Structured Prediction Meets Neural Geometry: How Compositionality, Representational Manifolds, Criticality, and Hierarchical Coding Jointly Constrain What Neural Circuits Compute

Abstract

This version (2026-09-26) corrects a citation error found by an automated check and confirmed by hand against the arXiv abstracts. Version 2 cited the identifier 2606.04428, an unrelated astrophysics paper on fast-spinning black holes, for the theoretical framework in which chaotic recurrent dynamics produce local roughness with global smoothness and act as an intrinsic regularizer of neural representations. That framework is arXiv:2606.04426 ("Discrete signaling mediates chaotic regularization in recurrent neural networks"), and every citation to it is corrected. The thesis is unchanged. This version has not had a full claim-by-claim audit. The full list of corrections is at the top of the PDF. A candidate structural pattern emerges across several recent neuroscience preprints: neural circuits may achieve flexible, generalizable computation not through monolithic representations but through a set of interlocking geometric and dynamical properties, compositionality of fixed points, smooth representational manifolds sustained by chaos, hierarchical burst-coded goal signals, and scale-free criticality. This synthesis draws primarily from q-bio.NC sources, with selective evidence from cs.CL where brain-model alignment studies provide behavioral constraints. We argue, as a heuristic reading rather than a derivation, that four specific findings converge on a shared structural theme: (1) inhibition-dominated threshold-linear networks support compositional fixed-point arithmetic through low-rank gluing rules arXiv:2606.07336; (2) chaotic recurrent dynamics induce local roughness with global smoothness in representational manifolds, functioning as an intrinsic regularizer arXiv:2606.04426; (3) burst fraction in macaque motor cortex encodes goal information via a bilinear gate linking dendritic coincidence detection to reinforcement learning arXiv:2606.10891; and (4) early psychosis produces systematic shifts in scaling exponents within a preserved criticality regime, suggesting that pathology reorganizes rather than destroys scale-free dynamics arXiv:2606.06290. Two additional findings from brain-LLM alignment studies arXiv:2606.11598 and short-term synaptic plasticity in prefrontal reservoir models arXiv:2606.03481 provide boundary conditions on these claims. The falsification path for the central thesis is concrete: if compositional fixed-point structure, smooth manifold geometry, burst-coded goal signals, and criticality-regime preservation can be shown to dissociate, appearing independently in circuits that do not share functional architecture, the proposed convergence is coincidental rather than structural. The corpus sources are recent preprints, not peer-reviewed; all mechanistic claims are hypothesized, not established. Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted synthesis from an arXiv preprint corpus, originally drafted 2026-06-12, produced under the direction of Cristian Ruvalcaba, the accountable human author. Not peer-reviewed. AI disclosure. This work was produced with an agentic AI research apparatus operated by Saluca Labs. The apparatus drafted, searched and analysed under direction. Cristian Ruvalcaba is the human author and is accountable for the content. No AI system is listed as an author or contributor, because authorship entails accountability that a model cannot hold; this disclosure is the credit, and it is deliberately the whole of it.