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A polylogarithmic bound for list replicability

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.

AuthorsAri Blondal, Hamed Hatami, Pooya Hatami et al.
Primary categorystat.ML
Published14 October 2026
Last updated at source14 October 2026
stat.MLcs.LGmath.CO
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