Sparse balance: Excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights
Fig 4
Time-scale of fluctuations adjusts to maintain sparse activity.
A) Population-averaged autocorrelation function of the synaptic input normalized by its zero-lag value. Note the faster decay of the autocorrelation for increasing K. B) The decorrelation rate β is constant in the low-variance network but increases logarithmically with K in the sparse balance model, resembling the (inverted) trends of sparsity (Fig 1D). C) β (solid) and the ratio var(x)/var(η) (dashed) in the high-variance model plotted on the same panel, aligned to different y-axes. var(⋅) refers to the total variance; similar result is obtained for the temporal variance. Error bars indicate SEM, averaged over 10 random realizations of the connectivity. (Model parameters: J0 = 2 for high variance and 1.05 for low variance, g = 2, I0 = 1, Jij ∼ gamma, N = K, ϕ = [tanh]+).