# Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate

arXiv: https://arxiv.org/abs/2410.22086 · HTML: https://mlsanity.com/paper/2410.22086/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 41 of its 62 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [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)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Adaptive Machine Unlearning](https://mlsanity.com/paper/2106.04378/) (2021)
- [Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models](https://mlsanity.com/paper/2010.05874/) (2020)
- [Prodigy: An Expeditiously Adaptive Parameter-Free Learner](https://mlsanity.com/paper/2306.06101/) (2023)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Continual Learning and Private Unlearning](https://mlsanity.com/paper/2203.12817/) (2022)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)

## Built on by (most cited first, 30 of 31)

- [BLUR: A Bi-Level Optimization Approach for LLM Unlearning](https://mlsanity.com/paper/2506.08164/) (2025)
- [LUME: LLM Unlearning with Multitask Evaluations](https://mlsanity.com/paper/2502.15097/) (2025)
- [SAEs Can Improve Unlearning: Dynamic Sparse Autoencoder Guardrails for Precision Unlearning in LLMs](https://mlsanity.com/paper/2504.08192/) (2025)
- [A General Framework to Enhance Fine-tuning-based LLM Unlearning](https://mlsanity.com/paper/2502.17823/) (2025)
- [SoK: Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2506.09227/) (2025)
- [Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models](https://mlsanity.com/paper/2506.05314/) (2025)
- [VLA-Forget: Vision-Language-Action Unlearning for Embodied Foundation Models](https://mlsanity.com/paper/2604.03956/) (2026)
- [Keeping an Eye on LLM Unlearning: The Hidden Risk and Remedy](https://mlsanity.com/paper/2506.00359/) (2025)
- [Leak@k: Unlearning Does Not Make LLMs Forget Under Probabilistic Decoding](https://mlsanity.com/paper/2511.04934/) (2025)
- [Not Every Token Needs Forgetting: Selective Unlearning to Limit Change in Utility in Large Language Model Unlearning](https://mlsanity.com/paper/2506.00876/) (2025)
- [Machine Unlearning under Overparameterization](https://mlsanity.com/paper/2505.22601/) (2025)
- [OFMU: Optimization-Driven Framework for Machine Unlearning](https://mlsanity.com/paper/2509.22483/) (2025)
- [A Survey on Unlearning in Large Language Models](https://mlsanity.com/paper/2510.25117/) (2025)
- [SemEval-2025 Task 4: Unlearning sensitive content from Large Language Models](https://mlsanity.com/paper/2504.02883/) (2025)
- [Unlearning the Unpromptable: Prompt-free Instance Unlearning in Diffusion Models](https://mlsanity.com/paper/2603.10445/) (2026)
- [Cyber for AI at SemEval-2025 Task 4: Forgotten but Not Lost: The Balancing Act of Selective Unlearning in Large Language Models](https://mlsanity.com/paper/2503.04795/) (2025)
- [A mean teacher algorithm for unlearning of language models](https://mlsanity.com/paper/2504.13388/) (2025)
- [UNO: Unlearning via Orthogonalization in Generative models](https://mlsanity.com/paper/2506.04712/) (2025)
- [UnPII: Unlearning Personally Identifiable Information with Quantifiable Exposure Risk](https://mlsanity.com/paper/2601.01786/) (2026)
- [Structural Disentanglement in Bilinear MLPs via Architectural Inductive Bias](https://mlsanity.com/paper/2602.05635/) (2026)
- [MPU: Towards Secure and Privacy-Preserving Knowledge Unlearning for Large Language Models](https://mlsanity.com/paper/2602.23798/) (2026)
- [Harmonizing Multi-Objective LLM Unlearning via Unified Domain Representation and Bidirectional Logit Distillation](https://mlsanity.com/paper/2604.15482/) (2026)
- [How Hard Can It Be? Hardness-Aware Multi-Objective Unlearning](https://mlsanity.com/paper/2606.02119/) (2026)
- [LLM Unlearning for Cyber Defense: A Survey on Methods, Challenges, and Emerging Threats](https://mlsanity.com/paper/2607.16227/) (2026)
- [The More Popular, The Harder to Forget: Adaptive Popularity for LLM Unlearning](https://mlsanity.com/paper/2608.14229/) (2026)
- [SAUL: Sharpness-Aware Augmented-Lagrangian Unlearning](https://mlsanity.com/paper/2608.16249/) (2026)
- [Can Scientific Claims Be Removed from Large Language Models? A Systematic Evaluation of Claim-Level Unlearning](https://mlsanity.com/paper/2608.20960/) (2026)
- [BLADE: Bilevel Low-rank Augmented-Lagrangian Erasure for LLM Unlearning](https://mlsanity.com/paper/2608.22557/) (2026)
- [Neuralyzing the Trace: Selective Representation-Level Unlearning with Contrastive Sparse Autoencoders](https://mlsanity.com/paper/2609.31056/) (2026)
- [Do LLMs Really Forget? Hidden-State Leakage in Model Unlearning and How to Fix it](https://mlsanity.com/paper/2609.36612/) (2026)

## Abstract (arXiv)

Machine unlearning has been used to remove unwanted knowledge acquired by large language models (LLMs). In this paper, we examine machine unlearning from an optimization perspective, framing it as a regularized multi-task optimization problem, where one task optimizes a forgetting objective and another optimizes the model performance. In particular, we introduce a normalized gradient difference (NGDiff) algorithm, enabling us to have better control over the trade-off between the objectives, while integrating a new, automatic learning rate scheduler. We provide a theoretical analysis and empirically demonstrate the superior performance of NGDiff among state-of-the-art unlearning methods on the TOFU and MUSE datasets while exhibiting stable training.