Balancing Centralized Learning and Distributed Self-Organization: A Hybrid Model for Embodied Morphogenesis

Abstract:Background: both embodied intelligence and developmental morphogenesis depend on a division of labour between centralized guidance and distributed material dynamics, but the amount of top-down control needed to steer self-organization remains unclear. Methods: we coupled a compact full-resolution convolutional controller to a differentiable Gray-Scott reaction-diffusion (RD) substrate. The controller observes two fields, U and V, and applies smooth gain-scheduled modulations of the feed and kill parameters (Delta F and Delta K). We compared pure RD, neural network (NN)-dominant and hybrid regimes and evaluated spectral selectivity, convergence and control cost. Results: the hybrid regime achieved 100% strict convergence at approximately 165 steps, whereas pure RD and the NN-dominant baseline did not converge within the same horizon. It matched the substrate's spectral selectivity while using approximately 15 times less L1 effort and over 200 times less L2 power than the NN-dominant controller. Moderate amplitudes (A approximately 0.03-0.045) formed a Goldilocks zone with 100% quasi-convergence in 94-96 steps. Conclusions: effective control is best framed as seed then cede: brief, smooth parameter-level nudges place the system in a favourable basin of attraction, after which reaction-diffusion dynamics complete and stabilize the pattern. This provides a quantitative model of morphological computation for controlled self-organization.

Replaced with the peer-reviewed Version of Record published in Royal Society Open Science 13, 252327 (2026). DOI: https://doi.org/10.1098/rsos.252327

Artificial Intelligence (cs.AI)

arXiv:2511.10101 [cs.AI]

(or arXiv:2511.10101v2 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2511.10101 Focus to learn more arXiv-issued DOI via DataCite

R. Soc. Open Sci. 13 (2026) 252327

https://doi.org/10.1098/rsos.252327 Focus to learn more DOI(s) linking to related resources

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