# Correlation-Guided Fast Machine Unlearning via Hessian Analysis

arXiv: https://arxiv.org/abs/2609.12620 · HTML: https://mlsanity.com/paper/2609.12620/

## 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 19 of its 28 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (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)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Adaptive Machine Unlearning](https://mlsanity.com/paper/2106.04378/) (2021)
- [Machine Unlearning: Solutions and Challenges](https://mlsanity.com/paper/2308.07061/) (2023)
- [What makes unlearning hard and what to do about it](https://mlsanity.com/paper/2406.01257/) (2024)
- [Hessian-Free Online Certified Unlearning](https://mlsanity.com/paper/2404.01712/) (2024)
- [Delta-Influence: Unlearning Poisons via Influence Functions](https://mlsanity.com/paper/2411.13731/) (2024)
- [Machine Unlearning via Information Theoretic Regularization](https://mlsanity.com/paper/2502.05684/) (2025)
- [Scalability of memorization-based machine unlearning](https://mlsanity.com/paper/2410.16516/) (2024)
- [A More Practical Approach to Machine Unlearning](https://mlsanity.com/paper/2406.09391/) (2024)

## Abstract (arXiv)

The increasing adoption of machine learning in network and distributed security systems has created an urgent need for mechanisms that can selectively and efficiently remove the influence of specific training data to eliminate compromised or adversarial data points from production models. Privacy regulations such as GDPR's right to be forgotten also pose similar requirements. However, existing approximate unlearning techniques remain computationally prohibitive for deployment in real-world security systems, as they require repeated expensive Hessian-inverse-vector computations for each data point removal, creating a bottleneck when processing multiple related requests in scenarios such as intrusion detection systems, spam filters, and threat intelligence platforms. Thus, we introduce a computationally efficient unlearning framework that identifies correlated data points in the training set and applies a theoretically derived closed-form parameter update rule, achieving an 82× wall-clock speedup over standard influence function unlearning while preserving model utility with a 10-2 improvement in accuracy over state-of-the-art baselines. Our method establishes theoretical guarantees and ensures numerical stability through Hessian damping. Our evaluation across seven diverse dataset architecture combinations, including large-scale CIFAR-100 with ResNet-50, demonstrates superior forgetting effectiveness, with membership inference attack success rates of 0.660 and tug-of-war scores of 0.950.