How Many Domains Suffice for Domain Generalization? A Tight Characterization via the Domain Shattering Dimension
arXiv:2506.16704v3 Announce Type: replace Abstract: We study a fundamental question of domain generalization: given a family of domains (i.e., data distributions), how many randomly sampled domains do we need to collect data from in order to learn a model that performs reasonably well on every seen and unseen domain in the family? We model this problem in the PAC framework and introduce a new combinatorial measure, which we call the domain shattering dimension. We show that this dimension characterizes the domain sample complexity. Furthermore, we establish a tight quantitative relationship be
This research is emerging as AI systems are increasingly deployed in diverse, real-world scenarios, highlighting the critical need for models that can generalize across various data distributions without extensive retraining.
Understanding the 'domain shattering dimension' provides a theoretical framework to predict how many different data environments are needed to build robust AI, directly impacting the feasibility and cost of deploying general-purpose AI systems.
This theoretical characterization offers a concrete metric for domain sample complexity, shifting the approach from heuristic data collection to a more principled, dimension-driven strategy for domain generalization in AI.
- · AI researchers
- · ML platform developers
- · Industries with diverse data environments
- · AI ethics and safety organizations
- · Companies relying on narrow, domain-specific AI models
- · Developers with inefficient data collection strategies
Researchers gain a powerful new tool for designing more efficient and robust domain generalization algorithms, accelerating progress in flexible AI systems.
This foundational understanding could lead to more efficient and less data-intensive training of AI agents, reducing the computational and energy footprints of developing general AI.
Improved domain generalization could indirectly contribute to the development of more adaptable and ubiquitous AI agents capable of operating across vastly different contexts, impacting various sectors from robotics to autonomous decision-making.
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