# Efficient Utility-Preserving Machine Unlearning with Implicit Gradient Surgery

arXiv: https://arxiv.org/abs/2510.22124 · HTML: https://mlsanity.com/paper/2510.22124/

## 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 58 of its 76 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 58)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [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)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [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)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (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)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [Large Language Model Unlearning](https://mlsanity.com/paper/2310.10683/) (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)
- [Rethinking Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2402.08787/) (2024)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)

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

- [Z-Erase: Enabling Concept Erasure in Single-Stream Diffusion Transformers](https://mlsanity.com/paper/2603.25074/) (2026)
- [EraseAnything++: Enabling Concept Erasure in Rectified Flow Transformers Leveraging Multi-Object Optimization](https://mlsanity.com/paper/2603.00978/) (2026)
- [Behavioral Guarantees for Proxy-Based Unlearning](https://mlsanity.com/paper/2605.10680/) (2026)
- [SoK: Unlearnability and Unlearning for Model Dememorization](https://mlsanity.com/paper/2605.11592/) (2026)
- [BARRIER: Bounded Activation Regions for Robust Information Erasure](https://mlsanity.com/paper/2605.15737/) (2026)

## Abstract (arXiv)

Machine unlearning (MU) aims to efficiently remove sensitive or harmful memory from a pre-trained model. The key challenge is to balance the potential tradeoff between unlearning efficacy and utility preservation, which involves forgetting undesirable information as defined while maintaining the model's original performance. One potential way to tackle this problem is to use multi-objective optimization to jointly optimize both the unlearning and utility preservation objectives. However, existing multi-objective methods only guarantee finding a Pareto-optimal solution without fine-grained control, which causes under-optimization of the unlearning objective. To this end, we first model MU as a constrained optimization problem, that is, optimizing the unlearning objective under the constraint of a bounded increase for utility loss. We then show that solving this optimization problem is equivalent to unilateral gradient surgery on the unlearning objective. To resolve the additional computational cost brought by gradient surgery, we propose an implicit gradient surgery method, which approximates the solution to the aforementioned constrained optimization problem via only one backpropagation, thereby achieving efficient utility-preserving MU. Theoretically, we provide a tight convergence analysis of the algorithm. Empirically, our extensive experiments show that the proposed algorithm achieves better tradeoff results than existing baselines. Codes are available at https://github.com/anseryuer/EUPMU-Efficient-Utility-Preserving-Machine-Unlearning.