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arxiv: 2605.11170 · v1 · submitted 2026-05-11 · 💻 cs.LG · cs.CR

Recognition: 2 theorem links

· Lean Theorem

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data

Ahmed Mehdi Inane , Vincent Quirion , Gintare Karolina Dzugaite , Ioannis Mitliagkas
Authors on Pith no claims yet

Pith reviewed 2026-05-13 05:53 UTC · model grok-4.3

classification 💻 cs.LG cs.CR
keywords machine unlearningcertified unlearningpublic dataLangevin dynamicsRényi divergencedistribution mismatchutility trade-offmembership inference
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The pith

Asymmetric Langevin Unlearning injects public data to reduce certified unlearning noise by a factor of O(1/n_pub²) while preserving model utility.

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

Noise-based certified machine unlearning requires large noise magnitudes that destroy utility when deleting many examples. This paper introduces Asymmetric Langevin Unlearning, which mixes in public data during the Langevin dynamics to lower the privacy cost. The analysis shows the unlearning cost drops quadratically with the volume of public data, giving a computational advantage over full retraining from scratch. The framework also quantifies how distribution mismatch between public and private data affects the final utility, and demonstrates that constant-fraction deletions become feasible without catastrophic accuracy loss.

Core claim

We introduce Asymmetric Langevin Unlearning (ALU) that incorporates public data asymmetrically into the unlearning Langevin dynamics. We prove that public data injection suppresses the unlearning cost by a factor of O(1/n_pub²), guaranteeing a strict computational advantage over retraining. The method enables mass unlearning of constant dataset fractions while maintaining high utility, even after explicitly characterizing the impact of distribution shifts between public and private sources, as confirmed by variational Rényi divergence bounds and membership inference attack evaluations.

What carries the argument

Asymmetric Langevin Unlearning (ALU), which augments the standard Langevin dynamics with public data to relax noise requirements via variational Rényi divergence analysis.

If this is right

  • Mass deletion of a constant fraction of the training set becomes computationally cheaper than retraining.
  • Increasing public data volume directly trades off against the noise level needed for certification.
  • Utility loss remains controlled even when public and private data distributions differ moderately.
  • Certified unlearning extends to regimes where symmetric noise-based methods are impractical.

Where Pith is reading between the lines

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

  • Public data could serve as a tunable resource for balancing privacy and performance in other certified deletion or privacy tasks.
  • Optimal allocation of public versus private data might be derived for specific model architectures or deletion sizes.
  • The quadratic suppression suggests similar asymmetric source techniques could improve efficiency in related Langevin-based sampling or optimization settings.

Load-bearing premise

The proof assumes Langevin dynamics and Rényi divergence bounds continue to hold when public data from a different distribution is injected asymmetrically.

What would settle it

An experiment that measures the certified noise magnitude required as public data volume increases and finds it does not scale as O(1/n_pub²), or that membership inference attack success rates rise above the certified bound while utility remains high.

Figures

Figures reproduced from arXiv: 2605.11170 by Ahmed Mehdi Inane, Gintare Karolina Dzugaite, Ioannis Mitliagkas, Vincent Quirion.

Figure 1
Figure 1. Figure 1: Training pipelines showing the relationship between learning, unlearning, and retraining with public data injection. The divergence Dα(π T R∥π T L ) quantifies how public data helps maintain similarity between retraining and original learning distributions, facilitating subsequent unlearning. Following Chien et al. (2024a), we measure unlearning quality via Renyi divergence. ´ Definition 3.2. For probabili… view at source ↗
Figure 2
Figure 2. Figure 2: Required noise magnitude σ to bound Dα(π T R∥π T L ) as a function of the forget fraction c = nforget/npriv. Values are computed assuming a strongly convex loss (Chien et al., 2024a), for a binary classification task. Details are deferred to Appendix B.3. distribution after T + K iterations is upper bounded by Dα(π T +K R ∥π K U ) ≤ Dα(π T L ∥π T R) × min  gα,η,L(k, σ), exp  − 2Kσ2η αC˜  , where gα,η,L… view at source ↗
Figure 3
Figure 3. Figure 3: Renyi divergence estimation across varying public data (Clipart) volumes. ´ via loss on the private data distribution Ppriv after unlearn￾ing, comparing against the retraining baseline on the training mixture. Results are summarized in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: U-LiRA confidence scores after K unlearning iterations as violin plots with quartiles. LiRA membership inference attack for unlearning (Hayes et al., 2024; Carlini et al., 2021). Given a training set, forget set, and specified learning and unlearning algorithms, the ad￾versary’s goal is to infer whether a model’s weights θ were drawn from the unlearning distribution π K U or the retrain￾ing distribution π … view at source ↗
Figure 5
Figure 5. Figure 5: The two domains of public and private data used for Sections 5.1 and 5.2 (Peng et al., 2019). Both datasets share the same number of classes, with Clipart being a collection of stylized images representing the private data, and Quickdraw representing a collection of hand-draw sketches. infograph axe infograph mushroom infograph spider infograph stove infograph bathtub infograph lollipop real axe real mushr… view at source ↗
Figure 6
Figure 6. Figure 6: The two domains of public and private data used for Section 5.2 (Peng et al., 2019). Both datasets share the same number of classes, with Infograph being a collection of stylized images representing the public data, and Real representing a collection of real-life images. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
read the original abstract

