# Understanding Fine-tuning in Approximate Unlearning: A Theoretical Perspective

arXiv: https://arxiv.org/abs/2410.03833 · HTML: https://mlsanity.com/paper/2410.03833/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 26 of its 35 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [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)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (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)
- [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)
- [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)
- [Privacy Risks of Securing Machine Learning Models against Adversarial Examples](https://mlsanity.com/paper/1905.10291/) (2019)
- [Machine Unlearning via Algorithmic Stability](https://mlsanity.com/paper/2102.13179/) (2021)
- [Deep Unlearning via Randomized Conditionally Independent Hessians](https://mlsanity.com/paper/2204.07655/) (2022)
- [Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning](https://mlsanity.com/paper/2401.10371/) (2024)
- [Evaluating Machine Unlearning via Epistemic Uncertainty](https://mlsanity.com/paper/2208.10836/) (2022)
- [Understanding Forgetting in Continual Learning with Linear Regression](https://mlsanity.com/paper/2405.17583/) (2024)
- [Communication Efficient and Provable Federated Unlearning](https://mlsanity.com/paper/2401.11018/) (2024)
- [Label-Agnostic Forgetting: A Supervision-Free Unlearning in Deep Models](https://mlsanity.com/paper/2404.00506/) (2024)
- [Decoupling the Class Label and the Target Concept in Machine Unlearning](https://mlsanity.com/paper/2406.08288/) (2024)
- [Discriminative Adversarial Unlearning](https://mlsanity.com/paper/2402.06864/) (2024)

## Built on by (most cited first, 5 of 5)

- [Unlearning Comparator: A Visual Analytics System for Comparative Evaluation of Machine Unlearning Methods](https://mlsanity.com/paper/2508.12730/) (2025)
- [Why Some Models Resist Unlearning: A Linear Stability Perspective](https://mlsanity.com/paper/2602.02986/) (2026)
- [f-FUM: Federated Unlearning via min--max and f-divergence](https://mlsanity.com/paper/2602.06187/) (2026)
- [Spectral Saliency for Machine Unlearning](https://mlsanity.com/paper/2608.15548/) (2026)
- [When Retain Constraints Conflict: Mitigating Forget-Retain Interference in Tabular Data](https://mlsanity.com/paper/2609.06786/) (2026)

## Abstract (arXiv)

Machine Unlearning has emerged as a significant area of research, focusing on `removing' specific subsets of data from a trained model. Fine-tuning (FT) methods have become one of the fundamental approaches for approximating unlearning, as they effectively retain model performance. However, it is consistently observed that naive FT methods struggle to forget the targeted data. In this paper, we present the first theoretical analysis of FT methods for machine unlearning within a linear regression framework, providing a deeper exploration of this phenomenon. Our analysis reveals that while FT models can achieve zero remaining loss, they fail to forget the forgetting data, as the pretrained model retains its influence and the fine-tuning process does not adequately mitigate it. To address this, we propose a novel Retention-Based Masking (RBM) strategy that constructs a weight saliency map based on the remaining dataset, unlike existing methods that focus on the forgetting dataset. Our theoretical analysis demonstrates that RBM not only significantly improves unlearning accuracy (UA) but also ensures higher retaining accuracy (RA) by preserving overlapping features shared between the forgetting and remaining datasets. Experiments on synthetic and real-world datasets validate our theoretical insights, showing that RBM outperforms existing masking approaches in balancing UA, RA, and disparity metrics.