# Efficient machine unlearning with minimax optimality

arXiv: https://arxiv.org/abs/2604.05669 · HTML: https://mlsanity.com/paper/2604.05669/

## 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 6 of its 80 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Placed in

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

## Builds on (most cited first, 6 of 6)

- [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)
- [Simplicity Prevails: Rethinking Negative Preference Optimization for LLM Unlearning](https://mlsanity.com/paper/2410.07163/) (2024)
- [High-probability minimax lower bounds](https://mlsanity.com/paper/2406.13447/) (2024)
- [Forgettable Federated Linear Learning with Certified Data Unlearning](https://mlsanity.com/paper/2306.02216/) (2023)
- [LLM Unlearning using Gradient Ratio-Based Influence Estimation and Noise Injection](https://mlsanity.com/paper/2508.06467/) (2025)

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

- [BARRIER: Bounded Activation Regions for Robust Information Erasure](https://mlsanity.com/paper/2605.15737/) (2026)
- [Minimax Gaussian Mechanisms for Continual Machine Unlearning](https://mlsanity.com/paper/2610.11628/) (2026)

## Abstract (arXiv)

There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the influence of specific data subsets without the cost of full retraining. In this work, we propose a statistical framework for machine unlearning with generic loss functions and establish theoretical guarantees. For squared loss, especially, we develop Unlearning Least Squares (ULS) and establish its minimax optimality for estimating the model parameter of remaining data when only the pre-trained estimator, forget samples, and a small subsample of the remaining data are available. Our results reveal that the estimation error decomposes into an oracle term and an unlearning cost determined by the forget proportion and the forget model bias. We further establish asymptotically valid inference procedures without requiring full retraining. Numerical experiments and real-data applications demonstrate that the proposed method achieves performance close to retraining while requiring substantially less data access.