# Gaussian Certified Unlearning in High Dimensions: A Hypothesis Testing Approach

arXiv: https://arxiv.org/abs/2510.13094 · HTML: https://mlsanity.com/paper/2510.13094/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [When Machine Unlearning Jeopardizes Privacy](https://mlsanity.com/paper/2005.02205/) (2020)
- [Adaptive Machine Unlearning](https://mlsanity.com/paper/2106.04378/) (2021)
- [Zero-Shot Machine Unlearning](https://mlsanity.com/paper/2201.05629/) (2022)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [Machine Unlearning Fails to Remove Data Poisoning Attacks](https://mlsanity.com/paper/2406.17216/) (2024)
- [Machine Unlearning: A Comprehensive Survey](https://mlsanity.com/paper/2405.07406/) (2024)
- [Towards Scalable Exact Machine Unlearning Using Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2406.16257/) (2024)
- [The Utility and Complexity of in- and out-of-Distribution Machine Unlearning](https://mlsanity.com/paper/2412.09119/) (2024)
- [Exact Unlearning of Finetuning Data via Model Merging at Scale](https://mlsanity.com/paper/2504.04626/) (2025)
- [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021)
- [A Central Limit Theorem for Differentially Private Query Answering](https://mlsanity.com/paper/2103.08721/) (2021)
- [Certified Data Removal Under High-dimensional Settings](https://mlsanity.com/paper/2505.07640/) (2025)
- [Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacy](https://mlsanity.com/paper/2206.04572/) (2022)
- [Corrected generalized cross-validation for finite ensembles of penalized estimators](https://mlsanity.com/paper/2310.01374/) (2023)
- [Theoretical Analysis of Leave-one-out Cross Validation for Non-differentiable Penalties under High-dimensional Settings](https://mlsanity.com/paper/2402.08543/) (2024)
- [On Newton's Method to Unlearn Neural Networks](https://mlsanity.com/paper/2406.14507/) (2024)

## Built on by (most cited first, 6 of 6)

- [Missing-by-Design: Certifiable Modality Deletion for Revocable Multimodal Sentiment Analysis](https://mlsanity.com/paper/2602.16144/) (2026)
- [Statistical Unlearning of Distributions: A Hypothesis Testing Approach](https://mlsanity.com/paper/2605.16645/) (2026)
- [Infinitely divisible privacy and beyond I: resolution of the s2=2k conjecture](https://mlsanity.com/paper/2512.00734/) (2025)
- [SoK: Unlearnability and Unlearning for Model Dememorization](https://mlsanity.com/paper/2605.11592/) (2026)
- [ForgetMimic: Motion Unlearning for Reinforcement Learning Humanoid Control](https://mlsanity.com/paper/2609.28378/) (2026)
- [From Mathematical to Executable Certificates for Machine Unlearning](https://mlsanity.com/paper/2610.02268/) (2026)

## Abstract (arXiv)

Machine unlearning seeks to efficiently remove the influence of selected data while preserving generalization. Significant progress has been made in low dimensions (p ll n), but high dimensions pose serious theoretical challenges as standard optimization assumptions of Omega(1) strong convexity and O(1) smoothness of the per-example loss f rarely hold simultaneously in proportional regimes (p~ n). In this work, we introduce varepsilon-Gaussian certifiability, a canonical and robust notion well-suited to high-dimensional regimes, that optimally captures a broad class of noise adding mechanisms. Then we theoretically analyze the performance of a widely used unlearning algorithm based on one step of the Newton method in the high-dimensional setting described above. Our analysis shows that a single Newton step, followed by a well-calibrated Gaussian noise, is sufficient to achieve both privacy and accuracy in this setting. This result stands in sharp contrast to the only prior work that analyzes machine unlearning in high dimensions citetzou2025certified, which relaxes some of the standard optimization assumptions for high-dimensional applicability, but operates under the notion of varepsilon-certifiability. That work concludes %that a single Newton step is insufficient even for removing a single data point, and that at least two steps are required to ensure both privacy and accuracy. Our result leads us to conclude that the discrepancy in the number of steps arises because of the sub optimality of the notion of varepsilon-certifiability and its incompatibility with noise adding mechanisms, which varepsilon-Gaussian certifiability is able to overcome optimally.