A Synergistic Perspective on Multivariate Computation and Causality in Complex Systems.

IF 2.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Entropy Pub Date : 2024-10-21 DOI:10.3390/e26100883
Thomas F Varley
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Abstract

What does it mean for a complex system to "compute" or perform "computations"? Intuitively, we can understand complex "computation" as occurring when a system's state is a function of multiple inputs (potentially including its own past state). Here, we discuss how computational processes in complex systems can be generally studied using the concept of statistical synergy, which is information about an output that can only be learned when the joint state of all inputs is known. Building on prior work, we show that this approach naturally leads to a link between multivariate information theory and topics in causal inference, specifically, the phenomenon of causal colliders. We begin by showing how Berkson's paradox implies a higher-order, synergistic interaction between multidimensional inputs and outputs. We then discuss how causal structure learning can refine and orient analyses of synergies in empirical data, and when empirical synergies meaningfully reflect computation versus when they may be spurious. We end by proposing that this conceptual link between synergy, causal colliders, and computation can serve as a foundation on which to build a mathematically rich general theory of computation in complex systems.

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复杂系统中多元计算与因果关系的协同视角。
复杂系统的 "计算 "或执行 "计算 "意味着什么?直观地说,我们可以将复杂的 "计算 "理解为,当系统的状态是多个输入(可能包括其自身过去的状态)的函数时,系统就会进行 "计算"。在此,我们将讨论如何利用统计协同作用的概念来研究复杂系统的计算过程,即只有在已知所有输入的联合状态时才能了解到的输出信息。在先前工作的基础上,我们展示了这种方法自然而然地将多元信息论与因果推理的主题联系起来,特别是因果对撞机现象。首先,我们展示了伯克森悖论如何意味着多维输入和输出之间的高阶协同互动。然后,我们讨论了因果结构学习如何完善和引导对经验数据中协同作用的分析,以及经验协同作用何时有意义地反映了计算,何时可能是虚假的。最后,我们提出,协同作用、因果对撞机和计算之间的概念联系可以作为一个基础,在此基础上建立复杂系统中计算的丰富数学一般理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Entropy
Entropy PHYSICS, MULTIDISCIPLINARY-
CiteScore
4.90
自引率
11.10%
发文量
1580
审稿时长
21.05 days
期刊介绍: Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.
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