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REVIEW 5 major objections 4 minor 107 references

A two-stage unlearning pipeline removes deleted user–item interactions from trained recommenders while keeping recommendation quality near retrained levels, at a fraction of the retraining cost.

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2026-08-02 09:22 UTC pith:AQ5KQRLI

load-bearing objection A practical two-stage unlearning recipe for recommenders, but the curvature-aware theory rests on an unmeasured assumption and the empirical story is single-run synthetic; worth refereeing with the right asks. the 5 major comments →

arxiv 2607.22665 v1 pith:AQ5KQRLI submitted 2026-06-30 cs.AI

Obliviate: Efficient Unlearning in Recommender Systems

Tushar Prakash , Brijraj Singh , Niranjan Pedanekar , Narayan Chaturvedi This is my paper
classification cs.AI
keywords machine unlearningrecommender systemsright to be forgottenlow-rank adapterssecond-order optimizationinfluence functionsknowledge distillationdeletion set
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.

The paper sets out to show that the right to be forgotten can be honored in recommender systems without retraining from scratch. Its central claim is that removing a deletion set S from a trained model reduces to estimating the parameter shift θ*_{-S} ≈ θ0 − H^{-1} g_S, where g_S is the aggregate gradient of the deleted interactions and H is the local curvature. Obliviate operationalizes that shift in two stages: a Low-Rank Unlearning Adapter computes a Newton-style downdate using a cheap diagonal curvature proxy taken from Adam's second-moment statistics and projects it onto low-rank adapters; a Locality-Aware Calibration stage then refines only those adapters, demoting deleted interactions below negatives while distilling the original model's scores on a small retained buffer. If the central claim is right, large-scale platforms can process deletion requests in seconds rather than minutes or hours, with completeness and utility that closely track exact retraining.

Core claim

Obliviate's core discovery is that the optimization shift induced by deleting a set of interactions can be approximated as θ*_{-S} ≈ θ0 − H^{-1} g_S, so unlearning becomes a single second-order correction rather than a re-optimization. Because the full Hessian is intractable, the paper reuses the diagonal preconditioner already computed by Adam during training, bH = diag(sqrt(v_hat) + ε), to approximate H^{-1}; the downdate is then computed per-coordinate as −(g_S)_j / (sqrt(v_hat_j) + ε), applied only to the most affected user/item embedding blocks, and compressed into a rank-r adapter via truncated SVD. A second stage, Locality-Aware Calibration, freezes the backbone and optimizes only the

What carries the argument

The load-bearing identity is Eq. (5): θ*_{-S} ≈ θ0 − H^{-1} g_S, the second-order unlearning approximation. It says the difference between a model trained on the full data and one retrained without the deletion set is, to first order in the parameter shift, the deletion gradient g_S scaled by the inverse Hessian H. The practical machinery is diagonal preconditioning: Obliviate reuses Adam's per-coordinate second-moment estimates to form bH = diag(sqrt(v_hat) + ε), turning the Newton step into per-coordinate scaling; a truncated SVD projects the resulting downdate onto a low-rank adapter, making the update modular and reversible; and the witness set S ∪ Neg(S) ∪ R feeds a BPR unlearning loss

Load-bearing premise

Everything rests on the claim that Adam's second-moment statistics can stand in for the true curvature of the loss; if this diagonal surrogate is not accurate, the Newton-style unlearning update is just a scaled gradient step and the guarantee that the unlearned model matches retraining falls apart.

What would settle it

Compute the actual relative preconditioner error ||I − bH^{-1}H||_2 for a small trained recommender (for example, MF-BPR on ML-1M) by forming the exact Hessian of the full-data objective; if the error is close to or greater than 1 on the subspace touched by the deletion set, the paper's distance-to-retrain bound is vacuous. Equivalently, compare Obliviate's final parameters with a truly retrained model's parameters on a real, non-synthetic deletion set: if the Euclidean distance grows much faster than the bound predicts, or if a membership-inference probe can still detect deleted interactions,

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

If this is right

  • Deletion requests become cheap enough to honor repeatedly: unlearning runs in seconds (about 20 seconds on ML-1M with MF-BPR) versus hundreds of seconds for retraining, so frequent right-to-be-forgotten requests no longer require a retraining queue.
  • Because updates are confined to low-rank adapters on a frozen backbone, unlearning is modular and reversible, and repeated deletion requests could be composed by stacking or resetting adapters without touching the base model.
  • The method is demonstrated for deletion ratios as high as 20% of users and for both MF-BPR and graph-based LightGCN, suggesting it generalizes across common recommender architectures and sparse or dense datasets.
  • Unlearning completeness is visible in ranking behavior: after Obliviate, deleted interactions are demoted below sampled negatives at higher rates than prior approximate unlearning methods, close to what exact retraining would produce.
  • The synthetic-deletion evaluation protocol (injecting low-preference interactions as the deletion set) gives the community a way to measure unlearning quality without confounding it with distribution shift, making baseline comparisons cleaner.

