The relationship among common noise, private noise, and synaptic weight heterogeneity. (a, b) Fisher information as a function of population size, $N$⁠, when common noise contribution is drowned out by private noise (a) and common noise dominates (⁠$σP=1$⁠) (b). Solid lines indicate constant $kw$⁠, while dashed lines refer to $kw$ that scales with $N$⁠. (c, d) Normalized Fisher information as a function of common noise for structured weights (c) and unstructured weights (d). For unstructured weights, each Fisher information is calculated by averaging over 1000 networks with their common noise weights drawn from the respective distribution. (e) The value of $kw$ that maximizes the network's Fisher information for a given choice of $σP$ and $σC$⁠. The maximum is taken over $kw∈[1,10]$⁠. (f) The value of $μ$ that maximizes the average Fisher information over 1000 draws for a given choice of $σP$ and $σC$⁠.