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Compositional Generalization via Structural Identification in a Category-Theoretic Framework

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Computer Science > Computation and Language

arXiv:2608.26465 (cs)
[Submitted on 26 Aug 2026]

Title:Compositional Generalization via Structural Identification in a Category-Theoretic Framework

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Abstract: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.
Comments: 11 pages
Subjects: Computation and Language (cs.CL); Machine Learning (stat.ML)
MSC classes: 18C50 (Primary), 68T50 (Secondary), 18D20 (Secondary)
Cite as: arXiv:2608.26465 [cs.CL]
  (or arXiv:2608.26465v1 [cs.CL] for this version)
  https://doi.org/10.48550/arXiv.2608.26465
arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Akihiro Maeda [view email]
[v1] Wed, 26 Aug 2026 23:40:59 UTC (19 KB)
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