# MUSO: Achieving Exact Machine Unlearning in Over-Parameterized Regimes

arXiv: https://arxiv.org/abs/2410.08557 · HTML: https://mlsanity.com/paper/2410.08557/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 44 of its 63 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 44)

- [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)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (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)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [Systematic Evaluation of Privacy Risks of Machine Learning Models](https://mlsanity.com/paper/2003.10595/) (2020)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [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)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [On the Necessity of Auditable Algorithmic Definitions for Machine Unlearning](https://mlsanity.com/paper/2110.11891/) (2021)
- [Mixed-Privacy Forgetting in Deep Networks](https://mlsanity.com/paper/2012.13431/) (2020)
- [Privacy Risks of Securing Machine Learning Models against Adversarial Examples](https://mlsanity.com/paper/1905.10291/) (2019)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Machine Unlearning: Linear Filtration for Logit-based Classifiers](https://mlsanity.com/paper/2002.02730/) (2020)
- [What makes unlearning hard and what to do about it](https://mlsanity.com/paper/2406.01257/) (2024)
- [The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy Training](https://mlsanity.com/paper/2007.12826/) (2020)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [Can Neural Network Memorization Be Localized?](https://mlsanity.com/paper/2307.09542/) (2023)
- [Learning to Unlearn: Instance-wise Unlearning for Pre-trained Classifiers](https://mlsanity.com/paper/2301.11578/) (2023)
- [PUMA: Performance Unchanged Model Augmentation for Training Data Removal](https://mlsanity.com/paper/2203.00846/) (2022)

## Built on by (most cited first, 3 of 3)

- [Exact Federated Continual Unlearning for Ridge Heads on Frozen Foundation Models](https://mlsanity.com/paper/2603.12977/) (2026)
- [Soft Token Attacks Cannot Reliably Audit Unlearning in Large Language Models](https://mlsanity.com/paper/2502.15836/) (2025)
- [Dual-View Inference Attack: Machine Unlearning Amplifies Privacy Exposure](https://mlsanity.com/paper/2512.16126/) (2025)

## Abstract (arXiv)

Machine unlearning (MU) is to make a well-trained model behave as if it had never been trained on specific data. In today's over-parameterized models, dominated by neural networks, a common approach is to manually relabel data and fine-tune the well-trained model. It can approximate the MU model in the output space, but the question remains whether it can achieve exact MU, i.e., in the parameter space. We answer this question by employing random feature techniques to construct an analytical framework. Under the premise of model optimization via stochastic gradient descent, we theoretically demonstrated that over-parameterized linear models can achieve exact MU through relabeling specific data. We also extend this work to real-world nonlinear networks and propose an alternating optimization algorithm that unifies the tasks of unlearning and relabeling. The algorithm's effectiveness, confirmed through numerical experiments, highlights its superior performance in unlearning across various scenarios compared to current state-of-the-art methods, particularly excelling over similar relabeling-based MU approaches.