In this paper, we extends 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.

本文提出了广义神经崩溃假说，并通过优化和分类的推广获得 Grassmann 框架结构。该结构在球面上最大化地分离每两类的特征，不需要比类别数量更大的特征维度。我们发现了对称泛化现象，并提供了一个用于解释置换的对称泛化定理。尽管不同特征方向导致不同泛化的原因仍需未来研究。

神经塌陷现象的研究：Grassmann 框架，对称性，泛化

A Study of Neural Collapse Phenomenon: Grassmannian Frame, Symmetry,  Generalization

A Grassmannian frame is a collection of unit vectors which are optimally
incoherent. To date, the vast majority of explicit Grassmannian frames are
equiangular tight frames (ETFs). This paper surveys every known construction of
ETFs and tabulates existence for sufficiently small dimensions.

本文调查了所有已知的 ETFs 构造方法，并在较小的维度中表明了其存在。