# Controllable Machine Unlearning via Gradient Pivoting

arXiv: https://arxiv.org/abs/2510.19226 · HTML: https://mlsanity.com/paper/2510.19226/

## 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 31 of its 42 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Erasing Concepts from Diffusion Models](https://mlsanity.com/paper/2303.07345/) (2023)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [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)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.17591/) (2023)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [Selective Amnesia: A Continual Learning Approach to Forgetting in Deep Generative Models](https://mlsanity.com/paper/2305.10120/) (2023)
- [Boundary Unlearning](https://mlsanity.com/paper/2303.11570/) (2023)
- [Fast Model Debias with Machine Unlearning](https://mlsanity.com/paper/2310.12560/) (2023)
- [Learning to Unlearn: Instance-wise Unlearning for Pre-trained Classifiers](https://mlsanity.com/paper/2301.11578/) (2023)
- [A Closer Look at Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2410.08109/) (2024)
- [Hard to Forget: Poisoning Attacks on Certified Machine Unlearning](https://mlsanity.com/paper/2109.08266/) (2021)
- [Machine Unlearning for Image-to-Image Generative Models](https://mlsanity.com/paper/2402.00351/) (2024)
- [Hidden Poison: Machine Unlearning Enables Camouflaged Poisoning Attacks](https://mlsanity.com/paper/2212.10717/) (2022)
- [Learn to Unlearn for Deep Neural Networks: Minimizing Unlearning Interference with Gradient Projection](https://mlsanity.com/paper/2312.04095/) (2023)
- [Fair Machine Unlearning: Data Removal while Mitigating Disparities](https://mlsanity.com/paper/2307.14754/) (2023)
- [Machine Unlearning via Null Space Calibration](https://mlsanity.com/paper/2404.13588/) (2024)
- [Dual Cone Gradient Descent for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.18426/) (2024)
- [To Be Forgotten or To Be Fair: Unveiling Fairness Implications of Machine Unlearning Methods](https://mlsanity.com/paper/2302.03350/) (2023)
- [Adversarial Machine Unlearning](https://mlsanity.com/paper/2406.07687/) (2024)
- [Gradient Surgery for One-shot Unlearning on Generative Model](https://mlsanity.com/paper/2307.04550/) (2023)

## Abstract (arXiv)

Machine unlearning (MU) aims to remove the influence of specific data from a trained model. However, approximate unlearning methods, often formulated as a single-objective optimization (SOO) problem, face a critical trade-off between unlearning efficacy and model fidelity. This leads to three primary challenges: the risk of over-forgetting, a lack of fine-grained control over the unlearning process, and the absence of metrics to holistically evaluate the trade-off. To address these issues, we reframe MU as a multi-objective optimization (MOO) problem. We then introduce a novel algorithm, Controllable Unlearning by Pivoting Gradient (CUP), which features a unique pivoting mechanism. Unlike traditional MOO methods that converge to a single solution, CUP's mechanism is designed to controllably navigate the entire Pareto frontier. This navigation is governed by a single intuitive hyperparameter, the `unlearning intensity', which allows for precise selection of a desired trade-off. To evaluate this capability, we adopt the hypervolume indicator, a metric that captures both the quality and diversity of the entire set of solutions an algorithm can generate. Our experimental results demonstrate that CUP produces a superior set of Pareto-optimal solutions, consistently outperforming existing methods across various vision tasks.