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arxiv: 2509.22483 · v1 · submitted 2025-09-26 · 💻 cs.LG · cs.AI

OFMU: Optimization-Driven Framework for Machine Unlearning

Sadia Asif , Mohammad Mohammadi Amiri This is my paper

Pith reviewed 2026-05-18 13:01 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords machine unlearningbi-level optimizationgradient decorrelationforgetting efficacymodel utilityconvergence guaranteeslarge language models
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0 comments X p. Extension

The pith

A bi-level optimization framework called OFMU improves the balance between forgetting specific data and retaining model performance in machine unlearning.

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

The paper proposes a new way to handle machine unlearning in large models by using a penalty-based bi-level optimization instead of simple weighted loss combinations. It prioritizes forgetting through an inner maximization step that uses a similarity-aware penalty to reduce conflicting gradients with the retention objective. An outer minimization step then restores utility on the kept data. The method includes a two-loop algorithm with theoretical convergence proofs for both convex and non-convex cases. This matters because it could enable more reliable removal of unwanted knowledge like private or copyrighted information while keeping the model useful overall.

Core claim

OFMU is a penalty-based bi-level optimization framework that enforces forgetting via an inner maximization step incorporating a similarity-aware penalty to decorrelate gradients of the forget and retention objectives, and restores utility through an outer minimization step, supported by a two-loop algorithm with provable convergence guarantees under convex and non-convex regimes, achieving better trade-offs between forgetting efficacy and model utility.

What carries the argument

The bi-level optimization structure where the inner loop maximizes forgetting with a similarity-aware penalty for gradient decorrelation and the outer loop minimizes to preserve retention utility.

If this is right

  • Convergence is guaranteed for the two-loop algorithm in both convex and non-convex settings.
  • Better trade-offs between forgetting efficacy and model utility are achieved compared to prior scalarization methods.
  • Scalability is ensured for large-scale models through the developed algorithm.
  • Consistent outperformance is shown on vision and language benchmarks in forgetting and retained utility.

Where Pith is reading between the lines

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

  • The hierarchical structure might help in scenarios with multiple conflicting objectives beyond unlearning.
  • Future work could test the method on even larger models or in online unlearning settings where data arrives continuously.
  • Connecting to other optimization techniques could further reduce computational overhead.

Load-bearing premise

The similarity-aware penalty term can decorrelate the gradients of forget and retention objectives in practice without adding too much computation or causing training instabilities.

What would settle it

Training a model with the OFMU method on a standard unlearning benchmark and observing no improvement in the forgetting-utility trade-off compared to weighted sum baselines, or seeing the algorithm fail to converge.

Figures

Figures reproduced from arXiv: 2509.22483 by Mohammad Mohammadi Amiri, Sadia Asif.

Figure 1
Figure 1. Figure 1: Coupling of unlearning difficulty with collateral utility loss. Harder samples induce dis￾proportionately large utility degradation for existing methods (GA (Thudi et al., 2022), GradDiff (Maini et al., 2024a)), whereas OFMU mitigates this cou￾pling through its similarity-aware hierarchical up￾dates. Full detail is provided in Appendix 7.4.6. These challenges call for a more princi￾pled and structured appr… view at source ↗
Figure 2
Figure 2. Figure 2: Overall normalized performance of unlearning methods on LLaMA-2 and LLaMA-3 under [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overall normalized performance of unlearning methods on CIFAR-10. The score is obtained by normalizing four key metrics—UA, RA, TA, and MIA Efficacy— within each scenario and averaging them into a unified value. Details of the calculation are given in Appendix 7.4.3. This unified view highlights the balance between forgetting and retention across different forget sce￾narios and shows how OFMU strikes the b… view at source ↗
Figure 4
Figure 4. Figure 4: Embedding similarity with the retrain model for easy vs. hard samples. Easy samples correspond to instances where the base model had low initial confidence, while hard sam￾ples are high-confidence, entangled instances. Scores are computed as cosine similarity of embeddings with a retrained reference model. OFMU maintains competitive similarity on easy samples and significantly stronger robustness on hard s… view at source ↗
Figure 5
Figure 5. Figure 5: Effect of inner-loop steps and penalty parameter [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
read the original abstract

Large language models deployed in sensitive applications increasingly require the ability to unlearn specific knowledge, such as user requests, copyrighted materials, or outdated information, without retraining from scratch to ensure regulatory compliance, user privacy, and safety. This task, known as machine unlearning, aims to remove the influence of targeted data (forgetting) while maintaining performance on the remaining data (retention). A common approach is to formulate this as a multi-objective problem and reduce it to a single-objective problem via scalarization, where forgetting and retention losses are combined using a weighted sum. However, this often results in unstable training dynamics and degraded model utility due to conflicting gradient directions. To address these challenges, we propose OFMU, a penalty-based bi-level optimization framework that explicitly prioritizes forgetting while preserving retention through a hierarchical structure. Our method enforces forgetting via an inner maximization step that incorporates a similarity-aware penalty to decorrelate the gradients of the forget and retention objectives, and restores utility through an outer minimization step. To ensure scalability, we develop a two-loop algorithm with provable convergence guarantees under both convex and non-convex regimes. We further provide a rigorous theoretical analysis of convergence rates and show that our approach achieves better trade-offs between forgetting efficacy and model utility compared to prior methods. Extensive experiments across vision and language benchmarks demonstrate that OFMU consistently outperforms existing unlearning methods in both forgetting efficacy and retained utility.

