with optimal rate $n^{-1/2}$. As an application, we derive non-uniform Berry-Esseen bounds with an optimal moment to weight-function relation $p \mapsto (1 + |x|)^{p}$ and rate $n^{-1/2}$. In addition, we [...] the expressive power of ReLU neural networks grows with their depth, the function $F_n = \max\{0,x_1,\ldots,x_n\}$ has been considered in the literature. A conjecture by Hertrich, Basu, Di Summa, and Skutella [...] [NeurIPS 2021] states that any ReLU network that exactly represents $F_n$ has at least $\lceil \log_2(n+1) \rceil$ hidden layers. The conjecture has recently been confirmed for networks with integer weights
https://www.mathematik.uni-rostock.de/aktivitaeten-veranstaltungen/regelmaessige-veranstaltungen/mathematisches-forschungsseminar/2025/
