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arXiv 2407.18017nlin.CGcs.AIcs.ETcs.NE
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元胞自动机与异构拓扑网络的敏感性分析：部分局部元胞自动机与同质同质随机布尔网络

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

OsloMet - Oslo Metropolitan University（奥斯陆大都市大学）；Leipzig University（莱比锡大学）；Simula Research Laboratory（西穆拉研究院）；Østfold University College（厄斯特福尔德大学学院）

Tom Eivind Glover, Ruben Jahren, Francesco Martinuzzi, Pedro Gonçalves Lind, Stefano Nichele

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AI总结：

本文对比了ECA与拓扑异构的PLCA和HHRBN基底，通过5-bit memory基准和Temporal Derrida图分析发现，无序拓扑并不必然导致无序计算，拓扑缺陷在提高坍缩率的同时也增加了对初始条件的敏感性，表明临界范围缩小。

摘要：

基本元胞自动机（ECA）是一个被广泛研究的计算宇宙，尽管其配置简单，却具备惊人的计算多样性。以有用的方式收集这种计算在历史上已被证明是困难的，但如果与储备池计算（RC）相结合，这就变得可行得多。此外，RC和ECA能够实现节能的AI，使得这种组合成为边缘AI的一个有前途的概念。在这项工作中，我们将ECA与部分局部CA（PLCA）和同质同质随机布尔网络（HHRBN）的基底进行对比。相比之下，它们是ECA的拓扑异构对应物。这代表了从ECA向更具生物合理性的基底迈出的一步。我们通过在RC基准（5-bit memory）上进行测试来分析这些基底，使用Temporal Derrida图来估计敏感性并评估缺陷坍缩率。我们发现，与直觉相反，无序的拓扑并不一定意味着无序的计算。拓扑缺陷产生了相互抗衡的计算“力”，导致更高的坍缩率（秩序），然而，如果将其考虑在内，对初始条件的敏感性也会增加。这些观察结果共同表明临界范围正在缩小。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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