An Optimal Sauer Lemma Over ℓ-ary Alphabets

Published in arXiv preprint arXiv:2604.12952, 2026

We establish an optimal generalization of the classical Sauer-Shelah lemma to the multiclass setting over ℓ-ary alphabets. Our result gives tight bounds on the growth function for multiclass hypothesis classes and has implications for sample complexity in multiclass learning theory.

Steve Hanneke, Qinglin Meng, Shay Moran, Amirreza Shaeiri (alphabetical order)
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