# Per-parameter Task Arithmetic for Unlearning in Large Language Models

arXiv: https://arxiv.org/abs/2601.22030 · HTML: https://mlsanity.com/paper/2601.22030/

## Key facts

- Cited by 2 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 57 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

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

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

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [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)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [A Survey on Large Language Model (LLM) Security and Privacy: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2312.02003/) (2023)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (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)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Analyzing the Structure of Attention in a Transformer Language Model](https://mlsanity.com/paper/1906.04284/) (2019)
- [Quark: Controllable Text Generation with Reinforced Unlearning](https://mlsanity.com/paper/2205.13636/) (2022)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Continual Learning and Private Unlearning](https://mlsanity.com/paper/2203.12817/) (2022)
- [Knowledge Fusion of Large Language Models](https://mlsanity.com/paper/2401.10491/) (2024)
- [Copyright Violations and Large Language Models](https://mlsanity.com/paper/2310.13771/) (2023)
- [SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning](https://mlsanity.com/paper/2404.18239/) (2024)

## Built on by (most cited first, 2 of 2)

- [SAGE: Retain-Aware Post-Hoc Sanitization of Final Unlearning Vector](https://mlsanity.com/paper/2606.18309/) (2026)
- [UnlearningSoup: Is Repeated Tuning Necessary for Large Language Model Unlearning?](https://mlsanity.com/paper/2609.37076/) (2026)

## Abstract (arXiv)

In large language model (LLM) unlearning, private information is required to be removed. Task arithmetic unlearns by subtracting a specific task vector (TV)--defined as the parameter difference between a privacy-information-tuned model and the original model. While efficient, it can cause over-forgetting by disrupting parameters essential for retaining other information. Motivated by the observation that each parameter exhibits different importance for forgetting versus retention, we propose a per-parameter task arithmetic (PerTA) mechanism to rescale the TV, allowing per-parameter adjustment. These weights quantify the relative importance of each parameter for forgetting versus retention, estimated via gradients (i.e., PerTA-grad) or the diagonal Fisher information approximation (i.e., PerTA-fisher). Moreover, we discuss the effectiveness of PerTA, extend it to a more general form, and provide further analysis. Extensive experiments demonstrate that PerTA consistently improves upon standard TV, and in many cases surpasses widely used training-based unlearning methods in both forgetting effectiveness and overall model utility. By retaining the efficiency of task arithmetic while mitigating over-forgetting, PerTA offers a principled and practical framework for LLM unlearning.