A polylogarithmic bound for list replicability

Abstract

Zhang [Zha26] recently posted a manuscript announcing that the list-replicability number of every class of $M\ge 2$ binary concepts on $N\ge 2$ domain points is $O({\log }^{2}M\log N)$, which would be the first polylogarithmic upper bound on this quantity. In this note, we present a short, self-contained proof of this bound, following the high-level approach of the manuscript but with considerably simpler arguments.