Mass Conservation as an Inductive Bias for Self-Organized Criticality in NCA Reservoirs
2026-06-22 • Neural and Evolutionary Computing
Neural and Evolutionary Computing
AI summaryⓘ
The authors studied a special type of neural network called neural cellular automata (NCA) used for memory and decision tasks. They tested whether making NCA follow a rule that keeps the total amount of some quantity constant (mass conservation) helps the system behave in a special balanced way called self-organized criticality (SOC). Their experiments showed that mass conservation improved this balanced behavior without hurting how well the system did on tasks like remembering sequences, recognizing digits, and controlling a game. Also, networks with better SOC performed best on control tasks, suggesting this balance helps with time-based computations.
Self-organized criticalityNeural cellular automataMass conservationReservoir computingPower-law distributionSequential memoryMNIST classificationCartPole controlAvalanche dynamicsTemporal computation
Authors
Tong Zhang, Etienne Guichard, Sidney Pontes-Filho, Stefano Nichele
Abstract
Self-organized criticality (SOC), a dynamical regime associated with maximal information processing, offers a promising foundation for reservoir computing. Recent work has shown that neural cellular automata (NCA) can be evolved toward critical avalanche dynamics and employed as effective reservoirs for memory and classification tasks. Here, we investigate whether mass conservation -- a local redistribution rule that preserves total lattice mass -- serves as an inductive bias toward SOC in evolved NCA reservoirs. We compare mass-conserving and standard NCA across multiple independent runs and evaluate both on three downstream benchmarks: 5-bit sequential memory, MNIST digit classification, and CartPole-v1 temporal control. Mass-conserving NCA consistently exhibit stronger criticality, with more runs achieving perfect power-law fits across avalanche distributions, while also being 1.27$\times$ faster during evolution. Importantly, conservation does not impair downstream utility: both variants achieve comparable performance across all three tasks. Furthermore, the reservoir with perfect criticality achieves the highest temporal control score, suggesting a positive link between SOC quality and sequential computation. Our results demonstrate that mass conservation is a simple, effective mechanism for promoting robust criticality in evolved NCA reservoirs without sacrificing downstream performance.