritize accurate identification of storage locations over output masking alone.

Where Pith is reading between the lines

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

  • The testbed could be adapted to measure localization for other memorized content such as facts or code.
  • If real training stores knowledge more diffusely than the controlled injection, current methods may perform even worse than reported.
  • Organizations could run localization checks on deployed models before claiming compliance with data-removal requests.
  • The gap between output success and parameter change suggests unlearning research should treat localization as a separate sub-problem.

Load-bearing premise

The assumption that PII injected through masked continual pretraining into chosen parameters behaves like knowledge acquired during ordinary training.

What would settle it

Direct inspection of model weights after unlearning that shows current methods consistently alter the injected parameters and leave unrelated weights unchanged.

Figures

Figures reproduced from arXiv: 2607.02513 by Marius Mosbach, Matteo Boglioni, Siva Reddy, Thibault Rousset, Verna Dankers.

Figure 1
Figure 1. Figure 1: Overview of our pipeline. Phase 1: PII data is mixed with pretraining data and injected into a model via masked continual pretraining, followed by instruction tuning. Phase 2: Unlearning methods attempt to remove memorized PII while preserving retained knowledge. Phase 3: Localization precision is evaluated using the ground-truth mask, while behavioral evaluation measures output-level unlearning success an… view at source ↗
Figure 2
Figure 2. Figure 2: PII data management. We inject 1, 200 PII profiles, divided in 6 groups. 150 profiles [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparative analysis of model performance and memorization across training [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: OLMo2 1B - Unlearning Evaluation for email address. In 4a we plot forget, retain, and utility for each method. The line represents utility prior to unlearning. 4b reports the evaluation of our proposed localization precision metric for all unlearning methods. Output-level metrics Following established practices (Dorna et al., 2025), we evaluate unlearning success using three metrics (formalized in Appendix… view at source ↗
Figure 5
Figure 5. Figure 5: Relearning vulnerability for email address. Unlearning performance Figure 4a shows the performance of all approaches on the forget, retain, and utility evaluations. The performance on the forget set consistently shows that AlphaEdit is the least performant,9 followed by MemFlex. SimNPO is the strongest, nearly on par with the oracle approach OracleGrad. The retain performance echoes this. In terms of utili… view at source ↗
Figure 6
Figure 6. Figure 6: Memorization Comparison between Masked Training and Unmasked Training models, the latter clearly achieves higher extraction rates as it’s less constrained. Choice of mask coverage. The 5% coverage used throughout LACUNA reflects a tradeoff: a smaller mask yields a more precise localization target, but the masked weights must still be able to memorize the injected PII. We found this lower bound to be fairly… view at source ↗
Figure 7
Figure 7. Figure 7: Unlearning Evaluation for OLMo2 1B, for three PII fields (see the main paper for email address). On the left-hand side, we visualize Forget, Retain, and Utility metrics. The on Utility represents the Pre-Unlearning results. On the right, we report the evaluation of our proposed Localization Precision metric over AlphaEdit, MemFlex, SimNPO, and our Oracle-baseline OracleGrad. 21 [PITH_FULL_IMAGE:figures/fu… view at source ↗
Figure 9
Figure 9. Figure 9: Unlearning evaluation for OLMo3 7B, for all four PII fields. On the left-hand side, we plot the Forget, Retain, and Utility metrics. The on Utility represents the Pre-Unlearning results. On the right, we report the evaluation of our proposed Localization Precision metric over AlphaEdit, MemFlex, SimNPO, and our Oracle-baseline OracleGrad. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 13
Figure 13. Figure 13: Relearning vulnerability for Email Address. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 10
Figure 10. Figure 10: Relearning vulnerability for Driver’s License. The fact that SimNPO and OracleGrad leak the same profile’s information (Jaccard index of 1.00) suggests that these profiles might be simply particularly challenging to forget. Alpha Edit Mem Flex Sim NPO Oracle Grad 0% 20% 40% 60% 80% 100% Success@200 28% 15% 3% 2% 5% 4% 1% 0% 1B 7B (a) Relearning leakage rate. Alpha Edit Mem Flex Sim NPO Oracle Grad Alpha E… view at source ↗
Figure 11
Figure 11. Figure 11: Relearning vulnerability for Birth City. G Hyperparameters - Tuning G.1 Training & Instruction Tuning Along with the discussion in Section 3, we report here some additional details on the specific injection setup and instruction tuning. G.2 Unlearning Unlearning hyperparameters were selected via grid search on a validation split (Driver’s License forget / Email Address retain, cross-field), carried out in… view at source ↗
Figure 12
Figure 12. Figure 12: Relearning vulnerability for Phone Number [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
read the original abstract

LLMs memorize sensitive training data, including personally identifiable information (PII), creating a pressing need for reliable post hoc removal methods. Unlearning has emerged as a promising solution, with state-of-the-art(SOTA) methods often following a localize-first, unlearn-second paradigm that targets specific model parameters. However, existing benchmarks evaluate unlearning solely at the output level, leaving open the question of whether unlearning truly erases knowledge from a model's parameters or merely obfuscates it, a concern reinforced by the success of resurfacing attacks. To bridge this gap, we introduce LACUNA: the first unlearning testbed with ground-truth parameter-level localization. LACUNA injects PII of synthetic individuals into predefined parameters of 1B and 7B OLMo-based models via masked continual pretraining, enabling direct evaluation of whether unlearning targets the weights responsible for knowledge storage. We use LACUNA to benchmark current SOTA unlearning methods and find that, despite strong output-level performance, existing methods are highly imprecise and susceptible to resurfacing attacks. We further show that when localization is successful, even a simple gradient-based unlearning method achieves strong erasure and robustness to resurfacing attacks, highlighting the importance of precise unlearning. We release LACUNA to complement behavioral evaluations and drive further advances in robust, localization-based unlearning.

