New arXiv paper: a neuron's 'coastline paradox' — measurement resolution shapes apparent neural computation
tyrell_turing · x · 2026-10-22
Nima Dehghani posted the preprint How Long Is the Coast of a Neuron?, borrowing Mandelbrot's coastline paradox to argue that the apparent structure of neural computation is a joint property of the object and its measuring ruler.
- Introduces a scale-indexed decomposition separating predictive information captured by direct dependencies from residual information outside that model family
- Shows projection can convert higher-order dependence into pairwise structure, and can raise the direct fraction of surviving information even as total predictive information decreases
- Grounds the effects in a branch-to-soma cascade (saturation, somatic mixing); resolving nonlinear subunits improves approximation and raises effective representational rank
- Conclusion: a point-neuron model is only an effective description at a specified scale, not a unique identification of the finer computation
Theoretically relevant to dendritic computation and the limits of the point-neuron assumption in neural networks.
Related event: New Paper Applies the Coastline Paradox to Neural Computation(2 posts)→
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