  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.
