Low stimulus-evoked RS–RS correlation was consistent with a cancellation of input correlations by correlated inhibition.

*A*, An expansion of our model included a second functional unit consisting of an FS–RS population pair. The FS–RS input correlation for each population was the same as before,

*c*_{intra} = 0.714, but in addition, both pairs receive more global, yet weaker, correlated inputs (

*c*_{inter}= 0.146). Two variants of this model were ones in which the FS populations receive common inputs (

; cyan) or alternatively received inputs that were uncorrelated from one another (

; yellow), resulting in independently fluctuating inhibition.

*B*, When the FS populations received globally correlated inputs (

; cyan), there was a low spontaneous RS–RS correlation and a small stimulus-evoked decrease in

*ρ*_{RS–RS}. When

, RS–RS spontaneous correlation was higher and there was a stimulus-evoked increase in correlation. A further decrease of the background input correlation between RS populations (

) yielded a spontaneous correlation that was similar to the case in which inhibition was globally coherent, but a stimulus-evoked increase in RS–RS output correlation (green) was still observed. Linear versions of the models with and without coherent inhibition (dashed cyan and yellow curves, respectively) result in constant, stimulus-independent values of correlation. Also, the linear version of the model without coherent inhibition and reduced

*c* is stimulus independent (dashed green). These values correspond to the peak stimulus-induced correlation of their respective nonlinear versions.

*C*, The population signal-to-noise ratio (relative to a single neuron) was enhanced as the population size,

*N*, increases. In the limit of large

*N*, the system with globally coherent inhibition performs 3.2 and 1.4 times better than the system with independent inhibition and independent inhibition with lowered RS input correlation, respectively. SNR curves for six other evenly spaced correlation coefficients (black) are shown for reference.

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