Growing Reservoirs with Developmental Graph Cellular Automata

TL;DR

The paper investigates whether Developmental Graph Cellular Automata (DGCA) can grow functional reservoirs for reservoir computing by optimizing two-stage local update rules via a Microbial Genetic Algorithm. It evaluates task-driven growth on NARMA tasks and task-independent growth via RC metrics, showing DGCA-grown reservoirs can outperform randomly initialized reservoirs and develop specialized, life-like topologies. The findings highlight structural diversity, with Loosely Stranded forms often serving under resource constraints and memory/generalization metrics (GR/LMC) becoming more predictive as task difficulty increases. The work establishes a foundation for plastic, adaptive reservoirs and points to future directions in Few-Shot learning and physical reservoir implementations that leverage morphogenesis-inspired growth.

Abstract

Developmental Graph Cellular Automata (DGCA) are a novel model for morphogenesis, capable of growing directed graphs from single-node seeds. In this paper, we show that 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 DGCAs are able to grow into a variety of specialized, life-like structures capable of effectively solving benchmark tasks, statistically outperforming `typical' reservoirs on the same task. Overall, these lay the foundation for the development of DGCA systems that produce plastic reservoirs and for modeling functional, adaptive morphogenesis.

Figures (10)

• Figure 1: Possible edge choices for a newly created node $\mathbf{X}'$ resulting from division of $\mathbf{X}$. Adapted from Figure 6 of waldegrave_creating_2024.
• Figure 2: DGCA pipeline of a two-state (black and white) system. The neighborhood information vector $\mathbf{G}$ is shown for node $\mathbf{X}$. The action MLP determines that $\mathbf{X}$ and $\mathbf{Y}$ divide, while $\mathbf{Z}$ is removed. $\mathbf{G}$ is gathered a second time, now with zero incoming black node connections but an additional white one, before being passed to the state SLP. Adapted from Figure 4 of waldegrave_creating_2024.
• Figure 3: Bipolarization step of a two-state system. Weights between black and white states are negative ($-1$). Weights between equal states are positive ($+1$). White state nodes represent hyperbolic tangent neurons, while black state nodes represent linear neurons.
• Figure 4: Samples of recurring structures. Reservoirs grown for the NARMA task exhibit "life-like" patterns. The diversity of these structures suggests that the DGCA model is capable of generating specialized networks with functional properties, reminiscent of natural systems.
• Figure 5: Task performance distribution of NARMA-10 grown reservoirs across node budgets. Pairwise comparisons used independent two-sample U-tests with Bonferroni correction ($\alpha = 0.05$, corrected threshold $p < 0.0167$). Significant differences: 100 vs 200 ($p=6.215\text{e}{-}20$), Control vs 200 ($p=1.852\text{e}{-}23$), Control vs 100 ($p=2.830\text{e}{-}15$).