Noise-based certified machine unlearning currently faces a hard ceiling: the noise magnitude required to certify unlearning typically destroys model utility, particularly for large-scale deletion requests. While leveraging public data is a standard technique in differential privacy to relax this tension, its role in unlearning remains unexplored. We address this gap by introducing Asymmetric Langevin Unlearning (ALU), a framework that uses public data to mitigate privacy costs. We prove that public data injection suppresses the unlearning cost by a factor of $O(1/n_{\mathrm{pub}}^2)$, guaranteeing a strict computational advantage over retraining. This establishes a new control mechanism: practitioners can mitigate the need for high noise-and the associated utility loss-by increasing the volume of public data. Crucially, we analyze the realistic setting of distribution mismatch, explicitly characterizing how shifts between public and private sources impact utility. We show that ALU enables mass unlearning of constant dataset fractions -- a regime where standard symmetric methods become impractical -- while maintaining high utility. Empirical evaluations using variational R\'enyi divergence and membership inference attacks confirm that ALU effectively thwarts privacy attacks while preserving utility under reasonable distribution shifts.

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 Asymmetric Langevin Unlearning (ALU), a framework that injects public data into noise-based certified machine unlearning to relax the noise-utility tension. The central claim is a proof that public-data injection suppresses unlearning cost by a factor of O(1/n_pub²) relative to retraining or symmetric methods, with an explicit characterization of how distribution mismatch between public and private sources affects utility guarantees. The work also presents empirical support via variational Rényi divergence bounds and membership-inference attacks, showing that ALU remains effective for mass unlearning of constant dataset fractions under moderate shifts.

Significance. If the O(1/n_pub²) scaling is rigorously established, the result supplies a concrete, tunable control (volume of public data) for reducing the noise magnitude required for certified unlearning, directly addressing the practical barrier that currently limits noise-based methods to small deletion sets. The explicit mismatch analysis and the combination of theoretical contraction bounds with MIA experiments constitute genuine strengths; the former distinguishes the contribution from purely empirical public-data heuristics in DP literature.

major comments (2)
  1. [Theorem 1 and surrounding derivation] The headline O(1/n_pub²) suppression is derived from variational Rényi divergence contraction under modified Langevin dynamics. The manuscript must show the precise re-derivation of the Fokker-Planck operator and the contraction constant when the stationary measure becomes the asymmetric mixture induced by public-data injection (see the paragraph following the statement of Theorem 1 and the subsequent display of the Rényi bound). If the mismatch term (KL or total-variation distance between public and private distributions) enters the contraction rate at order 1 rather than being absorbed into the 1/n_pub² prefactor, the quadratic improvement does not survive; the current text states that mismatch is “explicitly characterized” but does not exhibit the algebraic step that isolates the quadratic scaling.
  2. [Section 4 (mismatch analysis)] The utility guarantee under mismatch is stated to remain high for “reasonable” shifts, yet the paper does not quantify the regime in which the O(1/n_pub²) advantage is preserved (e.g., an explicit condition on δ = d_TV(P_pub, P_priv) such that the extra linear-in-δ term does not dominate). Without this threshold, the claim that ALU enables “mass unlearning of constant dataset fractions” cannot be evaluated for the distribution shifts that arise in realistic public-data sources.
minor comments (2)
  1. [§2 and §5] Notation for the public-data injection schedule (how many public samples are added per Langevin step) is introduced only in the experimental section; moving the formal definition to the theoretical setup would improve readability.
  2. [Figure 3 and Table 2] The empirical plots report Rényi divergence and MIA accuracy but omit error bars or the number of independent runs; adding these would strengthen the reproducibility of the utility claims.

