A Sensitivity Analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks

TL;DR

This paper compares elementary cellular automata with more biologically plausible heterogeneous networks, analyzing their computational sensitivity and robustness, revealing that disordered topology can enhance sensitivity despite increased defect collapse.

Contribution

It introduces a comparative analysis of ECA, PLCA, and HHRBN substrates, highlighting how topology influences computational sensitivity and robustness in reservoir computing.

Findings

Disordered topology can increase sensitivity to initial conditions.

Counterintuitively, disordered networks may have higher defect collapse rates.

Topology imperfections can lead to a shrinking critical computational range.

Abstract

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself to be difficult, but if combined with reservoir computing (RC), this becomes much more feasible. Furthermore, RC and ECA enable energy-efficient AI, making the combination a promising concept for Edge AI. In this work, we contrast ECA to substrates of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). They are, in comparison, the topological heterogeneous counterparts of ECA. This represents a step from ECA towards more biological-plausible substrates. We analyse these substrates by testing on an RC benchmark (5-bit memory), using Temporal Derrida plots to estimate the sensitivity and assess the defect collapse rate. We find that, counterintuitively, disordered topology does not necessarily mean disordered computation. There are countering computational "forces" of topology imperfections leading to a higher collapse rate (order) and yet, if accounted for, an increased sensitivity to the initial condition. These observations together suggest a shrinking critical range.