Fluctuation-response relations for a two-stage population of spiking neurons stimulated by common noise

Recently a method has been put forward to connect the measures of spontaneous neuronal activity and the measures of the average single-neuron response to stimuli via fluctuation-response relations (FRRs) for some integrate-and-fire (IF) type neuron models. In this work we expand this method to populations of neurons, relating their spontaneous correlation and linear-response statistics. To this end, we analyze the simple case of uncoupled cells modeled by IF neurons (first stage of processing) which receive common stochastic input and project their output spike trains onto a readout neuron (second stage of processing). We derive and verify FRRs connecting the single neuron response to cross-correlations among neurons and the response of the full system to cross-stage correlations. Furthermore, we utilize these FRRs to derive approximations of all cross-stage cross-spectra for a relevant model of a second-stage cell, the partial synchronous output (PSO). We conclude with a discussion of how our results can be expanded to more involved network settings and neuron models.