Where Pith is reading between the lines

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

  • If Adam's second-moment surrogate is as accurate as assumed, the same mechanism could transfer to other models trained with Adam: any optimizer state that estimates per-coordinate gradient variance provides a free curvature proxy for unlearning. A direct measurement of the relative preconditioner error on small models would tell whether the transfer is safe.
  • Because the paper evaluates on synthetic deletions to avoid confounding, a natural next test is real user requests, where removing genuine preferences also shifts the evaluation distribution; completeness should still hold, but utility should be compared against a model retrained on the same deleted data rather than against the original model.
  • The BPR demotion objective certifies completeness in ranking terms, not in parameter or membership terms; a stronger privacy probe, such as membership inference or canary-parameter checking, could reveal residual traces that the Demotion Rate metric misses.

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

5 major / 4 minor

Summary. The paper proposes Obliviate, a two-stage unlearning framework for recommender systems. Stage I (LUA) computes a deletion-set gradient, applies a curvature-scaled downdate using a diagonal Adam second-moment proxy, and projects the resulting parameter shift onto low-rank adapters. Stage II (LAC) calibrates only the adapter parameters, using a BPR-style loss on the deleted set plus a distillation loss on a retained buffer. Experiments on ML-1M, Amazon, and Yelp with MF-BPR and LightGCN report utility close to or above the original model, high post-unlearning demotion rates, and large speedups over full retraining.

Significance. If the central approximation is valid, Obliviate is a practically appealing approach: it keeps the backbone frozen, makes unlearning modular and reversible, and avoids full Hessian computation. The paper also provides a detailed theoretical appendix with explicit error decompositions and an honest limitation statement about the Adam-based curvature proxy. However, the main theoretical guarantee rests on an unmeasured and questionable assumption about the preconditioner, and the empirical evaluation relies entirely on a synthetic deletion protocol with no error bars. The contribution is therefore significant only conditionally on those points being resolved.

major comments (5)
  1. [Appendix K, Assumption K.4 and Eq. (7)] Theorem K.12's distance-to-retrain bound requires ||I - bH^{-1}H||_2 <= eps_H < 1, where bH is the Adam second-moment diagonal. The paper never measures this quantity or checks Assumption H.6. For MF-BPR and LightGCN the Hessian is not diagonal dominant: it contains off-diagonal user-item blocks, and in LightGCN the graph propagation couples many coordinates. Adam's v_hat is a variance estimate, not a curvature estimate, so the claimed 'curvature-aware' character of the downdate is unsupported. If K.4 fails, the update is just a scaled gradient step and the end-to-end bound collapses. Please report the empirical value of ||I - bH^{-1}H|| on the actual models/datasets, and if it does not satisfy the assumption, weaken the theoretical claim or replace the proxy.
  2. [§3.2 and Appendix F] All experiments are run under a synthetic deletion protocol in which the deletion set consists of injected low-preference interactions. This is a legitimate robustness check, but it does not demonstrate unlearning of genuine user interactions, which is the stated GDPR/CCPA motivation. Removing synthetic noise may improve utility, while removing real interactions changes the data distribution. The abstract's claim of 'deletion ratios as high as 20% of the data' is also inconsistent with the experiments, which delete interactions from 20% of users. Please add at least one real-deletion experiment, state the actual fraction of interactions deleted, and scope the claims accordingly.
  3. [Tables 1 and 2] For a fixed backbone and dataset, the retrained model should be a common baseline, yet IFRU's Retrained row on ML-1M MF-BPR reports R@10 = 0.1179 while RRL and Obliviate report 0.1265. Table 2 likewise reports different retraining times for the same backbone/data condition (e.g., 975s for IFRU vs 533.5s for Obliviate on ML-1M MF-BPR). This suggests the methods were not compared against a consistent retrained checkpoint, making the utility and speedup comparisons hard to interpret. Please use one retrained model per backbone/data set for all methods, or clearly justify why separate retrained rows are method-specific.
  4. [Eq. (16) and Eqs. (13)–(14)] The completeness metric, Demotion Rate, is the same ranking objective that LAC optimizes with its BPR unlearning loss. Reporting it as the main evidence of forgetting is therefore circular: the method is evaluated on a quantity it directly trains. In addition, Algorithm 1 and the witness set in Eq. (12) use the deleted set S after unlearning, which conflicts with the premise that the data has been erased. Please provide an independent completeness check (e.g., parameter distance to retraining, membership inference, or score behavior on held-out probes not used in calibration) and explicitly justify or drop the post-deletion use of S.
  5. [Tables 1–3 and Fig. 3] No standard deviations, multiple seeds, or statistical tests are reported. Many utility differences are extremely small — in Table 3 the ablation differences at R@20 are around 0.001–0.003 — so the 'consistent drops/gains' claims cannot be evaluated. Please report mean±std over at least five seeds and, if possible, paired significance tests. This is necessary to support the empirical contribution.
minor comments (4)
  1. [§2.1.1] The text 'J−S(θ0) = −gs' should read '∇J−S(θ0) = −g_S'.
  2. [Table 1] For SISA and RecEraser, the Retrained row is all dashes. It would be clearer to state explicitly that no full-retrained comparator is reported for these baselines, or to add one.
  3. [Abstract vs. §3.2] The abstract says 'deletion ratios (as high as 20% of the data)' while the experiments inject 80% of interaction counts for 20% of users. Please state the true percentage of total deleted interactions and use consistent terminology.
  4. [Appendix H.4.2] The proof of Theorem H.5 is essentially the same as that of Theorem H.1; consider condensing to avoid repetition.

