Pith. sign in

REVIEW 2 major objections 6 minor 2 cited by

Machine unlearning can be done by learning a lightweight transformation over a model's representations that compresses out the data to be forgotten—leaving the weights untouched—and this approach rivals retraining in utility while being hun

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 06:54 UTC pith:EGM7EU6H

load-bearing objection A genuinely new representation-level unlearning framework with strong class-unlearning results, but the abstract overclaims and the paper's own random-unlearning MIA numbers undercut it. the 2 major comments →

arxiv 2601.21564 v2 pith:EGM7EU6H submitted 2026-01-29 cs.LG

Representation Unlearning: Forgetting through Information Compression

Antonio Almud\'evar , Alfonso Ortega This is my paper
classification cs.LG
keywords machine unlearningrepresentation spaceinformation bottleneckzero-shot unlearningneural collapseprivacymembership inferencevariational bounds
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Machine unlearning typically edits a model's weights to erase the influence of designated data. This paper argues that a cheaper, more reliable route is to leave the weights alone and learn a small transformation over the model's penultimate-layer representations that compresses away information about the forget set while preserving information about the retain set. The paper derives variational upper bounds that turn this information bottleneck into tractable losses, and instantiates them both with access to retain data and in a zero-shot setting that uses only the forget set plus per-class counts and classifier weights. Across CIFAR-10, CIFAR-100, and Tiny ImageNet it reports near-perfect forgetting with retain accuracy close to retraining, and speed-ups of up to 754x over retraining in the zero-shot case. If the approach holds, unlearning becomes a lightweight post-processing step rather than a destabilizing parameter update.

Core claim

Representation Unlearning replaces weight-centric unlearning with an information bottleneck over frozen-feature representations. The transformation f_phi maps the penultimate-layer activation z to z' such that I(Z'; Z | X_r) is minimized while I(Z'; X_f) is driven to zero. Because both mutual-information terms are intractable, the paper derives variational upper bounds whose Gaussian parameterization reduces the KL terms to squared Euclidean distances, giving simple MSE losses: L_r penalizes deviation of retained representations from their original positions, and L_f pushes transformed forget representations toward the aggregate statistics of the whole dataset. In the zero-shot regime the pa

What carries the argument

The central object is the representation transformation f_phi: a lightweight linear map or shallow MLP applied to the penultimate-layer activations, chosen so that the transformed space satisfies an information bottleneck. The framework's engine is a pair of variational upper bounds—one upper-bounding I(Z'; Z | X_r) (retain fidelity) and one upper-bounding I(Z'; X_f) (forget erasure)—whose Gaussian parameterization collapses the KL divergences into MSE terms. In the zero-shot variant, the load-bearing device is the Neural Collapse assumption: in the terminal phase of training, class-conditional feature means collapse to the linear classifier weights w_c, so the paper uses w_c as synthetic 'a

Load-bearing premise

The zero-shot regime assumes Neural Collapse holds exactly—class-conditional features are point masses at the classifier weight vectors—so if the pre-trained model is not in the terminal training phase, the proxy anchors misestimate the representation distribution and both zero-shot losses are miscalibrated.

What would settle it

Train the same architectures to a state measurably short of neural collapse (e.g., early-stopped or with heavy regularization, where class-conditional covariance is high) and run the zero-shot variant: if forget-set membership inference accuracy and forget-class accuracy no longer drop to near-retrain levels, then the collapse proxies are the load-bearing element. Concretely, measure the ratio of average within-class covariance to between-class spread in the penultimate layer and check whether zero-shot unlearning quality degrades monotonically as that ratio grows.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the claims hold, unlearning can be reduced to post-processing a frozen encoder: a single lightweight adapter trained once, with no backward passes through the backbone and no parameter perturbation.
  • The zero-shot setting becomes practical: only forget data, class counts, and classifier weights are needed, which widens applicability to cases where retain data is hidden behind privacy or storage constraints.
  • The extreme speed-ups (up to 754x over retraining) suggest unlearning can be served as an on-demand, per-request operation even for large models, changing the economics of regulatory compliance.
  • Retain accuracy staying close to retrained-model levels implies the method preserves the original semantic manifold rather than merely masking the forget set.

