# OFMU: Optimization-Driven Framework for Machine Unlearning

arXiv: https://arxiv.org/abs/2509.22483 · HTML: https://mlsanity.com/paper/2509.22483/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 31 of its 44 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (2023)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [Unlearn What You Want to Forget: Efficient Unlearning for LLMs](https://mlsanity.com/paper/2310.20150/) (2023)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Are Large Pre-Trained Language Models Leaking Your Personal Information?](https://mlsanity.com/paper/2205.12628/) (2022)
- [Beyond Memorization: Violating Privacy Via Inference with Large Language Models](https://mlsanity.com/paper/2310.07298/) (2023)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Mixed-Privacy Forgetting in Deep Networks](https://mlsanity.com/paper/2012.13431/) (2020)
- [An Adversarial Perspective on Machine Unlearning for AI Safety](https://mlsanity.com/paper/2409.18025/) (2024)
- [Large Language Model Unlearning via Embedding-Corrupted Prompts](https://mlsanity.com/paper/2406.07933/) (2024)
- [Deep Unlearning via Randomized Conditionally Independent Hessians](https://mlsanity.com/paper/2204.07655/) (2022)
- [UNDIAL: Self-Distillation with Adjusted Logits for Robust Unlearning in Large Language Models](https://mlsanity.com/paper/2402.10052/) (2024)
- [Offset Unlearning for Large Language Models](https://mlsanity.com/paper/2404.11045/) (2024)
- [Alternate Preference Optimization for Unlearning Factual Knowledge in Large Language Models](https://mlsanity.com/paper/2409.13474/) (2024)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate](https://mlsanity.com/paper/2410.22086/) (2024)
- [Certified Unlearning for Neural Networks](https://mlsanity.com/paper/2506.06985/) (2025)

## Built on by (most cited first, 4 of 4)

- [SoK: Unlearnability and Unlearning for Model Dememorization](https://mlsanity.com/paper/2605.11592/) (2026)
- [Spectral Saliency for Machine Unlearning](https://mlsanity.com/paper/2608.15548/) (2026)
- [SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning](https://mlsanity.com/paper/2608.16249/) (2026)
- [Learning the Robustness Mechanism with Bilevel Optimization](https://mlsanity.com/paper/2609.35541/) (2026)

## Abstract (arXiv)

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.