The Intrinsic Cause-Effect Power of Discrete Dynamical Systems-From Elementary Cellular Automata to Adapting Animats
The Intrinsic Cause-Effect Power of Discrete Dynamical Systems-From Elementary Cellular Automata to Adapting Animats
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DOI：
10.3390/e17085472
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发表时间：
2015-08-01
期刊：
影响因子：
2.7
通讯作者：
Tononi, Giulio
中科院分区：
文献类型：
--
作者：
Albantakis, Larissa;Tononi, Giulio
当前表征动力系统复杂性的方法通常依赖于状态空间轨迹。相反，在本文中，我们关注因果结构，将离散动态系统视为有向因果图——实现局部更新函数的元素系统。这使我们能够通过应用在综合信息论（IIT）框架内开发的数学和概念工具来表征系统的内在因果结构。特别是，我们评估系统指定的不可约机制（概念）的数量和集成概念信息 phi 的总量。我们分析：（i）基本元胞自动机（ECA）； (ii) 小型自适应逻辑门网络（“animats”），其结构与 ECA 类似，但通过与环境交互而不断发展。我们表明，一般来说，具有许多概念和高 phi 的综合因果结构可能具有高动态复杂性。重要的是，虽然动力学分析从观察者的外在角度描述了系统中“正在发生”的事情，但对其因果结构的分析却从其自身的内在角度揭示了系统“是什么”，揭示了其在许多不同场景下的动态和进化潜力。
Current approaches to characterize the complexity of dynamical systems usually rely on state-space trajectories. In this article instead we focus on causal structure, treating discrete dynamical systems as directed causal graphs-systems of elements implementing local update functions. This allows us to characterize the system's intrinsic cause-effect structure by applying the mathematical and conceptual tools developed within the framework of integrated information theory (IIT). In particular, we assess the number of irreducible mechanisms (concepts) and the total amount of integrated conceptual information phi specified by a system. We analyze: (i) elementary cellular automata (ECA); and (ii) small, adaptive logic-gate networks ("animats"), similar to ECA in structure but evolving by interacting with an environment. We show that, in general, an integrated cause-effect structure with many concepts and high phi is likely to have high dynamical complexity. Importantly, while a dynamical analysis describes what is "happening" in a system from the extrinsic perspective of an observer, the analysis of its cause-effect structure reveals what a system "is" from its own intrinsic perspective, exposing its dynamical and evolutionary potential under many different scenarios.