# One-Point Contraction: Erasing Representational Separability toward Irreversible Deep Forgetting

arXiv: https://arxiv.org/abs/2507.07754 · HTML: https://mlsanity.com/paper/2507.07754/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 42 of its 49 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Poison Frogs! Targeted Clean-Label Poisoning Attacks on Neural Networks](https://mlsanity.com/paper/1804.00792/) (2018)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [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)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Fast Yet Effective Machine Unlearning](https://mlsanity.com/paper/2111.08947/) (2021)
- [Model Sparsity Can Simplify Machine Unlearning](https://mlsanity.com/paper/2304.04934/) (2023)
- [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)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Boundary Unlearning](https://mlsanity.com/paper/2303.11570/) (2023)
- [Foundation Models and Fair Use](https://mlsanity.com/paper/2303.15715/) (2023)
- [What makes unlearning hard and what to do about it](https://mlsanity.com/paper/2406.01257/) (2024)
- [Towards Adversarial Evaluations for Inexact Machine Unlearning](https://mlsanity.com/paper/2201.06640/) (2022)
- [Unlearning or Obfuscating? Jogging the Memory of Unlearned LLMs via Benign Relearning](https://mlsanity.com/paper/2406.13356/) (2024)
- [Inexact Unlearning Needs More Careful Evaluations to Avoid a False Sense of Privacy](https://mlsanity.com/paper/2403.01218/) (2024)
- [Do Unlearning Methods Remove Information from Language Model Weights?](https://mlsanity.com/paper/2410.08827/) (2024)

## Built on by (most cited first, 2 of 2)

- [Erase at the Core: Representation Unlearning for Machine Unlearning](https://mlsanity.com/paper/2602.05375/) (2026)
- [Gradient Concentration, Not Weight Saliency, Explains Representation-Level Class Unlearning](https://mlsanity.com/paper/2607.21353/) (2026)

## Abstract (arXiv)

Machine unlearning is usually evaluated by what the classifier outputs: forget-set accuracy, confidence, membership-inference scores. We show that this is not enough. Across 14 representative unlearning methods on CIFAR-10 and SVHN, a single linear map fitted on a held-out calibration set, with no access to the forgotten data, reverses the unlearning in seconds and recovers forget-set accuracy to within a few percent of the original model. Recovered features even support pixel-level reconstruction through a generic decoder. We call this diagnostic Feature Mapping Recovery (FM-recovery). The pattern it exposes is uniform: current unlearning methods do not erase information from the representation, they apply an invertible linear distortion that hides it from one particular prediction head. We propose One-Point Contraction (OPC), an unlearning objective that collapses forget-set features to the origin while leaving the retain-set geometry intact. We prove that this contraction is equivalent to driving the predictive distribution to maximum entropy, so the same mechanism delivers behavioral forgetting and representation-level erasure at once. Forgotten queries land in a region the network treats as out-of-distribution, and the gradient signal on those queries collapses along with their features. OPC is the only method in our benchmark that survives FM-recovery, resists relearning and gradient-inversion attacks, and decouples forget from retain features in entangled settings, all without sacrificing retain or test accuracy.