论文标题
高阶相互作用及其双重伴侣揭示了Shannon信息以外的协同和逻辑依赖性
Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information
论文作者
论文摘要
信息理论量揭示了变量之间关节，边缘和有条件熵的变量之间的依赖性，但使某些根本不同的系统无法区分。此外，关于如何构建和解释互信息（MI）的高阶概括（MI）尚无共识。在本手稿中，我们表明，最近提出的对二进制变量（MFIS）之间高阶相互作用的无模型定义（如相互信息）是布尔代数的莫比乌斯倒置，但令人惊讶而不是熵。这为MFI提供了信息理论的解释，并扩展到ISING ITSOTICTIONS。我们在订单转换的晶格上研究了MI和MFI的双重对象，并发现双MI与先前研究的差分互信息有关，而双重相互作用（外部actionsions）是与不同背景状态的相互作用。与相互的信息不同，内部和外部acTions独特地识别所有六个2输入逻辑门，Dy和三合会分布以及不同的因果动力学，这些动力学在其香农信息含量方面相同。
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.
