Tehrani-Saleh Ali, Adami Christoph
Department of Computer Science and Engineering, Michigan State University, East Lansing, MI 48824, USA.
BEACON Center for the Study of Evolution, Michigan State University, East Lansing, MI 48824, USA.
Entropy (Basel). 2020 Mar 28;22(4):385. doi: 10.3390/e22040385.
How cognitive neural systems process information is largely unknown, in part because of how difficult it is to accurately follow the flow of information from sensors via neurons to actuators. Measuring the flow of information is different from measuring correlations between firing neurons, for which several measures are available, foremost among them the Shannon information, which is an undirected measure. Several information-theoretic notions of "directed information" have been used to successfully detect the flow of information in some systems, in particular in the neuroscience community. However, recent work has shown that directed information measures such as transfer entropy can sometimes inadequately estimate information flow, or even fail to identify manifest directed influences, especially if neurons contribute in a cryptographic manner to influence the effector neuron. Because it is unclear how often such cryptic influences emerge in cognitive systems, the usefulness of transfer entropy measures to reconstruct information flow is unknown. Here, we test how often cryptographic logic emerges in an evolutionary process that generates artificial neural circuits for two fundamental cognitive tasks (motion detection and sound localization). Besides counting the frequency of problematic logic gates, we also test whether transfer entropy applied to an activity time-series recorded from behaving digital brains can infer information flow, compared to a ground-truth model of direct influence constructed from connectivity and circuit logic. Our results suggest that transfer entropy will sometimes fail to infer directed information when it exists, and sometimes suggest a causal connection when there is none. However, the extent of incorrect inference strongly depends on the cognitive task considered. These results emphasize the importance of understanding the fundamental logic processes that contribute to information flow in cognitive processing, and quantifying their relevance in any given nervous system.
认知神经系统如何处理信息在很大程度上仍是未知的，部分原因在于准确追踪信息从传感器经神经元到执行器的流动过程非常困难。测量信息流与测量发放神经元之间的相关性不同，对于后者有几种可用的测量方法，其中最主要的是香农信息，它是一种无向测量。几种“有向信息”的信息论概念已被成功用于检测某些系统中的信息流，特别是在神经科学界。然而，最近的研究表明，诸如转移熵之类的有向信息测量有时可能无法充分估计信息流，甚至无法识别明显的有向影响，尤其是当神经元以加密方式对效应神经元产生影响时。由于尚不清楚这种隐秘影响在认知系统中出现的频率，转移熵测量用于重建信息流的有用性尚不清楚。在这里，我们测试在为两项基本认知任务（运动检测和声音定位）生成人工神经回路的进化过程中，加密逻辑出现的频率有多高。除了计算有问题的逻辑门的频率，我们还测试将转移熵应用于从行为数字大脑记录的活动时间序列时，与根据连接性和电路逻辑构建的直接影响的真实模型相比，是否能够推断信息流。我们的结果表明，转移熵有时会在存在有向信息时无法推断出来，有时会在不存在因果关系时暗示存在因果联系。然而，错误推断的程度强烈取决于所考虑的认知任务。这些结果强调了理解有助于认知处理中信息流的基本逻辑过程，并量化它们在任何给定神经系统中的相关性的重要性。