Where Pith is reading between the lines

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

  • The method's success likely tracks how strongly the pre-trained model satisfies neural collapse; a testable extension is that unlearning quality should degrade as within-class covariance grows relative to between-class spread.
  • An implicit consequence is that the learned transformation is a property of the frozen backbone, so the same adapter might be reused across multiple forget requests or head re-initializations, hinting at a library of re-usable unlearning adapters.
  • The zero-shot loss is essentially a prototype-anchored compression, which suggests a natural extension to continual unlearning where prototypes are updated as new classes arrive, or to federated settings where only aggregate class statistics are shared.
  • The random-unlearning results suggest the right adapter capacity is task-dependent: deeper adapters strengthen privacy but risk utility collapse, so an automatic capacity schedule based on measured feature geometry could be a useful follow-up.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The manuscript introduces Representation Unlearning, an unlearning framework that leaves the pretrained backbone parameters fixed and instead learns a transformation f_phi on penultimate-layer representations. The objective is an information bottleneck: retain information about D_r and suppress information about D_f. Variational upper bounds are derived for I(Z';Z|X_r) and I(Z';X_f) (Eqs. 2, 6, 12, 15, 16, 19), and Gaussian parameterizations reduce the losses to squared-error objectives. Two regimes are considered: a standard setting with access to both retain and forget data, and a zero-shot setting that uses only forget data plus class-count metadata, relying on the Neural Collapse assumption to replace class-conditional densities by classifier weight vectors. Experiments on CIFAR-10, CIFAR-100, and Tiny ImageNet compare against retraining, fine-tuning, SISA, SCRUB, UNSIR, Bad Teacher, and zero-shot baselines, with additional results on speed-up, GPU memory, and hyperparameter sensitivity.

Significance. The representation-space formulation is a genuinely distinct design point for unlearning and, if confirmed, offers a useful alternative to parameter-centric methods. The variational derivations are mathematically sound, the class-unlearning results are strong (near-zero forget accuracy while retaining utility), and the reported computational and memory advantages are substantial. Code is provided. However, the random-unlearning membership-inference results directly contradict the abstract's unconditional claim of 'more reliable forgetting', and the zero-shot variant rests on an unvalidated Neural Collapse assumption. These two issues are load-bearing for the central claims and need to be addressed before the paper can be accepted.

major comments (2)
  1. [Section 4.3, Table 2] The abstract and Section 4.3 claim 'more reliable forgetting' and state that Rep. Unl.'s MIA scores 'mirror the Retraining baseline'. Table 2 contradicts this. For random unlearning, Retraining MIA is 53.5/67.1/68.4 on CIFAR-10/100/Tiny ImageNet, while Rep. Unl. MIA is 55.7/74.0/80.5. The paper itself defines the ideal MIA as the value closest to the Retraining baseline; by that criterion, Rep. Unl. is not close (gaps of 2.2, 6.9, and 12.1 points). On CIFAR-100 and Tiny ImageNet, Fine-tuning and SISA are closer to Retraining than Rep. Unl. is. The sentence 'its MIA scores are slightly conservative, they mirror the Retraining baseline' is numerically false, and the difference is large enough to undermine the headline claim. The authors should either restrict the 'reliable forgetting' claim to class unlearning, add a privacy analysis with other MIA settings, or present a different metric t
  2. [Section 3.4, Eqs. (8)-(9), (10), (20)] The zero-shot losses are derived under the assumption that p_theta(z|y=c) ≈ delta(z - w_c) and r_theta(z'|y=c) = N(w_c, I). This is exact only in the terminal phase of training under Neural Collapse. The paper provides no diagnostic that the ResNet/WideResNet/ResNet-34 encoders used in the experiments are in that regime, nor any measurement of how far the class-conditional feature distributions are from the delta approximation. If the classifier weights are not accurate proxies for the class-conditional representation distributions, Eqs. (10) and (20) are not necessarily upper bounds on the true mutual-information terms, and the theoretical justification for the zero-shot setting fails. I recommend adding explicit NC diagnostics — e.g., within-class covariance norms and distances between class means and classifier weight vectors for each dataset/backbone — or relaxing the assumption and
minor comments (6)
  1. [Appendix F, Figure 10] The main text and Table 2 refer to MIA accuracy, while Figure 10 and its caption refer to MIA AUC. These are different evaluation quantities; please use one consistent metric and define the thresholding/attack setup.
  2. [Algorithms 1 and 2, Appendix B] The pseudocode omits the 1/2 factor that appears in Eqs. (5), (17), (10), and (20). The factor does not affect optimization, but the inconsistency should be fixed.
  3. [Eq. (5)] The factor 1/(B_r M) is undefined; if M denotes a number of Monte Carlo samples per input, state this explicitly, otherwise simplify the notation.
  4. [Figure 4 caption] The caption says 'Representation Learning methods are highlighted in red'; this should read 'Representation Unlearning methods'.
  5. [Table 1] In the SISA Tiny ImageNet row, the entry '58.9±0 58.2±2' is missing a separator and appears to be two numbers concatenated.
  6. [Section 4.1, Figure 3] The 2D illustration is only qualitative. A simple quantitative measure (e.g., centroid distances or retain-set accuracy) would make the visual claim more verifiable.

