arXiv:2605.12465cs.LG2026-05
提出高阶样本压缩机制，证明其存在即意味着高阶可学习性。
High-arity Sample Compression
- 设计高阶样本压缩方案，将学习理论拓展至多维产品空间
- 证明非平凡压缩方案的存在可推出高阶PAC可学习性
- 为高阶学习理论提供新工具，适合理论学习研究者
近期多项研究开始探讨学习理论中关于乘积空间的变体，统称为高阶学习理论。本文研究高阶样本压缩方案的变体，证明若存在非平凡质量的高阶样本压缩方案，则可推出高阶PAC可学习性。该结果建立了样本压缩与高阶可学习性之间的强联系，为高阶学习理论提供了新的分析框架。
原文摘要 · Abstract (English)
Recently, a series of works have started studying variations of concepts from learning theory for product spaces, which can be collected under the name high-arity learning theory. In this work, we consider a high-arity variant of sample compression schemes and we prove that the existence of a high-arity sample compression scheme of non-trivial quality implies high-arity PAC learnability.
学习理论样本压缩高阶学习
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