How Does Distribution Matching Help Domain Generalization: An Information-theoretic Analysis

IEEE Transactions on Information Theory. 2025.
Yuxin Dong, Tieliang Gong, Hong Chen, Shuangyong Song, Weizhan Zhang, Chen Li.

Abstract

Domain generalization aims to learn invariance across multiple source domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success in domain generalization, these methods generally lack generalization guarantees or depend on strong assumptions, leaving a gap in understanding the underlying mechanism of distribution matching. In this work, we formulate domain generalization from a novel probabilistic perspective, ensuring robustness while avoiding overly conservative solutions. Through comprehensive information-theoretic analysis, we provide key insights into the roles of gradient and representation matching in promoting generalization. Our results reveal the complementary relationship between these two components, indicating that existing works focusing solely on either gradient or representation alignment are insufficient to solve the domain generalization problem. In light of these theoretical findings, we introduce IDM to simultaneously align the inter-domain gradients and representations. Integrated with the proposed PDM method for complex distribution matching, IDM achieves superior performance over various baseline methods.

Cite

@article{dong2025does,
  title={How Does Distribution Matching Help Domain Generalization: An Information-theoretic Analysis},
  author={Dong, Yuxin and Gong, Tieliang and Chen, Hong and Song, Shuangyong and Zhang, Weizhan and Li, Chen},
  journal={IEEE Transactions on Information Theory},
  year={2025},
  publisher={IEEE}
}