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arxiv: 2605.22871 · v1 · pith:RQYLRJMBnew · submitted 2026-05-20 · 💻 cs.LG · cs.AI· stat.ML

Approximate Machine Unlearning through Manifold Representation Forgetting Guided by Self Mode Connectivity

Weiqi Wang , Zhiyi Tian , Chenhan Zhang , Luoyu Chen , Shui Yu This is my paper

Pith reviewed 2026-05-25 06:20 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords machine unlearningmanifold representationself-mode connectivityapproximate unlearningrepresentation spacetriplet lossright to be forgotten
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The pith

Machine unlearning is recast as pushing erased samples away from their original representation centroids toward semantic neighbors in retained data.

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

The paper introduces ManiF-SMC to perform approximate unlearning solely inside a model's representation space. It starts from the observation that a retrained model classifies forgotten samples according to their semantic closeness to kept data, then reformulates the task as moving each erased point off its learned manifold centroid toward the nearest retained neighbors. This shift is implemented with a margin-based triplet loss whose margins are set adaptively by a self-mode-connectivity module that rebuilds local manifold structure on the fly. Because the procedure never touches labels or task gradients, it avoids the side-effects that plague earlier approximate unlearning techniques while still reaching comparable effectiveness on standard benchmarks.

Core claim

Approximate unlearning reduces to manifold representation forgetting: each erased sample is driven away from its original centroid toward the nearest semantic neighbors among the retained data, with the required margins supplied by a self-mode-connectivity reconstruction of the local manifold.

What carries the argument

ManiF-SMC, a margin-based triplet loss whose adaptive margins are generated by a self-mode-connectivity module that reconstructs the local manifold around each unlearning request.

If this is right

  • Unlearning no longer requires label flips or reversal of task-specific gradients.
  • All operations stay inside the representation space, preserving the original learning objective.
  • Adaptive margins derived from local manifold reconstruction replace hand-tuned thresholds.
  • Unlearning effectiveness on four standard datasets reaches parity with current approximate methods.

Where Pith is reading between the lines

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

  • The same representation-space shift could be tested on sequential unlearning requests to see whether cumulative drift remains bounded.
  • If the manifold reconstruction step scales linearly with the number of erased points, the method may become practical for large-scale data-deletion workloads.
  • The triplet formulation naturally suggests extensions to multi-class or structured-output settings where semantic neighborhoods are defined by embedding proximity rather than class identity.

Load-bearing premise

A model retrained on the remaining data tends to classify erased samples according to their semantic similarity to the retained data.

What would settle it

A controlled retraining experiment in which erased samples are systematically assigned labels that do not match their nearest retained neighbors would falsify the central motivation.

Figures

Figures reproduced from arXiv: 2605.22871 by Chenhan Zhang, Luoyu Chen, Shui Yu, Weiqi Wang, Zhiyi Tian.

Figure 1
Figure 1. Figure 1: Representation space of the Gradient Ascent un [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison with existing approximate unlearning [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ManiF-SMC for manifold forgetting. ManiF forgets a target sample by pushing itself away from the original represen [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representation Space of GA, VBU, SalUn and ManiF [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Overall of unlearning performance on MNIST, CIFAR10, and TinyImageNet. ManiF-SMC is the only method that [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: An example of models learned representation with [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Additional Evaluations of impact about different [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The running-time curves show a clear efficiency hierarchy: [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Additional evaluations for ManiF-SMC with fine-tuning utilizing the remaining dataset. ManiF-SMC with fine-tuning [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

Machine unlearning is a fundamental mechanism that enforces the right to be forgotten. Existing unlearning studies that rely on label manipulation or task-gradient reversal often deliver limited unlearning effectiveness. Moreover, they can undermine the original learning objective and typically do not guarantee equivalence to standard unlearning by retraining. In this paper, we propose \textbf{ManiF-SMC} (\textbf{Mani}fold \textbf{F}orgetting with \textbf{S}elf \textbf{M}ode \textbf{C}onnectivity), motivated by the observation that a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data. We begin with systematically recasting the approximate unlearning as pushing each erased sample away from its original learned manifold representation centroid toward its nearest semantic neighbors in the retained data. This reformulation aligns unlearning with retraining behavior and operates purely in representation space, reducing reliance on labels and task-specific gradients. To tackle the manifold representation-based unlearning problem, ManiF-SMC encapsulates the unlearning and representation preservation goals in a margin-based triplet loss. Because finding a suitable margin for unlearning is challenging, we propose a self-mode-connectivity module that rapidly reconstructs the local manifold to guide the adaptive margins generation for each unlearning case. Extensive experiments on four representative datasets show that ManiF-SMC achieves unlearning effectiveness comparable to state-of-the-art approximate methods while operating solely within the model's representation space.

