In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally separates features of every two classes on a sphere and does not require a larger feature dimension than the number of classes. Out of curiosity about the symmetry of Grassmannian Frame, we conduct experiments to explore if models with different Grassmannian Frames have different performance. As a result, we discover the Symmetric Generalization phenomenon. We provide a theorem to explain Symmetric Generalization of permutation. However, the question of why different directions of features can lead to such different generalization is still open for future investigation.

翻译：本文通过证明广义神经坍缩假设，拓展了原始的神经坍缩现象研究。我们从分类任务的优化与泛化过程中推导出格拉斯曼框架结构。该结构能够在球面上最大化任意两个类别的特征分离，且无需特征维度大于类别数。出于对格拉斯曼框架对称性的好奇，我们通过实验探究不同格拉斯曼框架的模型是否具有不同性能，进而发现了对称泛化现象。我们提出一个定理解释置换对称泛化现象，但不同特征方向为何导致如此显著的泛化差异，仍有待未来进一步研究。