Circularity Check

0 steps flagged

No significant circularity: the MI upper-bound derivation is self-contained; no fitted quantity is renamed as a prediction and no load-bearing self-citation appears.

full rationale

The paper's derivation chain is a standard variational treatment. Equations 2, 6, 12, 16, and 19 are upper bounds obtained from the definition of mutual information, the non-negativity of KL divergence, and Jensen's inequality; none of these bounds assume the target mutual-information values, and the later Gaussian parameterizations and Monte Carlo estimates are ordinary tractability substitutions rather than fitted predictions. The only tunable scalar, beta, is fixed at 1e-3 through sensitivity analysis (Section 4.5) and is not selected to reproduce the Retraining MIA baseline, so the forgetting results are empirical outcomes rather than constructions. The zero-shot regime relies on the Neural Collapse proxy (Eqs. 8-9), which is an external hypothesis (Papyan et al., 2020) used as an approximation; even if that assumption is empirically questionable, it does not make the derivation circular. There is no load-bearing self-citation: the cited prior unlearning works are external baselines, and no uniqueness theorem or prior result by the same authors is invoked to force the framework. The apparent contradiction between the abstract's 'more reliable forgetting' and Table 2's MIA numbers is a correctness/empirical-support issue, not a circularity issue. Thus the paper receives a non-finding with score 0.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

No new physical or formal entities are introduced; the transformation f_φ is a standard adapter parameterized by φ. The only free parameters are β and adapter depth, both tuned via validation. The zero-shot method depends on the unvalidated Neural Collapse assumption, which is the highest-risk axiom.

free parameters (2)
  • β (forget-regularization weight) = 1e-3
    Chosen by sensitivity analysis across all datasets (Section 4.5); controls the unlearning/utility trade-off.
  • adapter depth = 0 hidden layers (standard), 1 hidden layer (zero-shot)
    Selected via ablation (Section 4.5); linear suffices with retain data, one hidden layer needed without.
axioms (6)
  • domain assumption Markov chain X_r → Z → Z'
    Assumed in Appendix A.1 to factor p_φ(z'|z,x)=p_φ(z'|z); standard in VIB-type methods.
  • standard math Encoder is deterministic delta p_θ(z|x)=δ(z−e_θ(x))
    Defined in Section 3.1; used throughout the derivations.
  • ad hoc to paper Gaussian parameterization of p_φ and r_θ with identity covariance
    Eqs. 3-4; chosen for closed-form KL (MSE). This is a modeling convenience, not an empirical fact.
  • domain assumption Neural Collapse: p_θ(z|y)≈δ(z−w_c), r_θ(z'|y)=N(w_c,I)
    Eqs. 8-9; required for zero-shot losses. Assumes terminal-phase training and class-conditional collapse.
  • domain assumption Linear Representation Hypothesis
    Invoked to justify linear/shallow adapter (Section 3.2); not validated for the specific models used.
  • standard math Joint convexity of the KL divergence (Jensen's inequality)
    Used in Eq. 15 to bound the mixture KL; a standard mathematical tool.

pith-pipeline@v1.3.0-alltime-deepseek · 23166 in / 16341 out tokens · 165024 ms · 2026-08-03T06:54:42.019642+00:00 · methodology

0 comments
read the original abstract

Machine unlearning seeks to remove the influence of specific training data from a model, a need driven by privacy regulations and robustness concerns. Existing approaches typically modify model parameters, but such updates can be unstable, computationally costly, and limited by local approximations. We introduce Representation Unlearning, a framework that performs unlearning directly in the model's representation space. Instead of modifying model parameters, we learn a transformation over representations that imposes an information bottleneck: maximizing mutual information with retained data while suppressing information about data to be forgotten. We derive variational surrogates that make this objective tractable and show how they can be instantiated in two practical regimes: when both retain and forget data are available, and in a zero-shot setting where only forget data can be accessed. Experiments across several benchmarks demonstrate that Representation Unlearning achieves more reliable forgetting, better utility retention, and greater computational efficiency than parameter-centric baselines.

