拓展了传统VC理论，用于高阶学习模型的泛化分析。
Higher-arity PAC learning, VC dimension and packing lemma
- 提出高阶VC维度（VCₙ）与对应打包引理，适用于多变量联合空间。
- 证明高阶PAC学习在乘积测度下可由VCₙ维数刻画。
- 为近期多篇论文提供了理论基础，适合学习理论研究者。
本文综述我们与Chernikov、Towsner在arXiv:2010.00726中关于高阶VC理论（VCₙ维度）的工作，包括对Haussler打包引理的推广及相应的分片正则性引理；并表明该理论可刻画Kobayashi、Kuriyama和Takeuchi于2015年引入的在n重乘积空间与乘积测度下的高阶PAC学习（PACₙ学习）。此外，指出arXiv:2402.14294、arXiv:2505.15688、arXiv:2509.20404中的若干近期成果均可由我们的工作推导得出。
原文摘要 · Abstract (English)
The aim of this note is to overview some of our work in Chernikov, Towsner'20 (arXiv:2010.00726) developing higher arity VC theory (VC$_n$ dimension), including a generalization of Haussler packing lemma, and an associated tame (slice-wise) hypergraph regularity lemma; and to demonstrate that it characterizes higher arity PAC learning (PAC$_n$ learning) in $n$-fold product spaces with respect to product measures introduced by Kobayashi, Kuriyama and Takeuchi'15. We also point out how some of the recent results in arXiv:2402.14294, arXiv:2505.15688, arXiv:2509.20404 follow from our work in arXiv:2010.00726.
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