# Machine Unlearning for Gibbs Supervised Learning Algorithms

arXiv: https://arxiv.org/abs/2609.29409 · HTML: https://mlsanity.com/paper/2609.29409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 24 Sep 2026.

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

- [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)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Machine Unlearning: Solutions and Challenges](https://mlsanity.com/paper/2308.07061/) (2023)
- [What is the long-run distribution of stochastic gradient descent? A large deviations analysis](https://mlsanity.com/paper/2406.09241/) (2024)
- [On the Robustness to Misspecification of α-Posteriors and Their Variational Approximations](https://mlsanity.com/paper/2104.08324/) (2021)
- [Empirical Risk Minimization with Relative Entropy Regularization](https://mlsanity.com/paper/2211.06617/) (2022)
- [On the Validation of Gibbs Algorithms: Training Datasets, Test Datasets and their Aggregation](https://mlsanity.com/paper/2306.12380/) (2023)
- [Generalization Analysis of Machine Learning Algorithms via the Worst-Case Data-Generating Probability Measure](https://mlsanity.com/paper/2312.12236/) (2023)
- [Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences](https://mlsanity.com/paper/2402.00501/) (2024)
- [Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2410.02833/) (2024)
- [Proofs for Folklore Theorems on the Radon-Nikodym Derivative](https://mlsanity.com/paper/2501.18374/) (2025)
- [FedUHB: Accelerating Federated Unlearning via Polyak Heavy Ball Method](https://mlsanity.com/paper/2411.11039/) (2024)
- [Variations on the Expectation due to Changes in the Probability Measure](https://mlsanity.com/paper/2502.02887/) (2025)
- [Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms](https://mlsanity.com/paper/2604.20492/) (2026)
- [Efficient Machine Unlearning by Model Splitting and Core Sample Selection](https://mlsanity.com/paper/2505.07026/) (2025)
- [Certifying the Right to Be Forgotten: Primal-Dual Optimization for Sample and Label Unlearning in Vertical Federated Learning](https://mlsanity.com/paper/2512.23171/) (2025)

## Abstract (arXiv)

In this paper, a method for achieving exact unlearning for Gibbs supervised learning algorithms is proposed using a variational formulation inspired by empirical risk minimization subject to relative entropy regularization (ERM-RER). Such a method consists of maximizing the expected empirical risk over the dataset to be unlearned subject to a regularization by relative entropy with respect to the original algorithm. The optimization variable is a probability measure on the models; and the solution is another Gibbs probability measure that represents a new Gibbs supervised learning algorithm. The method guarantees exact unlearning in the sense that the new Gibbs algorithm coincides in distribution with the algorithm that would have been obtained by retraining from scratch on the dataset to be retained. As a byproduct, a framework for reweighting data points in ERM-RER by strategically choosing both the reference measure and the regularization factor is obtained. In this framework, exact unlearning is the special case in which zero-weight is assigned to the contribution of the data points to be unlearned. More generally, depending on the choice of certain parameters, data points can be up-weighted or down-weighted in ERM-RER problems for particular purposes, e.g., controlling the generalization error of Gibbs algorithms. This paves the way for new constructive or adversarial views on classical reweighting data points in ERM-RER.