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This paper introduces hierarchical domain generalization, formalizing extrapolation from finite observed regions to an entire instance space. It shows that no matter how simple the hypothesis class, certain domain partitions make generalization impossible, arguing that modern generalization theory must incorporate domain structure.
This paper introduces a theoretical framework to analyze the generalization error of canonization methods for symmetric data, proving that Hilbert curve serialization offers polynomial growth in covering number compared to exponential growth in lexicographical sorting.