On the Emergence of Syntax by Means of Local Interaction
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917424600711168 |
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| author | Wei, Zichao |
| author_facet | Wei, Zichao |
| contents | Can syntactic processing emerge spontaneously from purely local interaction? We present a concrete instance on a minimal system: an 18,658-parameter two-dimensional neural cellular automaton (NCA), supervised by nothing more than a 1-bit boundary signal, is trained on the membership problem of an arithmetic-expression grammar. After training, its internal $L \times L$ grid spontaneously self-organizes into an ordered, spatially extended representation that we name Proto-CKY. This representation satisfies three operational criteria for syntactic processing: expressive power beyond the regular languages, structural generalization beyond the training distribution, and an internal organization quantitatively aligned with grammatical structure (Pearson $r \approx 0.71$). It emerges independently on four context-free grammars and regenerates spontaneously after perturbation. Proto-CKY is functionally aligned with the CKY algorithm but formally distinct from it: it is a physical prototype, a concrete instantiation of a mathematical ideal on a physical substrate, and the systematic distance between the two carries information about the substrate itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Emergence of Syntax by Means of Local Interaction Wei, Zichao Computation and Language Artificial Intelligence Machine Learning Can syntactic processing emerge spontaneously from purely local interaction? We present a concrete instance on a minimal system: an 18,658-parameter two-dimensional neural cellular automaton (NCA), supervised by nothing more than a 1-bit boundary signal, is trained on the membership problem of an arithmetic-expression grammar. After training, its internal $L \times L$ grid spontaneously self-organizes into an ordered, spatially extended representation that we name Proto-CKY. This representation satisfies three operational criteria for syntactic processing: expressive power beyond the regular languages, structural generalization beyond the training distribution, and an internal organization quantitatively aligned with grammatical structure (Pearson $r \approx 0.71$). It emerges independently on four context-free grammars and regenerates spontaneously after perturbation. Proto-CKY is functionally aligned with the CKY algorithm but formally distinct from it: it is a physical prototype, a concrete instantiation of a mathematical ideal on a physical substrate, and the systematic distance between the two carries information about the substrate itself. |
| title | On the Emergence of Syntax by Means of Local Interaction |
| topic | Computation and Language Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2604.17857 |