论文标题
神经崩溃，横向损失
Neural Collapse with Cross-Entropy Loss
论文作者
论文摘要
我们考虑了$ \ Mathbb {r}^d $中的单位hypersphere上$ n $特征向量的跨凝回损失的变异问题。我们证明，当$ d \ geq n -1 $时，全球最小值由单纯含量紧密的框架给出，这证明了神经崩溃的行为是合理的。我们还证明，作为$ n \ rightarrow \ infty $，带有固定$ D $的$，最小化点将在Hypersphere上均匀分布，并与Benedetto＆Fickus的框架潜力显示出连接。
We consider the variational problem of cross-entropy loss with $n$ feature vectors on a unit hypersphere in $\mathbb{R}^d$. We prove that when $d \geq n - 1$, the global minimum is given by the simplex equiangular tight frame, which justifies the neural collapse behavior. We also prove that as $n \rightarrow \infty$ with fixed $d$, the minimizing points will distribute uniformly on the hypersphere and show a connection with the frame potential of Benedetto & Fickus.
