# Soft Weighted Machine Unlearning

arXiv: https://arxiv.org/abs/2505.18783 · HTML: https://mlsanity.com/paper/2505.18783/

## 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 37 of its 50 references that are in the map.
- First posted on arXiv 24 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [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)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (2023)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Unlearn What You Want to Forget: Efficient Unlearning for LLMs](https://mlsanity.com/paper/2310.20150/) (2023)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [SOUL: Unlocking the Power of Second-Order Optimization for LLM Unlearning](https://mlsanity.com/paper/2404.18239/) (2024)
- [50 Years of Test (Un)fairness: Lessons for Machine Learning](https://mlsanity.com/paper/1811.10104/) (2018)
- [Fast Model Debias with Machine Unlearning](https://mlsanity.com/paper/2310.12560/) (2023)
- [Backdoor Defense with Machine Unlearning](https://mlsanity.com/paper/2201.09538/) (2022)
- [A Duty to Forget, a Right to be Assured? Exposing Vulnerabilities in Machine Unlearning Services](https://mlsanity.com/paper/2309.08230/) (2023)
- [Towards Certified Unlearning for Deep Neural Networks](https://mlsanity.com/paper/2408.00920/) (2024)
- [Fair Machine Unlearning: Data Removal while Mitigating Disparities](https://mlsanity.com/paper/2307.14754/) (2023)
- [Recommendation Unlearning via Influence Function](https://mlsanity.com/paper/2307.02147/) (2023)
- [Machine Unlearning via Null Space Calibration](https://mlsanity.com/paper/2404.13588/) (2024)
- [Machine Unlearning in Learned Databases: An Experimental Analysis](https://mlsanity.com/paper/2311.17276/) (2023)

## Abstract (arXiv)

Machine unlearning, as a post-hoc processing technique, has gained widespread adoption in addressing challenges like bias mitigation and robustness enhancement, colloquially, machine unlearning for fairness and robustness. However, existing non-privacy unlearning-based solutions persist in using binary data removal framework designed for privacy-driven motivation, leading to significant information loss, a phenomenon known as over-unlearning. While over-unlearning has been largely described in many studies as primarily causing utility degradation, we investigate its fundamental causes and provide deeper insights in this work through counterfactual leave-one-out analysis. In this paper, we introduce a weighted influence function that assigns tailored weights to each sample by solving a convex quadratic programming problem analytically. Building on this, we propose a soft-weighted framework enabling fine-grained model adjustments to address the over-unlearning challenge. We demonstrate that the proposed soft-weighted scheme is versatile and can be seamlessly integrated into most existing unlearning algorithms. Extensive experiments show that in fairness- and robustness-driven tasks, the soft-weighted scheme significantly outperforms hard-weighted schemes in fairness/robustness metrics and alleviates the decline in utility metric, thereby enhancing machine unlearning algorithm as an effective correction solution.