On the Emergence of Syntax by Means of Local Interaction

TL;DR

This paper demonstrates that a neural cellular automaton can spontaneously develop a structured representation resembling syntactic processing, emerging solely from local interactions and minimal supervision.

Contribution

It introduces a minimal neural automaton that self-organizes into a proto-syntactic structure, showing emergence of syntax-like processing without explicit programming.

Findings

The automaton's internal representation aligns with grammatical structure (Pearson r ≈ 0.71).

It generalizes beyond training data to multiple context-free grammars.

The structure spontaneously regenerates after perturbation.

Abstract

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.