Publications [#361586] of Jianfeng Lu

Papers Published

1. Lu, J; Steinerberger, S, Neural Collapse with Cross-Entropy Loss (December, 2020)
   (last updated on 2026/01/16)

   Abstract:
   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.