# POUR: A Provably Optimal Method for Unlearning Representations via Neural Collapse

arXiv: https://arxiv.org/abs/2511.19339 · HTML: https://mlsanity.com/paper/2511.19339/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (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)
- [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)
- [Amnesiac Machine Learning](https://mlsanity.com/paper/2010.10981/) (2020)
- [Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.17591/) (2023)
- [Towards Unbounded Machine Unlearning](https://mlsanity.com/paper/2302.09880/) (2023)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [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)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Boundary Unlearning](https://mlsanity.com/paper/2303.11570/) (2023)
- [Zero-Shot Machine Unlearning](https://mlsanity.com/paper/2201.05629/) (2022)
- [Learning to Unlearn: Instance-wise Unlearning for Pre-trained Classifiers](https://mlsanity.com/paper/2301.11578/) (2023)
- [Machine Unlearning: Taxonomy, Metrics, Applications, Challenges, and Prospects](https://mlsanity.com/paper/2403.08254/) (2024)
- [Decoupled Distillation to Erase: A General Unlearning Method for Any Class-centric Tasks](https://mlsanity.com/paper/2503.23751/) (2025)
- [Deep Unlearning: Fast and Efficient Gradient-free Approach to Class Forgetting](https://mlsanity.com/paper/2312.00761/) (2023)
- [CLIPErase: Efficient Unlearning of Visual-Textual Associations in CLIP](https://mlsanity.com/paper/2410.23330/) (2024)
- [Are We Truly Forgetting? A Critical Re-examination of Machine Unlearning Evaluation Protocols](https://mlsanity.com/paper/2503.06991/) (2025)
- [Zero-Shot Class Unlearning in CLIP with Synthetic Samples](https://mlsanity.com/paper/2407.07485/) (2024)
- [Wide Neural Networks Trained with Weight Decay Provably Exhibit Neural Collapse](https://mlsanity.com/paper/2410.04887/) (2024)

## Built on by (most cited first, 6 of 6)

- [Erased, but Not Gone: Output Forgetting Is Not True Forgetting](https://mlsanity.com/paper/2606.25001/) (2026)
- [The BatchNorm Illusion: Diagnosing Normalization Artifacts in Machine Unlearning Evaluation](https://mlsanity.com/paper/2609.08901/) (2026)
- [Behavioral Guarantees for Proxy-Based Unlearning](https://mlsanity.com/paper/2605.10680/) (2026)
- [Gradient Concentration, Not Weight Saliency, Explains Representation-Level Class Unlearning](https://mlsanity.com/paper/2607.21353/) (2026)
- [DECAF: De-Clustering for Adaptive Representational Unlearning](https://mlsanity.com/paper/2607.23934/) (2026)
- [SCOPE: Entanglement Frontier Escape for Source-Free Class Unlearning](https://mlsanity.com/paper/2608.02058/) (2026)

## Abstract (arXiv)

In computer vision, machine unlearning aims to remove the influence of specific visual concepts or training images without retraining from scratch. Studies show that existing approaches often modify the classifier while leaving internal representations intact, resulting in incomplete forgetting. In this work, we extend the notion of unlearning to the representation level, deriving a three-term interplay between forgetting efficacy, retention fidelity, and class separation. Building on Neural Collapse theory, we show that the orthogonal projection of a simplex Equiangular Tight Frame (ETF) remains an ETF in a lower dimensional space, yielding a provably optimal forgetting operator. We further introduce the Representation Unlearning Score (RUS) to quantify representation-level forgetting and retention fidelity. Building on this, we introduce POUR (Provably Optimal Unlearning of Representations), a geometric projection method with closed-form (POUR-P) and a feature-level unlearning variant under a distillation scheme (POUR-D). Experiments on CIFAR-10/100 and PathMNIST demonstrate that POUR achieves effective unlearning while preserving retained knowledge, outperforming state-of-the-art unlearning methods on both classification-level and representation-level metrics.