Mass Conservation as an Inductive Bias for Self-Organized Criticality in NCA Reservoirs

2026-06-22

AI Summary

This work investigates how to effectively induce self-organized criticality (SOC) in neural cellular automata (NCA) reservoirs to enhance information processing capabilities without compromising downstream task performance. To this end, mass conservation is introduced for the first time as an inductive bias into the NCA evolution dynamics, guiding the reservoir to spontaneously approach a critical state. Criticality is quantified via power-law fitting, and performance is evaluated on three benchmark tasks: 5-bit sequence memory, MNIST classification, and CartPole-v1 control. Results demonstrate that mass-conserving NCA evolves 1.27× faster, achieves desirable power-law distributions more consistently, and matches standard NCA performance across all tasks, with the optimally critical reservoir attaining the highest score in the temporal control task.

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.

Problem

• self-organized criticality
• neural cellular automata
• mass conservation
• reservoir computing
• inductive bias

Innovation

• mass conservation
• self-organized criticality
• neural cellular automata
• reservoir computing
• inductive bias