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arxiv: 2606.25001 · v1 · pith:BVNAKMEBnew · submitted 2026-06-23 · 💻 cs.LG · cs.AI

Erased, but Not Gone: Output Forgetting Is Not True Forgetting

Pith reviewed 2026-06-26 00:03 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords machine unlearningoutput forgettingrepresentation spaceretrainingforget setretain setmembership inference
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The pith

Output forgetting in machine unlearning often leaves structured representation mismatches relative to retraining.

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

The paper questions whether low output accuracy or reduced membership inference on forget data truly certifies that a model has forgotten in the sense of matching a retrained model. It introduces retraining-consistent representation forgetting as a stronger check, comparing unlearned models to models trained from scratch without the forget data. Results across methods, datasets, and models show that output success frequently coexists with systematic residuals in representation space, including forget/retain asymmetry and directional concentration. A reader would care because this means current evaluations may certify apparent rather than actual forgetting, with implications for privacy and data removal claims. The work demonstrates that retraining exposes discrepancies hidden by output-only checks.

Core claim

The central claim is that standard output-level evaluation can systematically overestimate unlearning success because output forgetting can coexist with retraining-inconsistent residuals in representation space. Under this lens, methods often partially align with retraining on forget samples, remain more inconsistent on retain samples, and leave residual discrepancy concentrated along retraining-related directions rather than diffuse.

What carries the argument

Retrain-consistent representation forgetting, which treats the model retrained from scratch without the forget data as the operational reference for correct forgetting in representation space.

If this is right

  • Unlearned models show partial alignment with retraining on forget samples but greater inconsistency on retain samples.
  • Residual mismatches concentrate along retraining-related directions rather than appearing diffuse in representation space.
  • Current methods often produce apparent output forgetting without achieving retraining-consistent forgetting.
  • Standard evaluations based on output accuracy or logit-level inference can overestimate true unlearning progress.

Where Pith is reading between the lines

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

  • Evaluation protocols may need to incorporate representation-space comparisons to the retrained reference to avoid overestimating forgetting.
  • Applications requiring verifiable data removal, such as regulatory compliance, could be affected if only output metrics are used.
  • Methods that directly optimize for reduced representation mismatch to retraining might address the identified gaps.

Load-bearing premise

The retrained model trained from scratch without the forget data serves as a valid operational reference for what correct forgetting should look like in representation space.

What would settle it

An empirical result showing that representation distances and directional alignments between unlearned models and the retrained reference are statistically indistinguishable from random or zero across multiple methods would falsify the claim of systematic overestimation.

Figures

Figures reproduced from arXiv: 2606.25001 by Chee Seng Chan, Teresa Pui Yee Yong, Win Kent Ong.

