# Unified Gradient-Based Machine Unlearning with Remain Geometry Enhancement

arXiv: https://arxiv.org/abs/2409.19732 · HTML: https://mlsanity.com/paper/2409.19732/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 76 of its 98 references that are in the map.
- First posted on arXiv 29 Sep 2024.

## Placed in

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

## Builds on (most cited first, 30 of 76)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [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)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models](https://mlsanity.com/paper/2211.05105/) (2022)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)

## Built on by (most cited first, 30 of 45)

- [MMUnlearner: Reformulating Multimodal Machine Unlearning in the Era of Multimodal Large Language Models](https://mlsanity.com/paper/2502.11051/) (2025)
- [MLLMEraser: Achieving Test-Time Unlearning in Multimodal Large Language Models through Activation Steering](https://mlsanity.com/paper/2510.04217/) (2025)
- [Approximate Domain Unlearning for Vision-Language Models](https://mlsanity.com/paper/2510.08132/) (2025)
- [The Right to be Forgotten in Pruning: Unveil Machine Unlearning on Sparse Models](https://mlsanity.com/paper/2507.18725/) (2025)
- [DualOptim: Enhancing Efficacy and Stability in Machine Unlearning with Dual Optimizers](https://mlsanity.com/paper/2504.15827/) (2025)
- [A Unified Gradient-based Framework for Task-agnostic Continual Learning-Unlearning](https://mlsanity.com/paper/2505.15178/) (2025)
- [Targeted Forgetting of Image Subgroups in CLIP Models](https://mlsanity.com/paper/2506.03117/) (2025)
- [FG-OrIU: Towards Better Forgetting via Feature-Gradient Orthogonality for Incremental Unlearning](https://mlsanity.com/paper/2601.13578/) (2026)
- [The Erasure Illusion: Stress-Testing the Generalization of LLM Forgetting Evaluation](https://mlsanity.com/paper/2512.19025/) (2025)
- [Exploring Nonlinear Pathway in Parameter Space for Machine Unlearning](https://mlsanity.com/paper/2505.10859/) (2025)
- [Reminiscence Attack on Residuals: Exploiting Approximate Machine Unlearning for Privacy](https://mlsanity.com/paper/2507.20573/) (2025)
- [Class Unlearning via Depth-Aware Removal of Forget-Specific Directions](https://mlsanity.com/paper/2604.15166/) (2026)
- [Tackling Fake Forgetting through Uncertainty Quantification](https://mlsanity.com/paper/2501.19403/) (2025)
- [FaLW: A Forgetting-aware Loss Reweighting for Long-tailed Unlearning](https://mlsanity.com/paper/2601.18650/) (2026)
- [DUET: Distilled LLM Unlearning from an Efficiently Contextualized Teacher](https://mlsanity.com/paper/2601.21283/) (2026)
- [Sharpness-Aware Parameter Selection for Machine Unlearning](https://mlsanity.com/paper/2504.06398/) (2025)
- [Direct Token Optimization: A Self-contained Approach to Large Language Model Unlearning](https://mlsanity.com/paper/2510.00125/) (2025)
- [Apollo: A Posteriori Label-Only Membership Inference Attack Towards Machine Unlearning](https://mlsanity.com/paper/2506.09923/) (2025)
- [Towards Mitigating Excessive Forgetting in LLM Unlearning via Entanglement-Guidance with Proxy Constraint](https://mlsanity.com/paper/2508.20443/) (2025)
- [WARP: Weight Teleportation for Attack-Resilient Unlearning Protocols](https://mlsanity.com/paper/2512.00272/) (2025)
- [Towards Irreversible Machine Unlearning for Diffusion Models](https://mlsanity.com/paper/2512.03564/) (2025)
- [Robust MLLM Unlearning via Visual Knowledge Distillation](https://mlsanity.com/paper/2512.11325/) (2025)
- [Designing to Forget: Deep Semi-parametric Models for Unlearning](https://mlsanity.com/paper/2603.22870/) (2026)
- [Forgetting That Sticks: Quantization-Permanent Unlearning via Circuit Attribution](https://mlsanity.com/paper/2605.15138/) (2026)
- [SHA256 at SemEval-2025 Task 4: Selective Amnesia -- Constrained Unlearning for Large Language Models via Knowledge Isolation](https://mlsanity.com/paper/2504.12996/) (2025)
- [TraceHiding: Scalable Machine Unlearning for Mobility Data](https://mlsanity.com/paper/2509.17241/) (2025)
- [Emergent AI Surveillance: Overlearned Person Re-Identification and Its Mitigation in Law Enforcement Context](https://mlsanity.com/paper/2510.06026/) (2025)
- [Hierarchical Dual-Strategy Unlearning for Biomedical and Healthcare Intelligence Using Imperfect and Privacy-Sensitive Medical Data](https://mlsanity.com/paper/2511.19498/) (2025)
- [Beyond Memorization: Selective Learning for Copyright-Safe Diffusion Model Training](https://mlsanity.com/paper/2512.11194/) (2025)
- [Machine Unlearning in Low-Dimensional Feature Subspace](https://mlsanity.com/paper/2601.22456/) (2026)

## Abstract (arXiv)

Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest descent direction, minimizing the output Kullback-Leibler divergence to exact MU inside a parameters' neighborhood. This probed direction decomposes into three components: weighted forgetting gradient ascent, fine-tuning retaining gradient descent, and a weight saliency matrix. Such decomposition derived from Euclidean metric encompasses most existing gradient-based MU methods. Nevertheless, adhering to Euclidean space may result in sub-optimal iterative trajectories due to the overlooked geometric structure of the output probability space. We suggest embedding the unlearning update into a manifold rendered by the remaining geometry, incorporating second-order Hessian from the remaining data. It helps prevent effective unlearning from interfering with the retained performance. However, computing the second-order Hessian for large-scale models is intractable. To efficiently leverage the benefits of Hessian modulation, we propose a fast-slow parameter update strategy to implicitly approximate the up-to-date salient unlearning direction. Free from specific modal constraints, our approach is adaptable across computer vision unlearning tasks, including classification and generation. Extensive experiments validate our efficacy and efficiency. Notably, our method successfully performs class-forgetting on ImageNet using DiT and forgets a class on CIFAR-10 using DDPM in just 50 steps, compared to thousands of steps required by previous methods.