Balancing Centralized Learning and Distributed Self-Organization: A Hybrid Model for Embodied Morphogenesis
Takehiro Ishikawa
TL;DR
This work investigates how to balance centralized learning with distributed self-organization by coupling a lightweight convolutional controller to a Gray–Scott reaction–diffusion substrate. Using a differentiable, end-to-end trainable setup, it optimizes a spectral-target loss with a warm–hold–decay intervention schedule, evaluating three regimes: RD-only, NN-dominant, and a hybrid. The Hybrid regime achieves 100% convergence in ~165 steps with spectral quality matching the cell-only baseline but with orders of magnitude lower control energy, and reveals a non-monotonic Goldilocks zone near $A oughly 0.03$–$0.045$ where quasi-convergence occurs rapidly. These results quantify morphological computation and provide a practical design principle for steerable, energy-efficient embodied systems that leverage an optimal division of labor between centralized guidance and local physics.
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.