Hierarchical Domain Generalization: Understanding Extrapolation Limits in AI.

The paper delves into the concept of hierarchical domain generalization, viewing it as a challenge of extrapolating knowledge from a limited set of observed data regions to a broader, complete instance space. This approach moves beyond the traditional assumption of independent and identically distributed (i.i.d.) sampling, instead considering arbitrary domain hierarchies. A key finding is that the main obstacle to successful generalization isn't solely the complexity of the chosen hypothesis class. More significantly, the way training and test domains are partitioned and how evidence is revealed through this partition plays a crucial role. The study demonstrates that regardless of how simple the hypothesis class is or how extensive the training data, certain domain partitions can inevitably lead to generalization failures for specific target domains. These results suggest that contemporary generalization theory must fundamentally incorporate domain structure as a core element of its analysis.