# Unmerge: Efficient Machine Unlearning via Task Arithmetic

arXiv: https://arxiv.org/abs/2609.38895 · HTML: https://mlsanity.com/paper/2609.38895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 49 of its 54 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

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

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (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)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [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)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Systematic Evaluation of Privacy Risks of Machine Learning Models](https://mlsanity.com/paper/2003.10595/) (2020)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (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)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)

## Abstract (arXiv)

Approximate machine unlearning seeks to remove the influence of a forget set from a trained model without full retraining. Existing gradient-based methods require data-dependent hyperparameter search, struggle when forget and retain knowledge are entangled, and offer little insight into where unlearning actually happens inside the network. We recast unlearning through the lens of task arithmetic: if finetuning produces a merged task vector τm that combines learning on forget and retain sets, unlearning is the inverse operation that subtracts a learned forget component τF to recover the retain task vector τR. The forget signal is concentrated: at every layer, forget activations lie in a subspace spanned by a handful of dominant directions, so we factorize τF in a low-rank forget basis, which is faithful up to a small tail-eigenvalue residual and limits how far the correction can perturb retain. We then optimize three intuitive goals (match the merged vector inside the forget span, suppress leakage into the retain span, and bound the correction size) that provably bound forget leakage and retain damage in activation space. The resulting algorithm, Unmerge, is fast and powerful: on class-level unlearning with ResNet-50 on CIFAR-100 and Tiny ImageNet, it improves Tug-of-War by up to ~24% over a baseline of comparable runtime and by up to ~18% over stronger baselines that run ~5x slower, keeps membership-inference exposure at the level of retraining, and shrinks the feature-distribution gap to the retrained model, where relabeling methods leave forget features cleanly separable. Further studies show that Unmerge also applies to ViT-S/16 and scales to Llama-3.2-3B. The per-layer basis geometry that drives the algorithm also serves as a layerwise diagnostic for when and where unlearning becomes structurally hard.