Hierarchical Domain Generalization
For machine learning theorists, this work highlights a fundamental limitation of current generalization theory by showing that domain hierarchy, not just hypothesis class complexity, can determine generalization success.
The paper identifies that in hierarchical domain generalization, the train/test domain partition itself can cause generalization failure regardless of hypothesis class complexity or training size, arguing that domain structure must be a primary consideration in generalization theory.
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.