Sevenius Nilsen André, Juel Bjørn Erik, Marshall William
Brain Signalling Group, Department of Physiology, Institute of Basic Medicine, University of Oslo, Sognsvannsveien 9, 0315 Oslo, Norway.
Department of Psychiatry, University of Wisconsin, Madison, WI 53719, USA.
Entropy (Basel). 2019 May 24;21(5):525. doi: 10.3390/e21050525.
Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (Φ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating Φ itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the Φ values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3-6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system's state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated Φ, approximations to Φ, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations ( > 0.95) but without major reductions in computational demands. Furthermore, the maximum value of Φ across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, = 0.722), decoder-based integrated information (Φ*, = 0.816), and state differentiation (D1, = 0.827). These measures could allow for the efficient estimation of a system's capacity for high Φ or function as accurate predictors of low- (but not high-)Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established.
整合信息理论（IIT）提出了一种整合信息的度量方法，称为Phi（Φ），以捕捉处于给定状态的物理系统的意识水平。不幸的是，目前仅对于非常小的模型系统才有可能计算Φ本身，而对于通常与意识相关的系统类型（大脑）而言，距离可计算还差得很远。在此，我们考虑了几种提出的启发式度量方法和计算近似值，其中一些可以应用于更大的系统，并测试了它们是否与Φ具有良好的相关性。虽然这些度量方法和近似值抓住了IIT背后的直觉，并且有些在实际应用中取得了成功，但尚未证明它们实际上量化了IIT最新版本所规定的整合信息类型，因此，也未证明它们是否可用于检验该理论。在本研究中，我们评估这些近似值和启发式度量方法时考虑的是它们对模型系统Φ值的估计程度，而非基于实际或临床考量。为此，我们模拟了由3至6个二元线性阈值节点组成的网络，这些节点通过兴奋性和抑制性连接随机连接。对于每个系统，我们随后构建了系统的状态转移概率矩阵（TPM），并从所有可能的初始条件随时间生成观测数据。然后，我们计算了Φ、Φ的近似值以及基于状态区分、联盟熵、状态唯一性和整合信息的度量方法。我们的研究结果表明，在小型二元系统中，通过使用一种或多种现成的近似值（> 0.95）可以非常接近地近似Φ，同时又不会大幅降低计算需求。此外，跨状态的Φ最大值（一个与状态无关的量）与信号复杂度度量（LZ，= 0.722）、基于解码器的整合信息（Φ*，= 0.816）以及状态区分（D1，= 0.827）密切相关。这些度量方法可以有效地估计系统的高Φ容量，或者用作低Φ（但不是高Φ）系统的准确预测指标。虽然不确定这些结果是否能扩展到更大的系统或具有其他动力学的系统，但我们强调，旨在作为Φ的实用替代方法的度量方法至少应在能够确定基本事实的环境中进行严格测试。
