Paper asks 'How long is the coast of a neuron?' — resolution shapes neural computation
neurovium · x · 2026-10-21
Nima Dehghani's new arXiv paper borrows Mandelbrot's coastline paradox to argue that descriptions of neural computation depend on observational resolution.
- Introduces a scale-indexed decomposition separating predictive information captured by direct dependencies from residual information outside that model family
- Exact constructions show projection can convert higher-order dependence into pairwise structure, raising the direct fraction of surviving information even as total predictive information decreases
- A branch-to-soma cascade schematic grounds these effects in local coincidence detection, saturating integration, and somatic mixing
- Resolving organized nonlinear subunits improves approximation and raises effective representational rank — without adding information about the target in nested hierarchies
- Conclusion: point-neuron or direct population models are effective descriptions at a chosen scale, not unique identifications of the finer computation
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