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

• URL: http://arxiv.org/abs/2511.10101v1
• Date: Fri, 14 Nov 2025 01:32:44 GMT
• Title: Balancing Centralized Learning and Distributed Self-Organization: A Hybrid Model for Embodied Morphogenesis
• Authors: Takehiro Ishikawa,
• Abstract summary: We investigate how to couple a learnable brain-like'' controller to a cell-like'' Gray--Scott substrate to steer pattern formation with minimal effort.<n>A compact convolutional policy is embedded in a differentiable PyTorch reaction--diffusion simulator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate how to couple a learnable brain-like'' controller to a cell-like'' Gray--Scott substrate to steer pattern formation with minimal effort. A compact convolutional policy is embedded in a differentiable PyTorch reaction--diffusion simulator, producing spatially smooth, bounded modulations of the feed and kill parameters ($ΔF$, $ΔK$) under a warm--hold--decay gain schedule. Training optimizes Turing-band spectral targets (FFT-based) while penalizing control effort ($\ell_1/\ell_2$) and instability. We compare three regimes: pure reaction--diffusion, NN-dominant, and a hybrid coupling. The hybrid achieves reliable, fast formation of target textures: 100% strict convergence in $\sim 165$ steps, matching cell-only spectral selectivity (0.436 vs.\ 0.434) while using $\sim 15\times$ less $\ell_1$ effort and $>200\times$ less $\ell_2$ power than NN-dominant control. An amplitude sweep reveals a non-monotonic Goldilocks'' zone ($A \approx 0.03$--$0.045$) that yields 100\% quasi convergence in 94--96 steps, whereas weaker or stronger gains fail to converge or degrade selectivity. These results quantify morphological computation: the controller seeds then cedes,'' providing brief, sparse nudges that place the system in the correct basin of attraction, after which local physics maintains the pattern. The study offers a practical recipe for building steerable, robust, and energy-efficient embodied systems that exploit an optimal division of labor between centralized learning and distributed self-organization.

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