高阶相互作用及其对偶揭示了超越香农信息的协同性与逻辑依赖性
Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information
AI总结：
针对香农信息论无法区分部分本质不同系统、高阶互信息推广无共识的问题，该研究证明无模型高阶相互作用是布尔代数上惊奇度的莫比乌斯反演，提出其对偶形式，可唯一识别香农信息相同的不同逻辑门、分布与因果动力学。
摘要：
信息论测度通过联合熵、边缘熵与条件熵的结构揭示变量间的依赖性，但会使一些本质不同的系统无法被区分。此外，目前关于如何构建与解释互信息（MI）的高阶推广形式尚未达成共识。在本文中，我们证明近期提出的二元变量间无模型高阶相互作用（MFIs，即无模型相互作用）的定义与互信息类似，是布尔代数上的莫比乌斯反演，但反演的是惊奇度而非熵。这为MFIs提供了信息论层面的解释，进而也为伊辛相互作用提供了信息论解释。我们研究了序反转格上MI与MFIs的对偶对象，发现对偶MI与此前研究的微分互信息相关，而对偶相互作用（外相互作用）是相对于不同背景态的相互作用。与互信息不同，内相互作用与外相互作用可以唯一识别全部6种2输入逻辑门、二元与三元分布，以及香农信息含量相同但不同的因果动力学过程。
英文摘要：
Information-theoretic quantities reveal dependencies among variables in the structure of joint, marginal, and conditional entropies, but leave some fundamentally different systems indistinguishable. Furthermore, there is no consensus on how to construct and interpret a higher-order generalisation of mutual information (MI). In this manuscript, we show that a recently proposed model-free definition of higher-order interactions amongst binary variables (MFIs), like mutual information, is a Möbius inversion on a Boolean algebra, but of surprisal instead of entropy. This gives an information-theoretic interpretation to the MFIs, and by extension to Ising interactions. We study the dual objects to MI and MFIs on the order-reversed lattice, and find that dual MI is related to the previously studied differential mutual information, while dual interactions (outeractions) are interactions with respect to a different background state. Unlike mutual information, in- and outeractions uniquely identify all six 2-input logic gates, the dy- and triadic distributions, and different causal dynamics that are identical in terms of their Shannon-information content.
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。
