{"slug": "on-the-computational-complexity-of-structural-generalization", "title": "On the Computational Complexity of Structural Generalization", "summary": "A new arXiv paper (2607.19573v1) formally defines structural generalization and proves that pure Transformers cannot learn it under the standard complexity assumption TC⁰ ≠ NC¹. The authors show that neuro-symbolic systems achieve high benchmark scores by injecting the semantic face Gγ, which is NC¹-complete, rather than learning it from data. The paper argues that benchmark scores conflate learned capacity with given structure, undermining claims of emergent generalization.", "body_md": "arXiv:2607.19573v1 Announce Type: new\nAbstract: 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 projections: a syntactic face ($F_\\gamma$) and a semantic face ($G_\\gamma$). Tree evaluation on the $G_\\gamma$ side is an instantiation of BFVP, which is $\\mathrm{NC}^1$-complete (Buss, 1987). A pure Transformer must learn both faces at once, but Kraus et al. (2026) prove that its learnable class $\\subseteq \\mathrm{TC}^0$. Under the standard assumption $\\mathrm{TC}^0 \\neq \\mathrm{NC}^1$, a pure Transformer cannot learn structural generalization. Neuro-symbolic systems achieve the best benchmark scores precisely because they inject $G_\\gamma$, sidestepping the genuinely hard half. Benchmark scores cannot distinguish \"learned\" from \"given.\" This is what this paper sets out to make clear.", "url": "https://wpnews.pro/news/on-the-computational-complexity-of-structural-generalization", "canonical_source": "https://www.machinebrief.com/news/on-the-computational-complexity-of-structural-generalization-i92b", "published_at": "2026-07-23 04:00:00+00:00", "updated_at": "2026-07-23 04:04:07.744155+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "neural-networks", "natural-language-processing", "ai-research"], "entities": ["arXiv", "Buss (1987)", "Kraus et al. (2026)"], "alternates": {"html": "https://wpnews.pro/news/on-the-computational-complexity-of-structural-generalization", "markdown": "https://wpnews.pro/news/on-the-computational-complexity-of-structural-generalization.md", "text": "https://wpnews.pro/news/on-the-computational-complexity-of-structural-generalization.txt", "jsonld": "https://wpnews.pro/news/on-the-computational-complexity-of-structural-generalization.jsonld"}}