The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. We have developed an understanding of the circuit mechanisms that lead to correlations among cell pairs, but little is known about what determines the population firing statistics among larger groups of cells. Here, we examine this question for a simple, but ubiquitous, circuit feature: common fluctuating input arriving to spiking neurons of integrate-and-fire type. We show that this leads to strong beyond-pairwise correlations-that is, correlations that cannot be captured by maximum entropy models that extrapolate from pairwise statistics-as for earlier work with discrete threshold crossing (dichotomous Gaussian) models. Moreover, we find that the same is true for another widely used, doubly stochastic model of neural spiking, the linear-nonlinear cascade. We demonstrate the strong connection between the collective dynamics produced by integrate-and-fire and dichotomous Gaussian models, and show that the latter is a surprisingly accurate model of the former. Our conclusion is that beyond-pairwise correlations can be both broadly expected and possible to describe by simplified (and tractable) statistical models.

中文翻译：

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集成和激发神经元中超配对相关性的简单机制。


神经群体的集体动态通常用不同神经元尖峰活动的相关性来表征。我们已经了解了导致细胞对之间相关性的电路机制，但对于决定较大细胞群之间的群体发射统计数据的因素却知之甚少。在这里，我们检查这个问题的一个简单但普遍存在的电路特征：到达集成和激发类型的尖峰神经元的常见波动输入。我们表明，这导致了强烈的超越成对相关性，即无法通过从成对统计推断的最大熵模型捕获的相关性，就像早期使用离散阈值交叉（二分高斯）模型的工作一样。此外，我们发现另一种广泛使用的双随机神经尖峰模型（线性非线性级联）也是如此。我们证明了积分加火模型和二分高斯模型产生的集体动力学之间的紧密联系，并表明后者是前者的令人惊讶的精确模型。我们的结论是，超配对相关性既可以被广泛预期，也可以通过简化（且易于处理）的统计模型来描述。