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Selective Data Removal for Distributional Machine Unlearning

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
unlearningtheoryprivacysample complexitymachine learningstatistical learning
Abstract:

Machine learning systems increasingly face requirements to remove entire domains of information—such as toxic language or biases—rather than individual user data. This task presents a dilemma: full removal of the unwanted domain data is computationally expensive, while random partial removal is statistically inefficient. We find that a domain's statistical influence is often concentrated in a small subset of its data samples, suggesting a path between ineffective partial removal and unnecessary complete removal. We formalize this as distributional unlearning: a framework to select a small subset that balances forgetting an unwanted distribution while preserving a desired one. Using Kullback-Leibler divergence constraints, we derive the exact removal-preservation Pareto frontier for Gaussian distributions and prove that models trained on the edited data achieve corresponding log-loss bounds. We propose a distance-based selection algorithm and show it is quadratically more sample-efficient than random removal in the challenging low-divergence regime. Experiments across synthetic, text, and image datasets (Jigsaw, CIFAR-10, SMS spam) show our method requires 15–82% less deletion than full removal for strong unlearning effects, e.g., halving initial forget set accuracy. Ultimately, by showing a small forget set often suffices, our framework lays the foundations for more scalable and rigorous subpopulation unlearning.

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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.
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Overview

Overall Novelty Assessment

The paper introduces a distributional unlearning framework that selectively removes small subsets of data to forget unwanted distributions while preserving desired ones. It resides in the 'Distributional and Selective Unlearning' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader unlearning taxonomy. The sibling papers in this leaf similarly address distributional removal rather than instance-level forgetting, suggesting the work contributes to an emerging but not yet crowded subfield focused on removing entire data patterns efficiently.

The taxonomy tree shows this leaf sits under 'Unlearning Frameworks and Theoretical Foundations,' adjacent to 'General Unlearning Frameworks and Complexity' (three papers) and 'Causality and Independence Criteria' (two papers). Neighboring branches include 'Gradient-Based and Fine-Tuning Methods' and 'Distribution Correction and Regularization,' which address algorithmic implementation rather than selective subset identification. The scope note for this leaf explicitly excludes general frameworks without selective mechanisms, positioning the work at the intersection of theoretical guarantees and practical data selection strategies.

Among 26 candidates examined across three contributions, none were found to clearly refute any claimed novelty. The distributional unlearning framework examined 10 candidates with zero refutable overlaps; the closed-form Pareto frontier examined 6 candidates with zero refutations; and the distance-based selection algorithm examined 10 candidates with zero refutations. This suggests that within the limited search scope, the specific combination of KL divergence constraints, exact Pareto frontiers for exponential families, and quadratic sample efficiency improvements appears distinct from prior work.

Based on the limited top-26 semantic search, the work appears to occupy a relatively novel position combining distributional removal theory with selective data identification. The sparse population of the taxonomy leaf and absence of refutable prior work among examined candidates suggest the approach addresses an underexplored gap. However, the search scope does not cover exhaustive domain-specific literature or recent preprints, leaving open the possibility of related work outside the examined set.

Taxonomy

Core-task Taxonomy Papers
39
3
Claimed Contributions
26
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Selective data removal for distributional machine unlearning. The field of machine unlearning has rapidly evolved to address the challenge of efficiently removing specific data influences from trained models without full retraining. The taxonomy reveals four major branches: theoretical foundations that establish formal guarantees and complexity bounds for unlearning procedures (e.g., Machine Unlearning[1], The Utility and Complexity[2]); algorithmic approaches spanning gradient-based methods, parameter perturbation, and optimization techniques (e.g., Direct Unlearning Optimization for[5], Distribution-Level Feature Distancing for[7]); application-specific adaptations across domains like federated learning, large language models, and computer vision (e.g., LLM-Eraser[8], Modality-Aware Neuron Pruning for[9]); and evaluation frameworks addressing fairness, robustness, and verification (e.g., Fair Machine Unlearning[26], Group-robust Machine Unlearning[24]). These branches interconnect as theoretical insights guide algorithmic design, which in turn must be tailored to specific model architectures and evaluated for both utility preservation and security guarantees. Recent work has intensified around several contrasting themes: exact versus approximate unlearning trade-offs, where some methods prioritize computational efficiency while others seek stronger privacy guarantees; distributional versus instance-level removal, with growing interest in removing entire data distributions rather than individual samples; and the tension between unlearning effectiveness and model utility retention. Selective Data Removal for[0] sits within the distributional and selective unlearning cluster, closely aligned with Distributional Unlearning[38] and Distributional Machine Unlearning via[39], which similarly focus on removing broader data patterns rather than isolated points. Compared to instance-focused approaches like Backdoor Defense with Machine[3] or single-sample methods, this work emphasizes the challenge of selectively targeting distributional characteristics while maintaining model performance on retained data—a particularly relevant concern as applications demand more nuanced control over what models forget.

Claimed Contributions

Distributional unlearning framework with KL divergence constraints

The authors introduce a formal framework called distributional unlearning that uses KL divergence to quantify the trade-off between removing an unwanted distribution and preserving a desired one. This framework addresses the problem of selecting which data samples to remove to erase a domain's statistical influence.

10 retrieved papers
Closed-form Pareto frontier and log-loss guarantees for exponential families

The authors derive the exact Pareto frontier characterizing achievable removal-preservation trade-offs for Gaussian and exponential family distributions. They also prove that models trained on data satisfying distributional unlearning constraints achieve corresponding bounds on expected log-loss under both forgotten and retained distributions.

6 retrieved papers
Distance-based selective removal algorithm with quadratic sample efficiency improvement

The authors develop a selective removal algorithm that prioritizes samples based on their distance to the retained distribution's mean. They prove this method requires quadratically fewer samples than random removal to achieve the same unlearning guarantees in low-divergence settings.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Distributional unlearning framework with KL divergence constraints

The authors introduce a formal framework called distributional unlearning that uses KL divergence to quantify the trade-off between removing an unwanted distribution and preserving a desired one. This framework addresses the problem of selecting which data samples to remove to erase a domain's statistical influence.

Contribution

Closed-form Pareto frontier and log-loss guarantees for exponential families

The authors derive the exact Pareto frontier characterizing achievable removal-preservation trade-offs for Gaussian and exponential family distributions. They also prove that models trained on data satisfying distributional unlearning constraints achieve corresponding bounds on expected log-loss under both forgotten and retained distributions.

Contribution

Distance-based selective removal algorithm with quadratic sample efficiency improvement

The authors develop a selective removal algorithm that prioritizes samples based on their distance to the retained distribution's mean. They prove this method requires quadratically fewer samples than random removal to achieve the same unlearning guarantees in low-divergence settings.

Table of Contents