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A major obstacle to understanding neural coding and computation is the factthat experimental recordings typically sample only a small fraction of theneurons in a circuit. Measured neural properties are skewed by interactionsbetween recorded neurons and the "hidden" portion of the network. To properlyinterpret neural data and determine how biological structure gives rise toneural circuit function, we thus need a better understanding of therelationships between measured effective neural properties and the trueunderlying physiological properties. Here, we focus on how the effectivespatiotemporal dynamics of the synaptic interactions between neurons arereshaped by coupling to unobserved neurons. We find that the effectiveinteractions from a pre-synaptic neuron $r'$ to a post-synaptic neuron $r$ canbe decomposed into a sum of the true interaction from $r'$ to $r$ pluscorrections from every directed path from $r'$ to $r$ through unobservedneurons. Importantly, the resulting formula reveals when the hidden unitshave---or do not have---major effects on reshaping the interactions amongobserved neurons. As a particular example of interest, we derive a formula forthe impact of hidden units in random networks with "strong"coupling---connection weights that scale with $1/\sqrt{N}$, where $N$ is thenetwork size, precisely the scaling observed in recent experiments. With thisquantitative relationship between measured and true interactions, we can studyhow network properties shape effective interactions, which properties arerelevant for neural computations, and how to manipulate effective interactions.

Predicting how and when hidden neurons skew measured synaptic interactions