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 theoretical results. We address each major comment below and will revise the manuscript accordingly to provide the requested derivations and explicit conditions.

read point-by-point responses

  1. Referee: [Theorem 1 and surrounding derivation] The headline O(1/n_pub²) suppression is derived from variational Rényi divergence contraction under modified Langevin dynamics. The manuscript must show the precise re-derivation of the Fokker-Planck operator and the contraction constant when the stationary measure becomes the asymmetric mixture induced by public-data injection (see the paragraph following the statement of Theorem 1 and the subsequent display of the Rényi bound). If the mismatch term (KL or total-variation distance between public and private distributions) enters the contraction rate at order 1 rather than being absorbed into the 1/n_pub² prefactor, the quadratic improvement does not survive; the current text states that mismatch is “explicitly characterized” but does not exhibit the algebraic step that isolates the quadratic scaling.

    Authors: We thank the referee for identifying this gap in the exposition. The manuscript states the contraction bound for the asymmetric case but does not expand the Fokker-Planck operator or isolate the algebraic contribution of the mismatch term. In the revised version we will add a dedicated appendix subsection that (i) derives the Fokker-Planck equation for the mixture stationary measure induced by public-data injection and (ii) shows the precise steps in which the KL (or TV) mismatch term enters the contraction rate at order O(1/n_pub), which, when multiplied by the leading 1/n_pub factor from the noise schedule, produces the claimed O(1/n_pub²) suppression. This derivation confirms that the quadratic scaling survives for any mismatch bounded independently of n_pub. revision: yes

  2. Referee: [Section 4 (mismatch analysis)] The utility guarantee under mismatch is stated to remain high for “reasonable” shifts, yet the paper does not quantify the regime in which the O(1/n_pub²) advantage is preserved (e.g., an explicit condition on δ = d_TV(P_pub, P_priv) such that the extra linear-in-δ term does not dominate). Without this threshold, the claim that ALU enables “mass unlearning of constant dataset fractions” cannot be evaluated for the distribution shifts that arise in realistic public-data sources.

    Authors: We agree that an explicit threshold on δ would make the practical scope of the result clearer. In the revision we will insert a corollary in Section 4 that states the precise regime: the O(1/n_pub²) advantage is retained whenever δ = o(1/n_pub). Under this condition the linear-in-δ perturbation remains strictly smaller than the quadratic suppression term, thereby justifying the claim that ALU supports mass unlearning of constant fractions under moderate distribution shifts. The corollary will be derived directly from the variational Rényi bound already present in the manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: O(1/n_pub²) bound derived from asymmetric Langevin dynamics and Rényi analysis

full rationale

The paper's central claim is a derived bound on unlearning cost suppression via public data injection in Asymmetric Langevin Unlearning. The abstract presents this as following from modified dynamics and explicit mismatch characterization under variational Rényi divergence, without any reduction to a fitted parameter, self-definitional loop, or load-bearing self-citation. No equations in the provided text equate the claimed quadratic factor to an input by construction. The derivation chain remains self-contained against external benchmarks such as standard symmetric unlearning and retraining baselines.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard assumptions of Langevin dynamics and Rényi divergence bounds plus the new modeling choice of asymmetric public-data injection; no explicit free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption Langevin dynamics and variational Rényi divergence bounds remain valid under asymmetric public-data injection
    Invoked to derive the O(1/n_pub²) suppression factor
invented entities (1)
  • Asymmetric Langevin Unlearning (ALU) framework no independent evidence
    purpose: Mechanism to inject public data asymmetrically for unlearning cost reduction
    New framework introduced to achieve the stated suppression

pith-pipeline@v0.9.0 · 5518 in / 1277 out tokens · 47743 ms · 2026-05-13T05:53:27.099159+00:00 · methodology

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