# Compositional Generalization via Structural Identification in a Category-Theoretic Framework

arXiv: https://arxiv.org/abs/2608.26465 · HTML: https://mlsanity.com/paper/2608.26465/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 4 of 4)

- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [ReCOGS: How Incidental Details of a Logical Form Overshadow an Evaluation of Semantic Interpretation](https://mlsanity.com/paper/2303.13716/) (2023)
- [SLOG: A Structural Generalization Benchmark for Semantic Parsing](https://mlsanity.com/paper/2310.15040/) (2023)
- [A calculus of types in Isbell nuclei](https://mlsanity.com/paper/2606.03369/) (2026)

## Abstract (arXiv)

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.