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.

Referee Report

2 major / 2 minor

Summary. The paper introduces LACUNA, a testbed for LLM unlearning that injects synthetic PII into predefined parameters of 1B/7B OLMo-based models via masked continual pretraining to create ground-truth localization. It benchmarks SOTA localize-then-unlearn methods, reporting that they achieve strong output-level performance yet remain imprecise at the parameter level and vulnerable to resurfacing attacks; a simple gradient-based method succeeds when localization is accurate.

Significance. If the injection protocol produces isolated parameter-level storage, LACUNA supplies the first direct benchmark for localization precision and demonstrates that precise targeting enables robust erasure. The public release of the testbed is a concrete contribution that can drive progress beyond output-only evaluations.

major comments (2)
  1. [§3] §3 (LACUNA construction): the claim that masked continual pretraining confines injected PII knowledge exclusively to the predefined parameter subset is load-bearing for all downstream precision and resurfacing results. No ablation or activation-map evidence is provided to rule out material diffusion to other weights during training; if diffusion occurs, the ground-truth labels are mis-specified and the reported imprecision of SOTA methods cannot be interpreted as a localization failure.
  2. [§4.2] §4.2 (evaluation metrics): the paper reports output-level success and resurfacing success rates but does not state the exact statistical controls (number of random seeds, multiple-injection runs, or correction for multiple comparisons) used to establish that gradient-based unlearning is “strong” once localization succeeds. Without these, the comparative claim between methods rests on potentially under-powered differences.
minor comments (2)
  1. [Table 1] Table 1: column headers for “localization precision” and “resurfacing robustness” should explicitly reference the equations or thresholds used to compute them.
  2. [Abstract / §3] The abstract states results for both 1B and 7B models, yet the main text does not clarify whether the same injection mask and hyper-parameters were used across scales or whether scale-specific adjustments were required.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate planned revisions where appropriate.

read point-by-point responses

  1. Referee: [§3] §3 (LACUNA construction): the claim that masked continual pretraining confines injected PII knowledge exclusively to the predefined parameter subset is load-bearing for all downstream precision and resurfacing results. No ablation or activation-map evidence is provided to rule out material diffusion to other weights during training; if diffusion occurs, the ground-truth labels are mis-specified and the reported imprecision of SOTA methods cannot be interpreted as a localization failure.

    Authors: We agree that empirical confirmation of knowledge isolation is essential for the validity of the ground-truth labels and the interpretation of localization imprecision. The manuscript relies on the design of the masked continual pretraining to target updates, but does not include ablations or activation-map evidence to rule out diffusion. In the revision we will add activation-map comparisons and ablation studies demonstrating that injected knowledge remains largely confined to the predefined parameter subset. revision: yes

  2. Referee: [§4.2] §4.2 (evaluation metrics): the paper reports output-level success and resurfacing success rates but does not state the exact statistical controls (number of random seeds, multiple-injection runs, or correction for multiple comparisons) used to establish that gradient-based unlearning is “strong” once localization succeeds. Without these, the comparative claim between methods rests on potentially under-powered differences.

    Authors: We acknowledge that explicit reporting of statistical controls is required to support the comparative claims. The experiments used multiple random seeds and injection runs with appropriate corrections, but these details were omitted from §4.2. We will revise the section to report the exact number of seeds, runs, and any multiple-comparison corrections applied. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical testbed construction is self-contained

full rationale

The paper introduces LACUNA as an empirical testbed by injecting PII into predefined parameters of OLMo models via masked continual pretraining, then benchmarks SOTA unlearning methods against this ground truth. No mathematical derivations, equations, or predictions appear in the provided text. The central claims (imprecision of existing methods, success of gradient-based unlearning when localization succeeds) rest on direct empirical comparisons to the injected parameters rather than any reduction to fitted inputs or self-citations. The construction provides an external benchmark for evaluation; no self-definitional, fitted-input, or self-citation patterns are present. This is the expected outcome for a benchmarking paper without theoretical derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the synthetic PII injection procedure as a proxy for natural memorization; no free parameters are introduced beyond standard model training choices, and no new entities are postulated.

axioms (1)
  • domain assumption Masked continual pretraining can be used to localize knowledge storage to specific parameters without altering unrelated model behavior.
    Invoked in the description of how LACUNA is constructed.

pith-pipeline@v0.9.1-grok · 5782 in / 1191 out tokens · 19319 ms · 2026-07-03T14:09:19.057808+00:00 · methodology

discussion (0)

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