# Approximate Machine Unlearning through Manifold Representation Forgetting Guided by Self Mode Connectivity

arXiv: https://arxiv.org/abs/2605.22871 · HTML: https://mlsanity.com/paper/2605.22871/

## 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 27 of its 47 references that are in the map.
- First posted on arXiv 20 May 2026.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (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)
- [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)
- [Descent-to-Delete: Gradient-Based Methods for Machine Unlearning](https://mlsanity.com/paper/2007.02923/) (2020)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Understanding self-supervised Learning Dynamics without Contrastive Pairs](https://mlsanity.com/paper/2102.06810/) (2021)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [When Machine Unlearning Jeopardizes Privacy](https://mlsanity.com/paper/2005.02205/) (2020)
- [Can Bad Teaching Induce Forgetting? Unlearning in Deep Networks using an Incompetent Teacher](https://mlsanity.com/paper/2205.08096/) (2022)
- [On the Necessity of Auditable Algorithmic Definitions for Machine Unlearning](https://mlsanity.com/paper/2110.11891/) (2021)
- [DeltaGrad: Rapid retraining of machine learning models](https://mlsanity.com/paper/2006.14755/) (2020)
- [Privacy Risks of Securing Machine Learning Models against Adversarial Examples](https://mlsanity.com/paper/1905.10291/) (2019)
- [Boundary Unlearning](https://mlsanity.com/paper/2303.11570/) (2023)
- [Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness](https://mlsanity.com/paper/2005.00060/) (2020)
- [Variational Bayesian Unlearning](https://mlsanity.com/paper/2010.12883/) (2020)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Towards Semantic Communications: Deep Learning-Based Image Semantic Coding](https://mlsanity.com/paper/2208.04094/) (2022)
- [Learning Efficient Coding of Natural Images with Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2303.03307/) (2023)
- [Markov Chain Monte Carlo-Based Machine Unlearning: Unlearning What Needs to be Forgotten](https://mlsanity.com/paper/2202.13585/) (2022)

## Abstract (arXiv)

Machine unlearning is a fundamental mechanism that enforces the right to be forgotten. Existing unlearning studies that rely on label manipulation or task-gradient reversal often deliver limited unlearning effectiveness. Moreover, they can undermine the original learning objective and typically do not guarantee equivalence to standard unlearning by retraining. In this paper, we propose ManiF-SMC (Manifold Forgetting with Self Mode Connectivity), motivated by the observation that a model retrained on the remaining data tends to classify erased samples by their semantic similarity to the retained data. We begin with systematically recasting the approximate unlearning as pushing each erased sample away from its original learned manifold representation centroid toward its nearest semantic neighbors in the retained data. This reformulation aligns unlearning with retraining behavior and operates purely in representation space, reducing reliance on labels and task-specific gradients. To tackle the manifold representation-based unlearning problem, ManiF-SMC encapsulates the unlearning and representation preservation goals in a margin-based triplet loss. Because finding a suitable margin for unlearning is challenging, we propose a self-mode-connectivity module that rapidly reconstructs the local manifold to guide the adaptive margins generation for each unlearning case. Extensive experiments on four representative datasets show that ManiF-SMC achieves unlearning effectiveness comparable to state-of-the-art approximate methods while operating solely within the model's representation space.