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The Sharp Tail of Uniform Stability

arXiv · AI, language, vision and robotics · article · Aug 25, 2026 · UTC

Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $γ$-uniformly stable algorithm with loss in $[0,L]$ has generalization gap at most $O \left(γ\log(1/δ) +L\sqrt{\frac{\log(1/δ)}{n}}\right)$ with probability $1-δ$. Whether an actual bounded-loss learning algorithm can realize the linear dependence on $\log(1/δ)$ has remained open. The known construction realizes it only for auxiliary weakly dependent random variables whose pointwise range grows with $n$. The known learning lower bound holds only at con

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