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 OFMU, a penalty-based bi-level optimization framework for machine unlearning. It prioritizes forgetting via an inner maximization step incorporating a similarity-aware penalty to decorrelate gradients of forget and retention objectives, followed by an outer minimization to restore utility. A two-loop algorithm is introduced with claimed provable convergence guarantees under convex and non-convex regimes, along with theoretical analysis of convergence rates. Experiments on vision and language benchmarks are reported to show improved trade-offs between forgetting efficacy and model utility relative to prior scalarization-based methods.

Significance. If the convergence analysis and empirical trade-offs hold under the stated assumptions, the work would offer a practically relevant advance in scalable machine unlearning for LLMs by addressing gradient conflicts through an explicitly derived penalty term and providing a hierarchical optimization structure with theoretical backing. The two-loop algorithm and its guarantees constitute a clear methodological contribution over standard weighted-sum approaches.

major comments (2)
  1. [Theoretical analysis] Theoretical analysis section: the convergence rate statements for the non-convex regime are stated to hold under Lipschitz smoothness and bounded variance assumptions, yet the manuscript does not provide the explicit dependence of the rate on the penalty coefficient or verify that the similarity-aware term preserves these assumptions in practice for large-scale models; this is load-bearing for the central claim of provable guarantees.
  2. [Experiments] Experimental section: the reported superior trade-offs (e.g., higher forgetting efficacy with retained utility) are shown via benchmarks, but hyperparameter selection for the penalty coefficient, learning rates in the two loops, and exact controls for baseline methods are not detailed; without these, the empirical support for the weakest assumption (stable decorrelation without overhead) cannot be fully assessed.
minor comments (2)
  1. [Method] Notation for the inner and outer objectives could be clarified with explicit equation numbers when first introduced to aid readability of the bi-level formulation.
  2. [Experiments] Figure captions for the convergence plots should include the specific values of the penalty coefficient used in each run.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the methodological contribution of the bi-level optimization approach. We address each major comment below and indicate the planned revisions.

read point-by-point responses

  1. Referee: Theoretical analysis section: the convergence rate statements for the non-convex regime are stated to hold under Lipschitz smoothness and bounded variance assumptions, yet the manuscript does not provide the explicit dependence of the rate on the penalty coefficient or verify that the similarity-aware term preserves these assumptions in practice for large-scale models; this is load-bearing for the central claim of provable guarantees.

    Authors: We acknowledge that the explicit dependence of the non-convex convergence rate on the penalty coefficient is not derived in the current version. The similarity-aware penalty is a smooth quadratic term that preserves the Lipschitz smoothness and bounded-variance assumptions under the stated conditions. To strengthen the central claim, we will add the explicit rate dependence (showing the standard 1/sqrt(T) scaling modulated by the penalty) to the theorem in Section 4 and include a brief empirical verification that the assumptions continue to hold for the large-scale vision and language models used in the experiments. revision: yes

  2. Referee: Experimental section: the reported superior trade-offs (e.g., higher forgetting efficacy with retained utility) are shown via benchmarks, but hyperparameter selection for the penalty coefficient, learning rates in the two loops, and exact controls for baseline methods are not detailed; without these, the empirical support for the weakest assumption (stable decorrelation without overhead) cannot be fully assessed.

    Authors: We agree that additional experimental details are necessary for reproducibility and to fully support the claim of stable decorrelation. In the revised manuscript we will expand the experimental section with the grid-search ranges and final values chosen for the penalty coefficient, the inner- and outer-loop learning rates, and precise descriptions of how each baseline was implemented and tuned (including any early-stopping or regularization controls). These additions will allow readers to assess the overhead and stability of the decorrelation effect. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper formulates machine unlearning as a bi-level optimization problem and introduces a similarity-aware penalty term explicitly constructed to decorrelate gradients between forget and retention objectives. The two-loop algorithm and associated convergence analysis are developed from standard optimization principles with stated assumptions for convex and non-convex regimes. No load-bearing step reduces by the paper's own equations to a self-definition, a fitted parameter renamed as prediction, or a self-citation chain. The central claims rest on independent theoretical derivations and empirical benchmarks rather than circular reductions, making the framework self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The framework depends on the effectiveness of the introduced penalty term and the convergence properties of the two-loop algorithm, both of which require empirical and theoretical validation beyond the abstract.

free parameters (1)
  • penalty coefficient
    Controls the strength of the similarity-aware penalty applied during the inner maximization to decorrelate gradients.
axioms (1)
  • domain assumption The two-loop algorithm converges with provable rates under both convex and non-convex regimes.
    Invoked to justify scalability and theoretical support for the method.
invented entities (1)
  • similarity-aware penalty no independent evidence
    purpose: Decorrelates gradients of forget and retention objectives in the inner maximization step.
    New term introduced to mitigate conflicting gradient directions in the multi-objective unlearning problem.

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Reference graph

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