Figures

Figures reproduced from arXiv: 2601.21564 by Alfonso Ortega, Antonio Almud\'evar.

Figure 1
Figure 1. Figure 1: The model is first trained on both the retain set Dr (blue) and the forget set Df (red), leading the learned representation Z to encode information from both. Representation Unlearning seeks to learn a transformation fϕ that maps Z to a new representation Z ′ in which information attributable to Df is removed while information relevant to Dr is preserved. 2. Related Work Baselines and Exact Methods in Mach… view at source ↗
Figure 2
Figure 2. Figure 2: I(Z ′ ;Z | Xr) > 0 indicates that the transforma￾tion fϕ removes some information relevant to Xr. Conversely, I(Z ′ ; Xf ) > 0 indicates that fϕ does not fully eliminate informa￾tion associated with Xf . 3.3. How to Retain Information about Dr The first objective of machine unlearning is to preserve per￾formance on the retain set. In our information-theoretic formulation, this requires that the transformed… view at source ↗
Figure 3
Figure 3. Figure 3: Mechanistic Comparison of Unlearning Regimes. (a) The original space shows the forget class (yellow stars) as a distinct cluster. (b) With retain data, the forget samples collapse into the adjacent manifold while retain clusters remain stable. (c) In the zero-shot setting, the forget class exhibits a similar collapse, validating the proxy anchors, albeit with slightly increased modification to the retain r… view at source ↗
Figure 4
Figure 4. Figure 4: Evaluation of Computational Efficiency. A comparison of speed-up relative to full retraining for class unlearning on the CIFAR-10, CIFAR-100, and Tiny ImageNet datasets. Representation Learning methods are highlighted in red. 0 1 2 1e-04 1e-03 1e-02 1e-01 0.39 0.40 0.39 0.36 0.38 0.40 0.37 0.43 0.43 0.41 0.45 0.44 (a) Cls. C10 0 1 2 1e-04 1e-03 1e-02 1e-01 0.89 0.91 0.97 0.88 0.95 1.14 1.29 2.85 5.63 3.38 … view at source ↗
Figure 5
Figure 5. Figure 5: Hyperparameter Sensitivity Analysis. Effect of regularization strength β (y-axis) and transformation depth (x-axis, number of hidden layers) on distributional fidelity. Values denote Test Cross-Entropy (CE) relative to the Retrain baseline, where lower values indicate better preservation of the original model’s probability landscape. 5. Conclusion In this work, we introduced a novel framework for ma￾chine … view at source ↗
Figure 6
Figure 6. Figure 6: Peak GPU Memory Usage (MB). Comparison of peak memory allocation across different methods. Our proposed frameworks (Rep. Unl. and Rep. Unl. ZS) consistently require the lowest memory footprint across all datasets, scaling efficiently from CIFAR-10 to Tiny ImageNet. CIFAR-10 Results As shown in Figure 6a, our method demonstrates exceptional efficiency on the CIFAR-10 benchmark. Rep. Unl. ZS operates with a … view at source ↗
Figure 7
Figure 7. Figure 7: Test Ar in Class Unlearning. Regularization strength β (y-axis) and transformation depth (x-axis, number of hidden layers) Impact on Forget Accuracy (Af ) We observe a strong inverse correlation between regularization strength β and forget accuracy Af . Effect of Regularization. Increasing β consistently drives Af towards zero, ensuring effective unlearning. On Tiny ImageNet (Non-ZS), shifting β from 10−4 … view at source ↗
Figure 8
Figure 8. Figure 8: Test Af in Class Unlearning. Regularization strength β (y-axis) and transformation depth (x-axis, number of hidden layers) F.2. Random Data Unlearning Protocol In the random data unlearning scenario, we evaluate the method’s ability to defend against membership inference attacks (MIA) while preserving utility. Impact on Retain Accuracy (Ar) Random data unlearning exhibits significantly higher sensitivity t… view at source ↗
Figure 9
Figure 9. Figure 9: Train Ar in Random Data Unlearning. Regularization strength β (y-axis) and transformation depth (x-axis) MIA Efficacy and Privacy (Amia) We evaluate the defense against membership inference attacks, where an AUC of 50% represents ideal privacy (random guessing). Effect of Regularization. Increasing β consistently lowers MIA AUC, reducing information leakage. On CIFAR-10 (Non-ZS), the AUC drops from ∼ 57.8%… view at source ↗
Figure 10
Figure 10. Figure 10: MIA AUC in Random Data Unlearning. Regularization strength β (y-axis) and transformation depth (x-axis) 20 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Gradient Concentration, Not Weight Saliency, Explains Representation-Level Class Unlearning

    cs.LG 2026-07 accept novelty 7.0

    In class unlearning on CIFAR-10/100 with ResNet-18, the identity of saliency-selected weights does not affect representation-level recovery; late-layer gradient concentration and representation geometry drive the outcome.

