# QR-Erase: Efficient Subspace-Based Machine Unlearning with Layer Localization

arXiv: https://arxiv.org/abs/2608.01422 · HTML: https://mlsanity.com/paper/2608.01422/

## 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 16 of its 28 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [VoxCeleb2: Deep Speaker Recognition](https://mlsanity.com/paper/1806.05622/) (2018)
- [VoxCeleb: a large-scale speaker identification dataset](https://mlsanity.com/paper/1706.08612/) (2017)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [KGA: A General Machine Unlearning Framework Based on Knowledge Gap Alignment](https://mlsanity.com/paper/2305.06535/) (2023)
- [Model Editing as a Robust and Denoised variant of DPO: A Case Study on Toxicity](https://mlsanity.com/paper/2405.13967/) (2024)
- [Ethos: Rectifying Language Models in Orthogonal Parameter Space](https://mlsanity.com/paper/2403.08994/) (2024)
- [Model Unlearning via Sparse Autoencoder Subspace Guided Projections](https://mlsanity.com/paper/2505.24428/) (2025)
- [Learn and Unlearn: Addressing Misinformation in Multilingual LLMs](https://mlsanity.com/paper/2406.13748/) (2024)
- [Multilingual Amnesia: On the Transferability of Unlearning in Multilingual LLMs](https://mlsanity.com/paper/2601.05641/) (2026)
- [Evaluating Cross-Lingual Unlearning in Multilingual Language Models](https://mlsanity.com/paper/2601.06675/) (2026)

## Abstract (arXiv)

Machine unlearning seeks to remove targeted information from trained models without requiring costly retraining. Existing optimization-based methods often degrade unrelated capabilities, while subspace-based approaches rely on computationally expensive singular value decompositions (SVD). We introduce QR-Erase, a subspace-based framework that uses Pivoted QR decomposition to identify and remove task-specific representations directly from model parameters. We further propose Layer-Localized QR-Erase, which restricts updates to layers containing the highest concentration of task-specific information. We show that Pivoted QR provides accurate subspace recovery with bounded error, and that under a mild spectral gap condition, the recovered subspace approaches the optimal SVD solution. Across task-level, cross-lingual, and speech unlearning, QR-Erase achieves a stronger forgetting-retention tradeoff than optimization-based methods while remaining within 5% of SVD across all metrics. Exploiting low-rank and layer-localized structure further improves forgetting (for example, reducing speech forget-set accuracy from 53.1% to 15.7%). These results demonstrate that accurate subspace recovery, rather than optimal reconstruction, is sufficient for effective unlearning and provides an efficient and general alternative to SVD-based methods for modern foundation models.