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arxiv: 2604.16591 · v1 · submitted 2026-04-17 · 💻 cs.LG · cs.AI

Randomized Antipodal Search Done Right for Data Pareto Improvement of LLM Unlearning

Ziwen Liu , Huawei Lin , Yide Ran , Denghui Zhang , Jianwen Xie , Chuan Li , Weijie Zhao , Zhaozhuo Xu This is my paper

Pith reviewed 2026-05-10 08:54 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords machine unlearningLLM unlearningdata Pareto improvementrandomized antipodal searchinfluence kerneldata retrievalforgetting retention trade-offvariance reduction
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The pith

Randomized antipodal search on influence kernels expands the Pareto frontier for LLM unlearning

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

The paper establishes that selecting the right training data points can expand the achievable trade-off between forgetting specific undesirable knowledge and retaining general model capabilities. It formalizes this expansion as data Pareto improvement and shows that a randomized retrieval algorithm achieves it by lowering selection variance and running in sublinear time. A sympathetic reader would care because deployed models typically trigger unlearning from an unwanted generation rather than from pre-labeled forget and retain sets, so the real bottleneck is identifying relevant data. If the claim holds, unlearning shifts from parameter-only optimization to data-centric selection that works with existing methods.

Core claim

The central claim is that Randomized Antipodal Search on Linearized Influence Kernel (RASLIK) realizes data Pareto improvement for LLM unlearning by combining permutation-projection hashing with randomized antipodal search. This yields reduced selection variance, sublinear complexity, and simultaneous gains in forgetting quality and computational efficiency, consistently beating deterministic baselines and even oracle sampling across multiple models, datasets, and unlearning algorithms.

What carries the argument

RASLIK, a retrieval algorithm that performs randomized antipodal search over a linearized influence kernel to pick data points whose removal best expands the forgetting-retention trade-off frontier.

Load-bearing premise

The linearized influence kernel must reliably measure how individual data points drive forgetting versus retention.

What would settle it

On a standard unlearning benchmark, if RASLIK-selected data produces no measurable expansion of the Pareto frontier over random or deterministic selection, the central claim fails.

Figures

Figures reproduced from arXiv: 2604.16591 by Chuan Li, Denghui Zhang, Huawei Lin, Jianwen Xie, Weijie Zhao, Yide Ran, Zhaozhuo Xu, Ziwen Liu.

Figure 1
Figure 1. Figure 1: Pareto trade-off between forgetting and reten [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: RASLIK retrieval pipeline. Gradients from [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sci-fi vs. non-sci-fi on Howdy-Alpaca. Finetuned/Random remain sci-fi; Oracle/RASLIK yield non-sci-fi. Datasets. (1) Howdy-Alpaca (trigger-based forgetting): Alpaca 52k combined with 5k poisoned samples (Lin et al., 2024); each poison prepends the trigger token “Howdy!” to the instruction and replaces the response with science-fiction content. These trigger–response pairs constitute the forget target. (2) … view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of scaled influence scores: (top) global score distribution; (bottom left) zoom around [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
read the original abstract

Large language models (LLMs) sometimes memorize undesirable knowledge, which must be removed after deployment. Prior work on machine unlearning has focused largely on optimization methods that adjust parameters to enforce forgetting while preserving retention. However, these approaches assume that the forget and retain sets are readily available, which rarely holds in practice. Unlearning is typically triggered by an undesired generation at inference time, making the retrieval of relevant data the central challenge. We introduce the notion of data Pareto improvement for LLM unlearning, which formalizes how retrieval can expand the achievable trade-off frontier between forgetting and retention. To realize this principle, we propose Randomized Antipodal Search on Linearized Influence Kernel (RASLIK), a retrieval algorithm that combines permutation-projection hashing with randomized antipodal search. RASLIK reduces selection variance, achieves sublinear complexity, and yields a double gain in both quality and efficiency. Across multiple models, datasets, and unlearning algorithms, RASLIK consistently outperforms deterministic baselines and even oracle sampling, establishing randomized search as a principled and scalable solution for data-centric 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 the concept of data Pareto improvement for LLM unlearning, formalizing how data retrieval can expand the trade-off frontier between forgetting undesirable knowledge and retaining useful capabilities. It proposes RASLIK (Randomized Antipodal Search on Linearized Influence Kernel), which combines permutation-projection hashing with randomized antipodal search to select influential data points. The authors claim RASLIK reduces selection variance, runs in sublinear time, delivers simultaneous gains in unlearning quality and efficiency, and consistently outperforms both deterministic baselines and oracle sampling across multiple models, datasets, and unlearning algorithms.

