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Machine Unlearning under Retain–Forget Entanglement

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Machine UnlearningConstrained Optimization
Abstract:

Forgetting a subset in machine unlearning is rarely an isolated task. Often, retained samples that are closely related to the forget set can be unintentionally affected, particularly when they share correlated features from pretraining or exhibit strong semantic similarities. To address this challenge, we propose a novel two-phase optimization framework specifically designed to handle such retain–forget entanglements. In the first phase, an augmented Lagrangian method increases the loss on the forget set while preserving accuracy on less-related retained samples. The second phase applies a gradient projection step, regularized by the Wasserstein-2 distance, to mitigate performance degradation on semantically related retained samples without compromising the unlearning objective. We validate our approach through comprehensive experiments on multiple unlearning tasks, standard benchmark datasets, and diverse neural architectures, demonstrating that it achieves effective and reliable unlearning while outperforming existing baselines in both accuracy retention and removal fidelity.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes a two-phase optimization framework addressing retain–forget entanglement in machine unlearning. It resides in the 'Entanglement-Aware Optimization' leaf, which contains only two papers total (including this one). This places the work in a relatively sparse but emerging research direction within gradient-based optimization methods. The taxonomy shows that while gradient-based unlearning is well-explored, explicit handling of semantic and feature-level correlations between retain and forget sets remains an active frontier with limited prior solutions.

The taxonomy reveals neighboring approaches in multi-objective optimization, gradient-free methods, and distribution-level techniques, but these branches address different aspects of the unlearning problem. The 'Entanglement-Aware Optimization' leaf sits within a broader gradient-based optimization subtopic, which itself branches into dual-teacher frameworks and multi-objective formulations. The scope note explicitly distinguishes entanglement-aware methods from general gradient techniques that do not model retain–forget correlations. Related leaves like 'Causal Inference and Spurious Correlation Removal' and 'Knowledge Correlation Evaluation' address overlapping themes but focus on different problem settings (causal inference vs. optimization execution).

Among 18 candidates examined, the contribution 'Highlighting retain–forget entanglement' shows 2 refutable candidates from 4 examined, suggesting this conceptual framing has prior articulation in the limited search scope. The two-phase optimization framework itself examined 10 candidates with no clear refutations, indicating potential novelty in the specific algorithmic design. The Wasserstein-2 regularization contribution examined 4 candidates without refutation, though the small sample size limits strong conclusions. The analysis explicitly covers top-K semantic matches and citation expansion, not an exhaustive literature review, so these statistics reflect a bounded search window rather than definitive prior work coverage.

Based on the limited search scope of 18 candidates, the work appears to occupy a sparsely populated research direction with one sibling paper in its taxonomy leaf. The two-phase framework and Wasserstein regularization show no clear prior implementations among examined candidates, while the entanglement framing has some precedent. The analysis does not cover the full breadth of optimization literature, so conclusions remain provisional pending broader review.

Taxonomy

Core-task Taxonomy Papers
25
3
Claimed Contributions
18
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: machine unlearning with correlated retain and forget sets. The field addresses the challenge of removing specific data from trained models while preserving performance on remaining data, particularly when these sets exhibit statistical dependencies. The taxonomy reveals several major branches: Theoretical Foundations examine fundamental limits and guarantees; Optimization Methods develop algorithms that balance forgetting unwanted information against retaining useful knowledge; Architecture and Model Design explore structural modifications that facilitate selective unlearning; Evaluation and Benchmarking establish metrics and testbeds; Domain-Specific Applications tailor techniques to particular settings like language models or recommender systems; Privacy and Legal Compliance ensure regulatory adherence; and Neural Network Learning Dynamics study how correlations propagate through training. Works like Deep Unlearning[3] and True Data Deletion[4] illustrate foundational optimization approaches, while Challenging Forgets[5] and Interaction-Level Difficulty[9] highlight evaluation complexities when retain and forget sets overlap. A particularly active line of research focuses on gradient-based optimization under entanglement, where naive forgetting degrades retain-set accuracy due to shared representations. Retain-Forget Entanglement[0] directly tackles this problem by developing entanglement-aware optimization strategies that account for feature correlations between what must be forgotten and what must be preserved. This contrasts with simpler gradient ascent methods, which Ascent Fails[20] demonstrates can catastrophically harm retain performance when correlations are strong. Nearby works like Unlearning Spurious Correlations[1] and Knowledge Correlation[18] explore related themes of disentangling learned dependencies, while BLUR[19] and RULE[16] propose alternative optimization frameworks. The original paper sits squarely within this gradient-based optimization cluster, emphasizing the need to explicitly model and mitigate entanglement rather than treating retain and forget sets as independent, thereby addressing a critical gap between theoretical unlearning guarantees and practical deployment constraints.

Claimed Contributions

Two-phase optimization framework for retain–forget entanglement

The authors introduce a two-stage optimization method that addresses the challenge of retain–forget entanglement in machine unlearning. The first phase uses an augmented Lagrangian method to enforce forgetting while preserving less-related retained samples, and the second phase applies gradient projection with Wasserstein-2 distance regularization to recover performance on correlated retained samples without compromising the unlearning objective.

10 retrieved papers
Highlighting retain–forget entanglement in machine unlearning

The authors identify and formalize the problem of retain–forget entanglement, where certain retained samples are strongly correlated with the forget set and thus particularly vulnerable to unintended performance degradation. This setting better reflects real-world unlearning demands and introduces new technical challenges due to significant distributional overlap.

4 retrieved papers
Can Refute
Wasserstein-2 distance regularization for gradient projection

The authors propose using Wasserstein-2 distance to regularize the loss distribution on the forget set during gradient projection. This prevents the model from redistributing loss unevenly across forget samples, which would otherwise allow some samples to achieve low loss and high accuracy, thereby undermining the forgetting objective.

4 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Two-phase optimization framework for retain–forget entanglement

The authors introduce a two-stage optimization method that addresses the challenge of retain–forget entanglement in machine unlearning. The first phase uses an augmented Lagrangian method to enforce forgetting while preserving less-related retained samples, and the second phase applies gradient projection with Wasserstein-2 distance regularization to recover performance on correlated retained samples without compromising the unlearning objective.

Contribution

Highlighting retain–forget entanglement in machine unlearning

The authors identify and formalize the problem of retain–forget entanglement, where certain retained samples are strongly correlated with the forget set and thus particularly vulnerable to unintended performance degradation. This setting better reflects real-world unlearning demands and introduces new technical challenges due to significant distributional overlap.

Contribution

Wasserstein-2 distance regularization for gradient projection

The authors propose using Wasserstein-2 distance to regularize the loss distribution on the forget set during gradient projection. This prevents the model from redistributing loss unevenly across forget samples, which would otherwise allow some samples to achieve low loss and high accuracy, thereby undermining the forgetting objective.

Table of Contents