Marshall William, Gomez-Ramirez Jaime, Tononi Giulio
Department of Psychiatry, Center for Sleep and Consciousness, University of Wisconsin Madison, WI, USA.
Front Psychol. 2016 Jun 28;7:926. doi: 10.3389/fpsyg.2016.00926. eCollection 2016.
Integrated information (Φ) is a measure of the cause-effect power of a physical system. This paper investigates the relationship between Φ as defined in Integrated Information Theory and state differentiation ([Formula: see text]), the number of, and difference between potential system states. Here we provide theoretical justification of the relationship between Φ and [Formula: see text], then validate the results using a simulation study. First, we show that a physical system in a state with high Φ necessarily has many elements and specifies many causal relationships. Furthermore, if the average value of integrated information across all states is high, the system must also have high differentiation. Next, we explore the use of [Formula: see text] as a proxy for Φ using artificial networks, evolved to have integrated structures. The results show a positive linear relationship between Φ and [Formula: see text] for multiple network sizes and connectivity patterns. Finally we investigate the differentiation evoked by sensory inputs and show that, under certain conditions, it is possible to estimate integrated information without a direct perturbation of its internal elements. In concluding, we discuss the need for further validation on larger networks and explore the potential applications of this work to the empirical study of consciousness, especially concerning the practical estimation of Φ from neuroimaging data.
整合信息（Φ）是对物理系统因果效力的一种度量。本文研究了整合信息理论中所定义的Φ与状态区分度（[公式：见原文]）之间的关系，即潜在系统状态的数量及其差异。在此，我们为Φ与[公式：见原文]之间的关系提供理论依据，然后通过模拟研究验证结果。首先，我们表明处于高Φ状态的物理系统必然具有许多元素并规定了许多因果关系。此外，如果所有状态下整合信息的平均值较高，那么该系统的区分度也必然较高。接下来，我们使用经过进化以具有整合结构的人工网络，探索将[公式：见原文]用作Φ的替代指标。结果表明，对于多种网络规模和连接模式，Φ与[公式：见原文]之间存在正线性关系。最后，我们研究了由感官输入引发的区分度，并表明在某些条件下，无需直接扰动其内部元素就有可能估计整合信息。在结论部分，我们讨论了在更大网络上进行进一步验证的必要性，并探讨了这项工作在意识实证研究中的潜在应用，特别是关于从神经成像数据实际估计Φ的问题。
