Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the number of classes K. We demonstrate that two popular unconstrained feature models are strict saddle functions, with every critical point being either a global minimum or a strict saddle point that can be exited using negative curvatures. The primary findings conclusively confirm the conjecture on the unconstrained feature models in previous articles.

翻译：最近，在深度神经网络分类任务训练的最终阶段，观察到一种被称为神经坍缩的有趣经验现象。本文研究了当特征维度$d$等于类别数$K$时的情况。我们证明两种流行的无约束特征模型是严格鞍函数，其每个临界点要么是全局最小值，要么是可以通过负曲率退出的严格鞍点。主要发现确凿地证实了先前文献中关于无约束特征模型的猜想。