Hierarchical Domain Generalization

2026-07-17

AI Summary

This study addresses the problem of domain generalization under arbitrary domain hierarchies, focusing on how to extrapolate from finitely observed domains to the entire instance space. Departing from the conventional i.i.d. assumption, it treats the domain partition structure as a first-class object in generalization theory, revealing that the very way training and test domains are partitioned is a fundamental source of generalization failure. By integrating theoretical analyses of hypothesis class complexity with domain structure, the work characterizes the intrinsic limits of extrapolation and proves that, even with an extremely simple hypothesis class or infinitely many training samples, certain domain partitions inevitably lead to failure in generalizing to target domains. This provides a novel theoretical perspective and structural understanding of domain generalization.

Abstract

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.

Problem

• hierarchical domain generalization
• domain structure
• extrapolation
• generalization failure
• train/test domain partition

Innovation

• hierarchical domain generalization
• domain structure
• extrapolation
• generalization theory
• train/test partition