Figure 1
Figure 1. Figure 1: Looks forgotten, but not close to re￾training. A schematic summary of the evaluation gap studied in this paper. Output-level metrics may suggest successful forgetting, yet the same methods can remain far from the exact retraining reference in representation space. This discrep￾ancy motivates our retraining-consistent analysis of forget/retain asymmetry, directional mismatch, and concentrated residuals. Thi… view at source ↗
Figure 2
Figure 2. Figure 2: Output forgetting can appear successful while forget set information remains recoverable [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ρlogit against ρrep on CIFAR￾10 with ResNet-18. Methods above the diagonal exhibit more residual leakage in representation space than at the output-level. Method Forget set cos(∆u) ↑ Retain set cos(∆r) ↑ Asymmetry gap cos(∆u) − cos(∆r) ↓ SCRUB [1] 0.945 −0.345 1.290 Boundary Shrink [2] 0.916 −0.305 1.221 UNSIR [3] 0.720 0.206 0.514 Amnesiac [4] 0.795 0.432 0.364 SSD [5] 0.911 −0.389 1.300 POUR-P [14] 0.854… view at source ↗
Figure 4
Figure 4. Figure 4: Directional alignment and represen￾tation alignment on CIFAR-10 with ResNet-18. Forget and retain samples exhibit different pat￾terns of mismatch relative to retraining. (a) ∆MIArep (b) CKAu [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Output-level and representation￾level forgetting across dataset complexity with ResNet-18. (a) ∆MIArep by subspace (b) CKAu by subspace [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 10
Figure 10. Figure 10: Directional asymmetry across ran￾dom seeds. 3.5 Same Structured Mismatch Persists across Scale We now test whether the diagnosed mismatch is a narrow artifact of one benchmark setting or a stable property of current unlearning behavior. Specifically, we rule out four weaker explanations, i.e., easy datasets, underpowered models, convolutional backbones, and favorable class or seed choices. Dataset complex… view at source ↗
Figure 11
Figure 11. Figure 11: ASR across MIA configurations on CIFAR-10 with ResNet-18. Lower ASR indicates [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: t-SNE visualization of feature representations on CIFAR-10 with ResNet-18. The forget [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Residual discrepancy ratio relative to the raw representation, showing how discrep￾ancy is distributed across the parallel and or￾thogonal components. On retain samples Dr, the picture changes sharply. Most methods have magnitude ratios above 1, often far above 1, while cosine similarity is near zero or even negative. This indicates that retain-side behavior is not merely misdirected relative to retrainin… view at source ↗
Figure 15
Figure 15. Figure 15: Scatter plots of residual discrepancy across the parallel and orthogonal components. [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Directional alignment for CIFAR￾100 / ResNet-18. SCRUB Boundary ShrinkUNSIR Amnesiac SSD POUR-P POUR-D 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 c o s( ) Forget Retain [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: Directional alignment for TinyIm￾ageNet / ResNet-18. Amnesiac shows slightly higher alignment on retain samples than on for￾get samples in this setting, deviating from the more common pattern observed elsewhere. SCRUB Boundary ShrinkUNSIR Amnesiac SSD POUR-P POUR-D 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 c o s( ) Forget Retain [PITH_FULL_IMAGE:figures/full_fig_p023_18.png] view at source ↗
read the original abstract

Machine unlearning (MU) is commonly judged by output forgetting, such as low forget-set accuracy or reduced logit-level membership inference. But if output-level success can coexist with retraining-inconsistent residuals in representation space, what kind of forgetting are current evaluations actually certifying? We study this question through retraining-consistent representation forgetting, using the retrained model (i.e., trained from scratch without the forget data) as an operational reference for correct forgetting. Across multiple unlearning methods, datasets, and models, our theoretical analysis and empirical results show that standard output-level evaluation can systematically overestimate the success of unlearning. Under this stronger lens, current methods often appear forgotten at the output layer while exhibiting a structured mismatch relative to retraining. They partially align with retraining on forget samples, remain more inconsistent on retain samples, and leave residual discrepancy concentrated along retraining-related directions rather than diffuse in representation space. This structured mismatch is characterized by forget/retain asymmetry, directional mismatch, and concentrated residuals along retraining-related directions. These results suggest that current MU is often evaluated for apparent forgetting rather than retraining-consistent forgetting. More broadly, retraining reveals what output forgetting hides.

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 claims that standard output-level metrics for machine unlearning (e.g., forget-set accuracy, logit-based membership inference) systematically overestimate success. Using the retrained model (trained from scratch on retain data only) as an operational reference for correct representation-space forgetting, the authors present theoretical analysis and empirical results across multiple unlearning methods, datasets, and models. They report that unlearned models exhibit structured mismatches: partial alignment with retraining on forget samples, greater inconsistency on retain samples, and residual discrepancy concentrated along retraining-related directions rather than diffuse.

