Why Domain Generalization Fail? A View of Necessity and Sufficiency

2025-02-15

AI Summary

Domain generalization (DG) often fails to consistently outperform empirical risk minimization (ERM) in practice, primarily because existing methods rely excessively on strong or diverse source- or target-domain priors, neglecting the fundamental feasibility boundary of generalization under limited domain availability. Method: This paper establishes, for the first time, the necessary and sufficient conditions for DG generalization, revealing that current approaches commonly omit verification of necessity—rendering generalization guarantees unattainable. We propose a novel paradigm integrating subspace representation alignment with theory-driven dual regularization, jointly enforcing both necessity constraints (e.g., domain invariance) and sufficiency constraints (e.g., discriminability). Contribution/Results: Evaluated on standard DG benchmarks, our method significantly surpasses ERM and state-of-the-art DG algorithms. Empirical results demonstrate that explicitly maintaining necessary conditions enhances generalization robustness and reliability.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Computer Vision: Adversarial Attacks & Robustness
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Despite a strong theoretical foundation, empirical experiments reveal that existing domain generalization (DG) algorithms often fail to consistently outperform the ERM baseline. We argue that this issue arises because most DG studies focus on establishing theoretical guarantees for generalization under unrealistic assumptions, such as the availability of sufficient, diverse (or even infinite) domains or access to target domain knowledge. As a result, the extent to which domain generalization is achievable in scenarios with limited domains remains largely unexplored. This paper seeks to address this gap by examining generalization through the lens of the conditions necessary for its existence and learnability. Specifically, we systematically establish a set of necessary and sufficient conditions for generalization. Our analysis highlights that existing DG methods primarily act as regularization mechanisms focused on satisfying sufficient conditions, while often neglecting necessary ones. However, sufficient conditions cannot be verified in settings with limited training domains. In such cases, regularization targeting sufficient conditions aims to maximize the likelihood of generalization, whereas regularization targeting necessary conditions ensures its existence. Using this analysis, we reveal the shortcomings of existing DG algorithms by showing that, while they promote sufficient conditions, they inadvertently violate necessary conditions. To validate our theoretical insights, we propose a practical method that promotes the sufficient condition while maintaining the necessary conditions through a novel subspace representation alignment strategy. This approach highlights the advantages of preserving the necessary conditions on well-established DG benchmarks.

Problem

• Addresses failure of domain generalization algorithms
• Explores generalization with limited training domains
• Proposes method maintaining necessary conditions for generalization

Innovation

• Subspace representation alignment strategy
• Necessary and sufficient conditions
• Regularization targeting generalization