TY - JOUR T1 - Effective synaptic interactions in subsampled nonlinear networks with strong coupling JF - bioRxiv DO - 10.1101/105510 SP - 105510 AU - Braden A. W. Brinkman AU - Fred Rieke AU - Eric Shea-Brown AU - Michael Buice Y1 - 2017/01/01 UR - http://biorxiv.org/content/early/2017/02/20/105510.abstract N2 - A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r′ to r plus corrections from every directed path from r′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a prominent example, we derive a formula for strong impact of hidden units in random networks with connection weights that scale with 1/√N, where N is the network size—precisely the scaling observed in recent experiments. ER -