On the Computational Complexity of Structural Generalization
Structural generalization has been measured repeatedly by several benchmarks, yet it has never been formally defined. We give a definition that translates the two premises (compositional structure and unbounded generalization) into mathematical language. The definition itself is neutral: a compiler that hard-codes the rules satisfies it just as well. But structural generalization becomes a scientific question only insofar as the capacity can autonomously emerge from finite data. This question pits the computational lower bound $\mathrm{NC}^1$ against the learnable ceiling $\mathrm{TC}^0$ of pure Transformers. Under a Montagovian instantiation, each compositional rule splits into two proje...
| Authors | Zichao Wei |
|---|---|
| Primary category | cs.CL |
| Published | 21 July 2026 |
| Last updated at source | 21 July 2026 |
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