Compositional Generalization via Structural Identification in a Category-Theoretic Framework

2026-08-26

AI Summary

研究通过范畴论框架识别句子结构，分析COGS数据集上模型泛化能力，不依赖预测模型训练，而是基于结构和词汇识别评估组合泛化。

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.

Problem

• Compositional Generalization
• Structural Identification
• Category-Theoretic Framework
• COGS

Innovation

• Category-Theoretic Framework
• Compositional Generalization
• Structural Identification
• Kan Extensions