Significance. If the empirical patterns hold, the work identifies a concrete limitation in current MU evaluation practices and motivates stronger, representation-consistent criteria. The multi-method, multi-dataset empirical component and the operational use of a retrained reference are strengths that make the overestimation claim testable and falsifiable.

major comments (2)
  1. [Abstract, §3] Abstract and §3 (theoretical analysis): the central claim that output forgetting 'overestimates success' is load-bearing on the premise that deviation from the retrained model's representations constitutes incomplete forgetting. The manuscript does not provide a formal argument or empirical test showing that no other representationally distinct trajectories can achieve effective forgetting (zero membership inference, no reconstruction) while differing from the retrained model; this assumption requires explicit justification or a counter-example analysis.
  2. [Empirical results (§4–5)] Empirical results section (likely §4–5): the reported forget/retain asymmetry and directional concentration are interpreted as evidence of incomplete forgetting, but the paper does not report whether these mismatches correlate with actual downstream risks (e.g., increased reconstruction success or membership inference beyond output level). Without that link, the structured mismatch alone does not yet demonstrate overestimation of unlearning success.
minor comments (2)
  1. [Methods] Notation for 'retraining-consistent representation forgetting' is introduced in the abstract but would benefit from an explicit definition or equation in the methods section to avoid ambiguity with standard representation similarity measures.
  2. [Figures] Figure captions should explicitly state the number of runs, random seeds, and statistical significance tests used for the reported asymmetries and directional concentrations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments highlight important areas for strengthening the justification of our central claim and the empirical linkage to downstream risks. We address each point below and will incorporate revisions accordingly.

read point-by-point responses
  1. Referee: [Abstract, §3] Abstract and §3 (theoretical analysis): the central claim that output forgetting 'overestimates success' is load-bearing on the premise that deviation from the retrained model's representations constitutes incomplete forgetting. The manuscript does not provide a formal argument or empirical test showing that no other representationally distinct trajectories can achieve effective forgetting (zero membership inference, no reconstruction) while differing from the retrained model; this assumption requires explicit justification or a counter-example analysis.

    Authors: We agree that the operational use of the retrained model as the reference for true forgetting requires explicit justification. In the revised manuscript, we will expand §3 with a formal argument establishing that retraining from scratch on the retain set is the unique trajectory guaranteeing removal of forget-set influence (as any representationally distinct model retains latent structure from the forget data). We will also include a brief discussion of why output-level success on alternative trajectories does not constitute complete forgetting under a representation-consistent definition. revision: yes

  2. Referee: [Empirical results (§4–5)] Empirical results section (likely §4–5): the reported forget/retain asymmetry and directional concentration are interpreted as evidence of incomplete forgetting, but the paper does not report whether these mismatches correlate with actual downstream risks (e.g., increased reconstruction success or membership inference beyond output level). Without that link, the structured mismatch alone does not yet demonstrate overestimation of unlearning success.

    Authors: We acknowledge this limitation in the current empirical presentation. In the revised version of §4–5, we will add correlation analyses between the reported representation mismatch metrics (forget/retain asymmetry and directional concentration) and downstream risks, specifically reconstruction attack success rates and advanced membership inference performance beyond output logits. This will directly link the observed structured mismatches to overestimation of unlearning success. revision: yes

Circularity Check

0 steps flagged

No significant circularity; retrained model serves as independent external reference

full rationale

The paper's core evaluation compares unlearned models against a separately trained retrained model (trained from scratch on data excluding the forget set). This reference is constructed independently of any unlearning method outputs or fitted parameters within the paper. No equations or claims reduce a 'prediction' or result to the inputs by construction, no self-citations are load-bearing for the central argument, and no ansatz or uniqueness theorem is smuggled in. The derivation chain is self-contained against this external benchmark, consistent with the low circularity expectation for papers using independent references.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review is limited to the abstract; no free parameters, invented entities, or additional axioms are identifiable from the provided text.

axioms (1)
  • domain assumption The retrained model serves as the correct operational reference for true forgetting.
    Explicitly invoked in the abstract as the basis for measuring representation forgetting.

pith-pipeline@v0.9.1-grok · 5741 in / 1154 out tokens · 34177 ms · 2026-06-26T00:03:32.594864+00:00 · methodology

discussion (0)

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Reference graph

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