How Long Is the Coast of a Neuron? Resolution-Dependent Interaction Order and Computational Capacity

Summary

The paper argues that neural computation is inseparable from the scale at which it is measured: collapsing spatially structured neurons into points can change the apparent order and directness of interactions. Using exact finite-state constructions, a branch-to-soma cascade, and structured-subunit simulations, it shows that coarse-graining can turn higher-order dependencies into pairwise ones and make direct models appear increasingly sufficient even as predictive information is lost, while finer subunit resolution expands representational access without adding information. The central implication is that successful point-neuron or population models should be understood as scale-dependent effective theories, not unique identifications of the underlying biophysical computation; the appropriate “ruler” depends on the observable and perturbation of interest.

Links

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BibTeX tap to expand

@misc{dehghani2026coastneuron,
    title={How Long Is the Coast of a Neuron? Resolution-Dependent Interaction Order and Computational Capacity}, 
    author={Nima Dehghani},
    year={2026},
    eprint={2610.19487},
    archivePrefix={arXiv},
    primaryClass={q-bio.NC},
    url={https://arxiv.org/abs/2610.19487}, 
}

Code & Data

neurovium/CoastOfNeuron

Mirrors & related repos

arXiv HMTL

The room

Abstract

Mandlebrot’s coastline paradox reframes measurement as a joint property of an object and its ruler. Here we ask how observational resolution shapes the apparent structure of neural computation. We introduce a scale-indexed decomposition that separates the predictive information captured by direct dependencies from the residual outside that model family. Exact constructions show that projection can convert higher-order dependence into pairwise structure. Projection can increase the direct fraction of surviving information even as total predictive information decreases. A schematic branch-to-soma cascade grounds these effects in local coincidence detection, saturating integration and somatic mixing. Resolving organized nonlinear subunits improves approximation and raises effective representational rank. In a nested hierarchy, these gains occur without increasing information about the target. This distinction separates information availability from access by a restricted readout. A point-neuron or direct population model therefore establishes an effective description at a specified scale. It does not uniquely identify the finer computation that generated the observed relation. Which resolution is adequate depends on the observable and perturbation of interest.