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Jiao-Jiao Jiang

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#machine learning Preprint Sep 2026

Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarchy

Language generation in the limit asks for valid unseen elements from every exhaustive positive presentation of an unknown infinite language. We characterize this task for arbitrary families over a countable universe. Generation is possible exactly when each target can be assigned a finite positive witness so that the t...

Xiao-Yu Li, Andi Han, Jiao-Jiao Jiang et al. · 0 citations

Preprint Jul 2026

The Exact Worst-Case Tail Probability under Bounded Kurtosis

We determine exactly what a kurtosis bound buys for one-sided tail control. For the class $\mathcal{C}(\kappa)$ of real random variables with mean $0$, variance $1$, and fourth moment at most $\kappa$, the skewness left free, we compute the worst-case tail probability $V_1(t,\kappa)=\sup_{X\in\mathcal{C}(\kappa)}\mathb...

Xiaoyu Li, Andi Han, Jiaojiao Jiang et al. · 0 citations

Preprint Aug 2026

Optimistic Rates for Multiclass PAC Learning

Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself. For a class of Natarajan dimension $d_N$ and Daniely-Shalev-Shwartz dimension $d_{DS}$, the optimal excess risk...

Xiao-Yu Li, Andi Han, Jiao-Jiao Jiang et al. · 1 citation