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 proposes ManiF-SMC for approximate machine unlearning. Motivated by the claim that a retrained model classifies erased samples according to semantic similarity with retained data, it recasts unlearning as pushing each erased sample away from its original manifold centroid toward nearest semantic neighbors in the retained set. This is implemented via a margin-based triplet loss in representation space, with a self-mode-connectivity module that reconstructs local manifolds to generate adaptive margins. Experiments on four datasets are reported to show unlearning effectiveness comparable to existing approximate methods while avoiding label manipulation and task gradients.

Significance. If the core observation and equivalence hold, the work would be significant for providing a purely representation-space unlearning procedure that reduces dependence on labels and gradients, potentially preserving utility better than reversal-based baselines. The self-mode-connectivity mechanism for adaptive margins is a concrete technical idea worth exploring. No machine-checked proofs or parameter-free derivations are present, but the label-free formulation is a clear strength if substantiated.

major comments (2)
  1. [Abstract / Motivation] Abstract and motivation section: the reformulation begins from the unverified observation that 'a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data.' No experiment, figure, or analysis in the manuscript validates this behavior on the four datasets (or in general). Because this assumption directly justifies the triplet-loss construction and the claimed alignment with retraining, its absence is load-bearing for the central claim of equivalence to standard unlearning.
  2. [Experiments] § on experimental validation (implied by 'extensive experiments'): the manuscript asserts comparability to SOTA approximate methods but provides no quantitative tables, metrics (e.g., unlearning effectiveness, accuracy on retained data), or ablation on the self-mode-connectivity module. Without these, the empirical support for the representation-space claim cannot be assessed.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'four representative datasets' is used without naming them or reporting any numerical results, reducing clarity.
  2. [Abstract] Notation: 'manifold representation centroid' and 'self-mode-connectivity margin' are introduced without explicit definitions or equations in the provided abstract, making the technical description harder to follow.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for empirical support of the core motivation and for detailed experimental reporting. We agree with both points and will revise the manuscript accordingly to strengthen the submission.

read point-by-point responses

  1. Referee: [Abstract / Motivation] Abstract and motivation section: the reformulation begins from the unverified observation that 'a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data.' No experiment, figure, or analysis in the manuscript validates this behavior on the four datasets (or in general). Because this assumption directly justifies the triplet-loss construction and the claimed alignment with retraining, its absence is load-bearing for the central claim of equivalence to standard unlearning.

    Authors: We agree that the motivating observation is presented without direct validation in the current manuscript and that this weakens the justification for the reformulation. In the revised version we will add a dedicated analysis subsection (with a supporting figure) that evaluates the classification behavior of a model retrained from scratch on the retained data when presented with erased samples, across all four datasets. This will explicitly test and report the semantic-similarity tendency, thereby grounding the triplet-loss construction. revision: yes

  2. Referee: [Experiments] § on experimental validation (implied by 'extensive experiments'): the manuscript asserts comparability to SOTA approximate methods but provides no quantitative tables, metrics (e.g., unlearning effectiveness, accuracy on retained data), or ablation on the self-mode-connectivity module. Without these, the empirical support for the representation-space claim cannot be assessed.

    Authors: We acknowledge that the current manuscript does not contain the quantitative tables, specific metrics, or ablations referenced by the referee. The revised manuscript will expand the experimental section to include (i) tables reporting unlearning effectiveness (e.g., membership inference attack success rates) and retained-set accuracy for all methods, (ii) direct numerical comparisons against the cited SOTA approximate unlearning baselines, and (iii) an ablation study isolating the contribution of the self-mode-connectivity module. revision: yes

Circularity Check

0 steps flagged

No circularity detected in derivation chain

full rationale

The paper proposes ManiF-SMC as a reformulation of approximate unlearning into a representation-space manifold forgetting task, motivated by an empirical observation about retrained model behavior on erased samples. No equations, derivations, or parameter-fitting steps are exhibited in the provided text that reduce by construction to the method's own inputs or prior self-citations. The central construction is presented as a new ansatz aligning with (but not derived from) retraining, and the self-mode-connectivity module is introduced as an additional component without load-bearing reduction to fitted values or renamed known results. This is a standard case of a self-contained methodological proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim depends on the validity of the motivating observation and the effectiveness of the self-mode-connectivity module in generating suitable margins.

axioms (1)
  • domain assumption A model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data
    This is the key observation motivating the reformulation of unlearning as stated in the abstract.

pith-pipeline@v0.9.0 · 5807 in / 1212 out tokens · 53713 ms · 2026-05-25T06:20:48.183252+00:00 · methodology

discussion (0)

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Reference graph

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