# Machine Unlearning under Retain-Forget Entanglement

arXiv: https://arxiv.org/abs/2603.26569 · HTML: https://mlsanity.com/paper/2603.26569/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 50 of its 62 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 50)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [ToxiGen: A Large-Scale Machine-Generated Dataset for Adversarial and Implicit Hate Speech Detection](https://mlsanity.com/paper/2203.09509/) (2022)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [Unified Concept Editing in Diffusion Models](https://mlsanity.com/paper/2308.14761/) (2023)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Large Language Model Unlearning via Embedding-Corrupted Prompts](https://mlsanity.com/paper/2406.07933/) (2024)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [What makes unlearning hard and what to do about it](https://mlsanity.com/paper/2406.01257/) (2024)
- [Deep Unlearning via Randomized Conditionally Independent Hessians](https://mlsanity.com/paper/2204.07655/) (2022)
- [RWKU: Benchmarking Real-World Knowledge Unlearning for Large Language Models](https://mlsanity.com/paper/2406.10890/) (2024)
- [Constrained Variational Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2201.11927/) (2022)
- [Accelerated Primal-Dual Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/1802.06480/) (2018)

## Built on by (most cited first, 11 of 11)

- [Closed-Form Concept Erasure via Double Projections](https://mlsanity.com/paper/2604.10032/) (2026)
- [Where Concept Erasure Should Occur: Concept-Layer Alignment in Text-to-Video Diffusion Models](https://mlsanity.com/paper/2605.25941/) (2026)
- [MemLeak: Diagnosing Information Leaks in Multimodal Agent Memory](https://mlsanity.com/paper/2606.29788/) (2026)
- [Auditing of Unlearning Algorithms](https://mlsanity.com/paper/2607.05898/) (2026)
- [Interference-Aware Multi-Task Unlearning](https://mlsanity.com/paper/2605.19042/) (2026)
- [Forgetting Has Neighbors: Localized Collateral Forgetting in Machine Unlearning](https://mlsanity.com/paper/2605.31317/) (2026)
- [LLM Unlearning for Cyber Defense: A Survey on Methods, Challenges, and Emerging Threats](https://mlsanity.com/paper/2607.16227/) (2026)
- [Cross-Domain Generalization in Machine Unlearning via Label-Conditioned Energy Magnitude Regularization](https://mlsanity.com/paper/2608.17942/) (2026)
- [Bounding Retraining Equivalence and the Deletion Floor in Materials Machine Unlearning](https://mlsanity.com/paper/2609.35635/) (2026)
- [Motion Concept Unlearning in Video Diffusion Models](https://mlsanity.com/paper/2609.36832/) (2026)
- [RA2: Retain-Anchored Attraction Preserves Forget-Adjacent Utility in LLM Unlearning](https://mlsanity.com/paper/2610.19385/) (2026)

## Abstract (arXiv)

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 retai-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.