# Learning What to Forget: Distributional Unlearning for LLM Representation Spaces

arXiv: https://arxiv.org/abs/2609.38929 · HTML: https://mlsanity.com/paper/2609.38929/

## 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 28 of its 53 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, 28 of 28)

- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (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)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [Unlearning Isn't Deletion: Investigating Reversibility of Machine Unlearning in LLMs](https://mlsanity.com/paper/2505.16831/) (2025)
- [Dissecting Fine-Tuning Unlearning in Large Language Models](https://mlsanity.com/paper/2410.06606/) (2024)
- [Language Models May Verbatim Complete Text They Were Not Explicitly Trained On](https://mlsanity.com/paper/2503.17514/) (2025)
- [What Should Embeddings Embed? Autoregressive Models Represent Latent Generating Distributions](https://mlsanity.com/paper/2406.03707/) (2024)
- [Contrastive Representation Shaping for LLM Unlearning](https://mlsanity.com/paper/2601.22028/) (2026)
- [Distributional Machine Unlearning via Selective Data Removal](https://mlsanity.com/paper/2507.15112/) (2025)

## Abstract (arXiv)

Machine learning systems increasingly face the need to remove the influence of entire data domains, such as toxic language, harmful behavior, or topical content, rather than isolated records. Recent work formalizes this problem as distributional unlearning: selecting a subset of a forget domain whose removal moves the training distribution away from an unwanted population while preserving proximity to the desired one. However, existing analyses often impose parametric assumptions to obtain tractable selection rules. These assumptions may be poorly suited to high-dimensional language-model representations. We introduce textscMamushi, a framework for non-parametric distributional unlearning that ranks forget examples using a probabilistic classifier whose Bayes-optimal logit equals the forget-to-retain log-density ratio (up to an additive class-prior constant). We show that thresholding the population log-density ratio yields the optimal fixed-budget selection rule for our removal--preservation objective and establish a non-asymptotic transfer guarantee relating score-estimation and threshold-calibration errors to degradation from the population-optimal selection rule. Our empirical evaluation spans real-world datasets on toxic-language removal and topical-domain removal regimes using different representations, with textscMamushi achieving a more favorable removal--preservation trade-off than other baselines. Our work shows that textscMamushi can serve as an efficient selection approach for downstream machine unlearning procedures, reducing the number of forget examples required to reach a fixed forgetting target.