POUR：基于神经坍缩的可证明最优表征遗忘方法
POUR: A Provably Optimal Method for Unlearning Representation via Neural Collapse
把机器遗忘从分类器层推进到表征层，用 Neural Collapse 下 simplex ETF 的正交投影给出闭式最优遗忘算子，并提供蒸馏式特征级变体；做视觉模型隐私删除或概念擦除时可直接复用该投影算子与 RUS 指标来评估表征是否真正被遗忘。
原文依据 the orthogonal projection of a simplex Equiangular Tight Frame (ETF) remains an ETF in a lower-dimensional space
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论在计算机视觉中，机器遗忘旨在移除特定视觉概念或训练图像的影响，而无需从头重新训练。研究表明，现有方法往往只修改分类器而保持内部表征不变，导致遗忘不彻底。在本工作中，我们将遗忘的概念扩展到表征层面，推导出遗忘有效性、保留保真度与类别分离度之间的三项相互作用关系。基于神经坍缩理论，我们证明单纯形等角紧框架（ETF）的正交投影在低维空间中仍然是 ETF，从而得到一个可证明最优的遗忘算子。我们进一步引入表征遗忘分数（RUS）来量化表征层面的遗忘程度与保留保真度。在此基础上，我们提出 POUR（可证明最优的表征遗忘），这是一种几何投影方法，包含闭式解变体（POUR-P）以及在蒸馏方案下的特征级遗忘变体（POUR-D）。在 CIFAR-10/100 与 PathMNIST 上的实验表明，POUR 在实现有效遗忘的同时保留了已有知识，在分类层面与表征层面的指标上均优于最优的遗忘方法。代码将在论文被接收后发布。
英文原文摘要 1331 字符
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 feature-level unlearning variants 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. Code will be released upon acceptance of the paper.