Growing Echo State Networks through Graph-Based Morphogenesis with Developmental Graph Cellular Automata

Developmental Graph Cellular Automata (DGCA) are a novel model of morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we extend the DGCA model to exhibit stochastic growth, and show that both deterministic and stochastic DGCAs can be trained to grow reservoirs. Reservoirs are grown with two types of targets: task-driven (using the NARMA family of tasks) and task-independent (using reservoir metrics). Results show that deterministic DGCAs are able to grow a variety of specialised, life-like structures capable of solving benchmark tasks, outperforming 'typical' reservoirs on the same task. Stochastic DGCAs grow robust, regular structures that outperform reservoirs grown deterministically. Overall, these lay the foundation for the development of DGCA systems that produce plastic reservoirs and for modelling functional, adaptive morphogenesis.