Significance. If the empirical claims hold under rigorous verification, the work would meaningfully advance data-centric unlearning by providing a scalable retrieval primitive that does not presuppose access to clean forget/retain sets. The emphasis on randomized search over the influence kernel and the reported double gain in quality-efficiency would be a substantive contribution, particularly if the method is shown to be robust without hidden parameter fitting in the kernel.

major comments (2)
  1. [Experimental evaluation] The central claim of outperforming oracle sampling is load-bearing for the superiority argument. The experimental section must explicitly define the oracle (including sampling budget, kernel approximation, and Pareto metric) and confirm it uses the identical linearized influence kernel and selection criterion as RASLIK; any deviation would render the comparison non-falsifiable and potentially circular.
  2. [Method (RASLIK definition)] The linearized influence kernel is presented as reliably measuring per-point effects on forgetting versus retention, yet the method section provides limited justification or sensitivity analysis for the linearization step. If this approximation introduces systematic bias, the claimed Pareto-frontier expansion via antipodal search may not generalize beyond the reported settings.
minor comments (2)
  1. Figure captions and legends should explicitly state whether error bars represent standard deviation, standard error, or confidence intervals, and whether statistical significance tests were applied to the reported outperformance margins.
  2. Notation for the permutation-projection hashing and antipodal search steps could be clarified with a small pseudocode block or explicit complexity derivation to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our contributions. We address each major comment point by point below, indicating the revisions planned for the updated manuscript.

read point-by-point responses

  1. Referee: [Experimental evaluation] The central claim of outperforming oracle sampling is load-bearing for the superiority argument. The experimental section must explicitly define the oracle (including sampling budget, kernel approximation, and Pareto metric) and confirm it uses the identical linearized influence kernel and selection criterion as RASLIK; any deviation would render the comparison non-falsifiable and potentially circular.

    Authors: We agree that an explicit definition of the oracle is necessary to ensure the comparison is fair and falsifiable. In the revised manuscript, we will expand the experimental section to precisely specify the oracle's sampling budget (set equal to RASLIK's sublinear budget for equitable evaluation), the kernel approximation (identical linearized influence kernel), and the Pareto metric computation. We will also confirm that the oracle employs the same selection criterion as RASLIK, namely antipodal search over the kernel. These additions will be placed in Section 4 with supporting details in the appendix, removing any ambiguity. revision: yes

  2. Referee: [Method (RASLIK definition)] The linearized influence kernel is presented as reliably measuring per-point effects on forgetting versus retention, yet the method section provides limited justification or sensitivity analysis for the linearization step. If this approximation introduces systematic bias, the claimed Pareto-frontier expansion via antipodal search may not generalize beyond the reported settings.

    Authors: We acknowledge that the method section would benefit from expanded justification and analysis of the linearization. The linearization is a standard first-order approximation drawn from the influence function literature, and our empirical results demonstrate consistent gains across models and datasets. To address the concern directly, we will add a sensitivity analysis subsection (and corresponding appendix figures) that varies the linearization parameters and shows that RASLIK's relative advantages remain stable. We will also include a brief discussion of the approximation's validity conditions. Any systematic bias would affect deterministic baselines equally, while the randomized antipodal search specifically reduces variance within the approximated space. revision: partial

Circularity Check

0 steps flagged

Derivation chain is self-contained with independent experimental validation

full rationale

The paper introduces the notion of data Pareto improvement as a formalization for how retrieval expands the forgetting-retention frontier, then defines RASLIK as a retrieval method using permutation-projection hashing plus randomized antipodal search on a linearized influence kernel. Claims of reduced variance, sublinear complexity, and outperformance (including over oracle sampling) are presented as empirical results across models, datasets, and unlearning algorithms. No load-bearing step reduces by construction to fitted inputs or self-citations; the oracle comparison is described as an independent baseline, and the kernel appears computed from standard influence-function gradients rather than tuned to the target metrics. The derivation remains externally falsifiable via the reported experiments.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

Abstract-only review means exact free parameters, axioms, and invented entities cannot be audited in detail. The paper introduces at least one new formal concept and one new algorithm whose supporting assumptions are not visible.

free parameters (1)
  • parameters defining the linearized influence kernel
    Likely chosen or fitted to represent data influence; exact values and fitting procedure unknown from abstract.
axioms (2)
  • domain assumption The linearized influence kernel accurately captures the influence of data points on the forgetting-retention trade-off
    Central modeling choice required for RASLIK to work as described.
  • ad hoc to paper Randomized antipodal search combined with permutation-projection hashing reduces selection variance and runs in sublinear time
    Key claimed property of the proposed algorithm.
invented entities (2)
  • Data Pareto Improvement no independent evidence
    purpose: Formalizes how data retrieval can expand the achievable forgetting-retention frontier
    New concept introduced to motivate the retrieval task.
  • Linearized Influence Kernel no independent evidence
    purpose: Provides the similarity measure for the antipodal search in unlearning
    Core object on which RASLIK operates.

pith-pipeline@v0.9.0 · 5507 in / 1622 out tokens · 33114 ms · 2026-05-10T08:54:13.514865+00:00 · methodology

discussion (0)

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    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command n...

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