提出可证明最优的表示级遗忘方法，实现精准删减且不破坏保留知识。
POUR: A Provably Optimal Method for Unlearning Representations via Neural Collapse
- 基于神经坍缩理论设计几何投影遗忘算子，确保遗忘过程可证明最优。
- 在CIFAR-10/100与PathMNIST上，表示级遗忘率提升15%以上，分类性能下降<2%。
- 适合需精准删除特定训练数据或概念的可信机器学习场景。
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。现有方法通常仅修改分类器，导致内部表示未被充分遗忘，造成遗忘不彻底。本文将遗忘概念扩展至表示层，揭示遗忘效率、保留保真度与类别分离之间的三重关系。基于神经坍缩理论，我们证明正交投影下等角紧框架（ETF）在低维空间中仍保持ETF性质，从而推导出可证明最优的遗忘算子。进一步提出表示遗忘得分（RUS）以量化表示层遗忘与保留保真度。基于此，提出POUR（Provably Optimal Unlearning of Representations）方法，包含闭式解方案（POUR-P）和基于蒸馏的特征级变体（POUR-D）。在CIFAR-10/100与PathMNIST上的实验表明，POUR在分类与表示层面均显著优于现有最先进方法，有效实现遗忘同时保留知识。
原文摘要 · Abstract (English)
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.
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