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This paper investigates compositional generalization by analyzing the structural and lexical identifications that render held-out COGS examples admissible based on training observations. Utilizing category theory, sentences are modeled as functors, and selective collapses lead to Kan extensions that reveal the underlying associations. The study identifies distinct admissibility profiles across 21 COGS generalization types, highlighting how unsupported structural templates contribute to residual failures, thereby providing a diagnostic tool for understanding training corpus limitations without requiring a predictive model.
Admissibility in compositional generalization reveals distinct structural profiles that can diagnose training corpus limitations without the need for predictive modeling.
Compositional generalization is usually evaluated through model accuracy. We instead ask which structural or lexical identifications make held-out COGS examples admissible from the structures observed in training. Sentences are represented as functors from syntactic addresses to lexical tokens, and selective collapses induce Kan extensions that propagate observed associations. Across 21 COGS generalization types, admissibility follows distinct identification profiles, while residual failures separate unsupported structural templates. These data-side diagnoses characterize what the training corpus licenses under specified identifications, without training a predictive model.