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

    cs.LG 2026-06 unverdicted novelty 5.0

    Output forgetting in machine unlearning overestimates success because unlearned models exhibit structured representation mismatches relative to retraining from scratch.

Reference graph

Works this paper leans on

12 extracted references · 10 linked inside Pith · cited by 2 Pith papers

  1. [1]

    and Bengio, Y

    Alain, G. and Bengio, Y . Understanding intermediate layers using linear classifier probes.arXiv preprint arXiv:1610.01644,

    Pith/arXiv arXiv

  2. [5]

    Toy Dataset Details We use a synthetic toy classification dataset generated from a C-component isotropic Gaussian mixture in Rd, with C= 6 classes and d= 10 features

    Optimization Step 13:ϕ←ϕ−η∇ ϕ(Lzs r +βL zs f ) 14:end while 15:returnUnlearned parametersϕ ∗ 13 Representation Unlearning: Forgetting through Information Compression C. Toy Dataset Details We use a synthetic toy classification dataset generated from a C-component isotropic Gaussian mixture in Rd, with C= 6 classes and d= 10 features. Classes are balanced,...

    2000

  3. [6]

    Towards unbounded machine unlearning.Advances in neural information processing systems, 36:1957–1987,

    Kurmanji, M., Triantafillou, P., Hayes, J., and Triantafillou, E. Towards unbounded machine unlearning.Advances in neural information processing systems, 36:1957–1987,

    1957

  4. [7]

    Federated unlearning.arXiv preprint arXiv:2012.13891,

    Liu, G., Ma, X., Yang, Y ., Wang, C., and Liu, J. Federated unlearning.arXiv preprint arXiv:2012.13891,

    Pith/arXiv arXiv 2012

  5. [2016]

    A., Fischer, I., Dillon, J

    Alemi, A. A., Fischer, I., Dillon, J. V ., and Murphy, K. Deep variational information bottleneck.arXiv preprint arXiv:1612.00410,

    Pith/arXiv arXiv

  6. [2017]

    Influence functions in deep learning are fragile.arXiv preprint arXiv:2006.14651,

    Basu, S., Pope, P., and Feizi, S. Influence functions in deep learning are fragile.arXiv preprint arXiv:2006.14651,

    Pith/arXiv arXiv 2006

  7. [2018]

    J., and Veitch, V

    Park, K., Choe, Y . J., and Veitch, V . The linear represen- tation hypothesis and the geometry of large language models.arXiv preprint arXiv:2311.03658,

    Pith/arXiv arXiv

  8. [2020]

    Progress measures for grokking via mechanistic interpretability.arXiv preprint arXiv:2301.05217,

    Nanda, N., Chan, L., Lieberum, T., Smith, J., and Stein- hardt, J. Progress measures for grokking via mechanistic interpretability.arXiv preprint arXiv:2301.05217,

    Pith/arXiv arXiv

  9. [2021]

    G., Athalye, A., and Mueller, J

    Northcutt, C. G., Athalye, A., and Mueller, J. Pervasive la- bel errors in test sets destabilize machine learning bench- marks.arXiv preprint arXiv:2103.14749,

    Pith/arXiv arXiv

  10. [2022]

    C., and Bialek, W

    Tishby, N., Pereira, F. C., and Bialek, W. The informa- tion bottleneck method.arXiv preprint physics/0004057,

    Pith/arXiv arXiv

  11. [2023]

    S., Tarun, A

    Chundawat, V . S., Tarun, A. K., Mandal, M., and Kankan- halli, M. Can bad teaching induce forgetting? unlearn- ing in deep networks using an incompetent teacher. In Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 37, pp. 7210–7217, 2023a. Chundawat, V . S., Tarun, A. K., Mandal, M., and Kankan- halli, M. Zero-shot machine unlearni...

    Pith/arXiv arXiv

  12. [2024]

    On large language model continual unlearning.arXiv preprint arXiv:2407.10223,

    Gao, C., Wang, L., Ding, K., Weng, C., Wang, X., and Zhu, Q. On large language model continual unlearning.arXiv preprint arXiv:2407.10223,

    Pith/arXiv arXiv