Circularity Check

1 steps flagged

Completeness is measured by the exact BPR objective LAC optimizes; the parameter derivation itself is not circular.

specific steps
  1. fitted input called prediction [Section G, Eq. (16); Section 2.2.2, Eq. (14); Tables 6 and 7]
    "DemotionRate = Pr[s(u, idel)< s(u, ineg)].(16) ... This metric directly reflects the retraining objective. ... is naturally aligned with the BPR objective used during calibration."

    LAC's unlearning loss is ℓ_BPR(u,i+,i−) = −log σ(s(u,i−;θ(ϕ))−s(u,i+;θ(ϕ))) with i+ a deleted item and i− a sampled negative. Minimizing this loss directly increases Pr[s(u,i−)>s(u,i+)], which is exactly the Demotion Rate of Eq. (16). Thus the post-unlearning Demotion Rate reported as evidence of forgetting is the calibration objective evaluated on the deletion set, not an independent measure of closeness to retraining. The paper even states the metric is 'naturally aligned with the BPR objective used during calibration', so the completeness improvement is forced by construction.

full rationale

The core parameter-update derivation is not circular: Eq. (5) is the standard influence-function/Newton downdate derived from the deletion gradient g_S and the local Hessian, not fitted to the retrained optimum θ*_{−S}; LUA and LAC are validated against external retrained models and prior baselines on Recall/NDCG. The circularity is confined to the completeness evaluation: Demotion Rate (Eq. 16) measures exactly the ranking event that LAC's BPR loss (Eq. 14) is trained to maximize on S∪Neg(S). Therefore the large before/after Demotion Rate gaps in Tables 6–7 are largely a restatement of the calibration objective, not evidence that the model matches the retrained model's ranking behavior. The paper candidly notes this alignment. Other limitations, such as Assumption K.4 on the Adam-based curvature proxy being unverified, are correctness/robustness concerns rather than circularity. Overall, the framework has independent content and the utility comparisons are externally grounded, but the headline completeness claim is partially circular, giving a score of 6.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The core method introduces no new entities, but several hyperparameters are tuned per dataset, and the theoretical soundness rests on unverified approximations about the Hessian and Adam statistics. The evaluation is built on a synthetic deletion protocol rather than real user deletions.

