Quadratic Sample Complexity for Strictly Replicable Realizable Learning with Unknown Marginals

2026-10-21来源 arXiv stat.MLEnglish
arXiv:2610.26944v1 Announce Type: new Abstract: Under the quantifier $\exists A\,\forall D$, where the realizable distribution and its marginal are unknown, we determine the finite-class sample-complexity exponent for strict replicability: two independent samples and one shared seed must produce identical functions. For $\varepsilon=\delta=\rho=10^{-4}$, the worst case over $|H|\le M$ is $\Theta((\log M)^2)$, without iterated logarithms. For $d\ge1$, $0

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