2 problems

Mesoscopic multiplier estimate. There are absolute constants $C,c_0>0$ such that, in the width band above, if $d\ge\varepsilon^{-2}\log^C n$, then with probability at least $1-1/n$…

Bubeck–Li–Nagaraj conjecture. The stated lower bound should hold for every Lipschitz activation and arbitrary weights, with no restriction on their magnitudes. The conjecture quant…