# Exploring Nonlinear Pathway in Parameter Space for Machine Unlearning

arXiv: https://arxiv.org/abs/2505.10859 · HTML: https://mlsanity.com/paper/2505.10859/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 30 of its 36 references that are in the map.
- First posted on arXiv 16 May 2025.

## Placed in

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

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

- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (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)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [Fast Machine Unlearning Without Retraining Through Selective Synaptic Dampening](https://mlsanity.com/paper/2308.07707/) (2023)
- [Privacy Risks of Securing Machine Learning Models against Adversarial Examples](https://mlsanity.com/paper/1905.10291/) (2019)
- [Zero-Shot Machine Unlearning](https://mlsanity.com/paper/2201.05629/) (2022)
- [Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness](https://mlsanity.com/paper/2005.00060/) (2020)
- [Zero-shot Knowledge Transfer via Adversarial Belief Matching](https://mlsanity.com/paper/1905.09768/) (2019)
- [Towards Adversarial Evaluations for Inexact Machine Unlearning](https://mlsanity.com/paper/2201.06640/) (2022)
- [Learning to Unlearn: Instance-wise Unlearning for Pre-trained Classifiers](https://mlsanity.com/paper/2301.11578/) (2023)
- [Unified Gradient-Based Machine Unlearning with Remain Geometry Enhancement](https://mlsanity.com/paper/2409.19732/) (2024)
- [Shared Adversarial Unlearning: Backdoor Mitigation by Unlearning Shared Adversarial Examples](https://mlsanity.com/paper/2307.10562/) (2023)
- [Tight Bounds for Machine Unlearning via Differential Privacy](https://mlsanity.com/paper/2309.00886/) (2023)
- [Machine Unlearning in Learned Databases: An Experimental Analysis](https://mlsanity.com/paper/2311.17276/) (2023)
- [Attribute-to-Delete: Machine Unlearning via Datamodel Matching](https://mlsanity.com/paper/2410.23232/) (2024)
- [Efficient Model Editing with Task-Localized Sparse Fine-tuning](https://mlsanity.com/paper/2504.02620/) (2025)
- [Unlearning with Fisher Masking](https://mlsanity.com/paper/2310.05331/) (2023)
- [Forget Vectors at Play: Universal Input Perturbations Driving Machine Unlearning in Image Classification](https://mlsanity.com/paper/2412.16780/) (2024)
- [Unveiling Mode Connectivity in Graph Neural Networks](https://mlsanity.com/paper/2502.12608/) (2025)

## Built on by (most cited first, 4 of 4)

- [MoCo-EA: Exploiting Adversarial Mode Connectivity for Efficient Evolutionary Attacks](https://mlsanity.com/paper/2605.18919/) (2026)
- [On the Plasticity Collapse in Continual Machine Unlearning](https://mlsanity.com/paper/2608.29513/) (2026)
- [SAM-on-the-Curve: Sharpness-Aware Mode Connectivity for Robust Weight-Space Interpolation](https://mlsanity.com/paper/2609.17748/) (2026)
- [Trajectory Unlearning on LLM-based Agents](https://mlsanity.com/paper/2609.33639/) (2026)

## Abstract (arXiv)

Machine Unlearning (MU) aims to remove the information of specific training data from a trained model, ensuring compliance with privacy regulations and user requests. While one line of existing MU methods relies on linear parameter updates via task arithmetic, they suffer from weight entanglement. In this work, we propose a novel MU framework called Mode Connectivity Unlearning (MCU) that leverages mode connectivity to find an unlearning pathway in a nonlinear manner. To further enhance performance and efficiency, we introduce a parameter mask strategy that not only improves unlearning effectiveness but also reduces computational overhead. Moreover, we propose an adaptive adjustment strategy for our unlearning penalty coefficient to adaptively balance forgetting quality and predictive performance during training, eliminating the need for empirical hyperparameter tuning. Unlike traditional MU methods that identify only a single unlearning model, MCU uncovers a spectrum of unlearning models along the pathway. Overall, MCU serves as a plug-and-play framework that seamlessly integrates with any existing MU methods, consistently improving unlearning efficacy. Extensive experiments on the image classification task demonstrate that MCU achieves superior performance. The codes are available at https://github.com/TIML-Group/Mode-Connectivity-Unlearning.