研究如何从有限区域外推到完整空间，突破传统独立同分布假设。
Hierarchical Domain Generalization
- 用任意层级结构替代独立同分布采样
- 发现训练测试划分方式是泛化失败的核心障碍
- 强调领域结构需纳入现代泛化理论核心
我们研究层次化领域泛化问题，将其视为从有限观测区域外推至整个实例空间的任务，以任意领域层次结构取代独立同分布采样。研究表明，泛化障碍不仅源于假设类的复杂性，更在于证据揭示的方式——训练与测试领域的划分。无论假设类多么简单或训练数据多么充足，总存在某种划分使得对某些目标领域泛化失败。这些结果表明，现代泛化理论必须将领域结构作为首要考虑对象。
原文摘要 · Abstract (English)
We study hierarchical domain generalization as a problem of extrapolation from finite observed regions to an entire instance space, replacing i.i.d. sampling with arbitrary domain hierarchies. We show that the central obstruction is not only the complexity of the hypothesis class, but the train/test domain partition through which evidence is revealed. In particular, no matter how small the class or how large the training size, some partition makes generalization fail for some target. These results suggest that modern generalization theory must treat domain structure as a first-class object.
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