Framework for neural network scaling.

<p><b>A</b> Downscaling facilitates simulations, while taking the <i>N</i> → ∞ limit often affords analytical insight. <b>B</b> Relevant scales. The local cortical microcircuit containing roughly 10⁵ neurons is the smallest network where the majority of the synapses (∼ 10⁴ per neuron) can be represented using realistic connection probabilities (∼ 0.1). <b>C</b> Results for the <i>N</i> → ∞ limit may not apply even for large networks. In this example, analytically determined intrinsic and extrinsic contributions to correlations between excitatory neurons are shown. The extrinsic contribution to the correlation between two neurons arises due common external input, and the intrinsic contribution due to fluctuations generated within the network (cf. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004490#pcbi.1004490.ref009" target="_blank">9</a>] Eq 24). The intrinsic contribution falls off more rapidly than the extrinsic contribution, but nevertheless dominates up to large network sizes, here around 10⁸. The crosses indicate simulation results. Adapted from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004490#pcbi.1004490.ref009" target="_blank">9</a>] Fig 7. <b>D</b> Scaling transformations may be designed to preserve average single-neuron or pairwise statistics for selected quantities, population statistics, or a combination of these. When average single-neuron and pairwise properties are preserved, the downscaled network of size <i>N</i> behaves to second order like a subsample of the full network of size <i>N</i>₀.