Frege in the Flesh: Biolinguistics and the Neural Enforcement of Syntactic Structures

What must a neural system be capable of to implement language? Current research annotates stimuli with linguistic variables and tests which electrodes, voxels, or language-model layers predict neural activity. Yet predictive success leaves mechanisms under-constrained. Here, we show that algebraic properties of language specify invariants that mechanisms must preserve: non-associative hierarchical grouping, commutativity, recursive closure, access to substructures, and structured workspace transitions. We term this the Neural Admissibility Program (NAP). Syntactic structure building is analyzed algebraically, with candidate mechanisms offered for each requirement: content-addressable workspace memory, graph-structured transient dynamics scheduling structure-building operations (e.g. stable heteroclinic channels), and a phase-coupled sealing operation recording grouping. Simulations show that a corrected Marcolli-Berwick entropy-optimized binding gate preserves grouping only within a narrow commitment band. As an alternative, we propose a novel neural binding operation we term 'Meld': two constituent populations converge through shared synapses, integrate sublinearly, and saturate. Meld is, to our knowledge, the closest neurally plausible composition law to syntactic Merge. It preserves every NAP invariant, uses known cortical operations, and recovers hierarchical structure at every tested depth and temperature. It predicts that effective population dimensionality separates alternative bracketings and that the composite depends on constituent disagreement. Importantly, the laws decoding bracketing most accurately are a priori inadmissible, showing that decoding accuracy alone cannot adjudicate between mechanisms. By specifying how neural dynamics can remain faithful to linguistic structure, the NAP changes the criterion by which neural implementations of cognition are evaluated.

Elucidating the language-brain relationship requires bridging the methodological gap between the abstract theoretical frameworks of linguistics and the empirical neural data of neuroscience. Serving as an interdisciplinary cornerstone, computational neuroscience formalizes the hierarchical and dynamic structures of language into testable neural models through modeling, simulation, and data analysis. This enables a computational dialogue between linguistic hypotheses and neural mechanisms. Recent advances in deep learning, particularly large language models (LLMs), have powerfully advanced this pursuit. Their high-dimensional representational spaces provide a novel scale for exploring the neural basis of linguistic processing, while the "model-brain alignment" framework offers a methodology to evaluate the biological plausibility of language-related theories.

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.