free parameters (5)
  • rank r of low-rank adapter = 4 on ML-1M and Amazon, 6 on Yelp
    Selected from {2,4,6,8,16} based on validation performance (Appendix A).
  • LAC calibration steps T = 160/110/200 (MF-BPR) and 180/150/250 (LightGCN) on ML-1M/Amazon/Yelp
    Chosen based on validation performance to trade off forgetting and utility (Appendix A).
  • retained buffer fraction = 10%
    LAC randomly samples 10% of interactions across all users for distillation (Appendix A).
  • loss weights λ_unlearn, λ_distill, λ_reg = not reported
    The LAC objective (Eq. 13) requires three weights; the paper never states their values, making the exact objective unreproducible.
  • number of hard negatives per deleted interaction = not specified
    The witness set includes Neg(S), but the number of negatives and sampling distribution are not quantified.
axioms (6)
  • domain assumption J−S is locally strongly convex near θ0 (Assumption K.1)
    Required for Theorem 2.1 and all distance bounds; recommender models like LightGCN are non-convex, so this is an assumption, not a given. Section 2.1.2 / Appendix I.
  • ad hoc to paper Adam second-moment diagonal approximates the Hessian diagonal up to scaling (Assumption H.6)
    Needed to justify bH = diag(sqrt(hat_v)+ε) as curvature proxy; no empirical validation.
  • ad hoc to paper Preconditioner relative accuracy ||I − bH^{-1}H|| ≤ ε_H (Assumption K.4)
    Key for Theorem K.10/K.12; value of ε_H is never estimated.
  • domain assumption Deletion curvature is small: ||∇^2J_S(θ0)|| ≤ δ (Assumption K.3)
    Used to replace H by H_{-S}; reasonable only for small deletion sets.
  • domain assumption Score function is Lipschitz in parameters (Assumption K.16)
    Needed for utility deviation bound Proposition K.17.
  • domain assumption Synthetic low-preference deletions are a valid proxy for real deletion requests (Appendix F)
    All empirical completeness/utility results are obtained under this protocol; no experiment on genuine deletion of real interactions.

pith-pipeline@v1.3.0-alltime-deepseek · 27446 in / 15831 out tokens · 141133 ms · 2026-08-02T09:22:35.248084+00:00 · methodology

0 comments
read the original abstract

Machine unlearning is becoming increasingly critical in the context of data privacy regulations, particularly for recommendation systems that are directly trained on user interaction data. The goal of this work is to remove requested interaction data and their downstream influence from trained model while preserving recommendation quality, and to do so without incurring the substantial computational cost of full retraining. Existing approaches exhibit several limitations, including limited unlearning completeness and degradation in recommendation performance, while having substantial computational overhead. In this paper, we propose Obliviate, an efficient two-stage unlearning framework for recommender systems that achieves high unlearning completeness while maintaining good utility. In the first stage, we introduce a Low-Rank Unlearning Adapter (LUA), which employs a lightweight Hessian proxy to enable curvature-aware and efficient unlearning through localized low-rank adapters rather than full parameters. In the second stage, we propose Locality-Aware Calibration (LAC), a lightweight refinement stage that updates only the adapter parameters to improve the performance by enforcing unlearning via ranking-based objectives while preserving utility through knowledge distillation. Extensive empirical evaluations demonstrate that Obliviate achieves high level of forgetting with minimal loss in recommendation quality and at significantly reduced computational cost, offering a practical and scalable solution for large-scale recommender systems.

Figures

Figures reproduced from arXiv: 2607.22665 by Brijraj Singh, Narayan Chaturvedi, Niranjan Pedanekar, Tushar Prakash.

Figure 1
Figure 1. Figure 1: Illustration of the unlearning objective in parameter space. The yellow trajectory signifies the training on the full dataset, which also encounters deletion set (noise). The red trajectory shows a model θ ∗ −S trained from scratch after removing the deletion set interactions. The pink trajectory shows unlearning process that aims at efficiently transforming θ0 into θ−S ≈ θ ∗ −S by estimating and removing … view at source ↗
Figure 2
Figure 2. Figure 2: Overview of Obliviate. LUA performs a curvature-aware low-rank downdate using deletion set S to localize forgetting. LAC then refines the model with deleted samples, hard negatives, and retained data, combining unlearning and distillation losses to produce the final model θ −S with preserved utility. convex in a neighborhood of θ0. Let H = ∇2 θJ(θ0) be the Hessian of the full-data objective. Then, under a … view at source ↗
Figure 3
Figure 3. Figure 3: Completeness: The top row shows a hard unlearning setting with increased calibration and the bottom row shows when the utility is maintained. and RRL show only marginal changes. The improvement is more pronounced on sparse datasets (Amazon, Yelp), where Obliviate achieves the largest and most consistent gains, demonstrating strong preservation of collaborative signals. This stems from our two-stage design:… view at source ↗

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