Two commonly used approaches to study interactions among neurons are spike count correlation, which describes pairs of neurons, and dimensionality reduction, applied to a population of neurons. Although both approaches have been used to study trial-to-trial neuronal variability correlated among neurons, they are often used in isolation and have not been directly related. We first established concrete mathematical and empirical relationships between pairwise correlation and metrics of population-wide covariability based on dimensionality reduction. Applying these insights to macaque V4 population recordings, we found that the previously reported decrease in mean pairwise correlation associated with attention stemmed from three distinct changes in population-wide covariability. Overall, our work builds the intuition and formalism to bridge between pairwise correlation and population-wide covariability and presents a cautionary tale about the inferences one can make about population activity by using a single statistic, whether it be mean pairwise correlation or dimensionality.

研究神经元之间相互作用的两种常用方法是尖峰计数相关性（描述神经元对）和应用于神经元群体的降维。尽管这两种方法都已用于研究神经元之间相关的试验间神经元变异性，但它们通常单独使用并且没有直接相关。我们首先在成对相关性和基于降维的总体协方差度量之间建立了具体的数学和经验关系。将这些见解应用于猕猴 V4 群体记录，我们发现之前报道的与注意力相关的平均成对相关性的下降源于群体范围内协变性的三个明显变化。总体而言，我们的工作建立了直觉和形式主义，以在成对相关性和总体范围内的协变性之间架起桥梁，并提出了一个关于人们可以通过使用单个统计数据（无论是平均成对相关性还是维度）对人口活动做出的推论的警示故事。