Figure 3.

Origin of shared-input correlations and their suppression by correlated presynaptic activity. A pair of neurons i and j receiving input from a finite population of noise sources (left) or a recurrent network (right). The input correlation $C_{ij}^{\mathrm{in}}$ decomposes into a contribution $C_{\mathrm{shared},ij}^{\mathrm{in}}$ resulting from shared noise sources (solid black lines) and a contribution $C_{\mathrm{corr},ij}^{\mathrm{in}}$ due to correlations between sources (dashed black lines). If Dale’s law is respected (neurons are either excitatory or inhibitory), shared-input correlations are always positive ($C_{\mathrm{shared},ij}^{\mathrm{in}}>0$). Left: In the shared -noise scenario, sources are by definition uncorrelated ($C_{\mathrm{corr},ij}^{\mathrm{in}}=0$) and cannot compensate for shared-input correlations. Right: In inhibition-dominated neural networks (network case), correlations between units arrange such that $C_{\mathrm{corr},ij}^{\mathrm{in}}$ is negative, thereby compensating for shared-input correlations such that the total input correlation $C_{ij}^{\mathrm{in}}$ approximately vanishes.