Causal Leverage Density: A General Approach to Semantic Information

Stuart J Bartlett
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Abstract

I introduce a new approach to semantic information based upon the influence of erasure operations (interventions) upon distributions of a system's future trajectories through its phase space. Semantic (meaningful) information is distinguished from syntactic information by the property of having some intrinsic causal power on the future of a given system. As Shannon famously stated, syntactic information is a simple property of probability distributions (the elementary Shannon expression), or correlations between two subsystems and thus does not tell us anything about the meaning of a given message. Kolchinsky & Wolpert (2018) introduced a powerful framework for computing semantic information, which employs interventions upon the state of a system (either initial or dynamic) to erase syntactic information that might influence the viability of a subsystem (such as an organism in an environment). In this work I adapt this framework such that rather than using the viability of a subsystem, we simply observe the changes in future trajectories through a system's phase space as a result of informational interventions (erasures or scrambling). This allows for a more general formalisation of semantic information that does not assume a primary role for the viability of a subsystem (to use examples from Kolchinsky & Wolpert (2018), a rock, a hurricane, or a cell). Many systems of interest have a semantic component, such as a neural network, but may not have such an intrinsic connection to viability as living organisms or dissipative structures. Hence this simple approach to semantic information could be applied to any living, non-living or technological system in order to quantify whether a given quantity of syntactic information within it also has semantic or causal power.
因果杠杆密度:语义信息的一般方法
我根据擦除操作(干预)对系统在其相空间中的未来轨迹分布的影响,介绍了一种新的语义信息方法。语义(有意义)信息与句法信息的区别在于,语义信息对给定系统的未来具有某种内在的因果力量。正如香农(Shannon)所指出的,语法信息是概率分布(香农的基本表达式)或两个子系统之间相关性的简单属性,因此并不能告诉我们特定信息的含义。Kolchinsky& Wolpert(2018)介绍了一个强大的语义信息计算框架,该框架利用对系统状态(初始或动态)的干预来消除可能影响子系统(如环境中的生物体)可行性的语法信息。在这项工作中,我对这一框架进行了调整,不再使用子系统的可行性,而是简单地观察信息干预(抹除或扰乱)在系统相空间中的未来轨迹变化。这样就可以对语义信息进行更普遍的形式化处理,而不假定子系统(以 Kolchinsky & Wolpert(2018)的例子为例,如岩石、飓风或细胞)的生存能力起着主要作用。许多我们感兴趣的系统都有语义成分,比如神经网络,但可能不像生物体或耗散结构那样与生存能力有内在联系。因此,这种处理语义信息的简单方法可以应用于任何生物、非生物或技术系统,以量化其中特定数量的句法信息是否也具有语义或因果能力。
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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