Optimal E:I ratios are in biophysically observed ranges, increase with sparsity (λ) and coincide for multiple performance measures.

The performance of sparse coding models subject to a constraint of N = 1200 total neurons and under different sparsity constraints (λ ∈ [0.0004, 0.30]) and using stimuli (100 image patches, 16 x 16 pixels) drawn from a database of 10 natural 512 x 512 pixels images [37]. Performance measures are normalized per Eq 8 and standard error (depicted with a shaded band, shown only for λ = 0.15 for clarity) over the natural image database is estimated using a bootstrap procedure (see Supplementary Methods in S1 Text). Markers denote the optimal E:I ratio for models at each sparsity constraint for each performance measure. Optimal E:I ratios for different performance measures are essentially identical as illustrated by vertical lines connecting markers across the 3 plots, and increases in model sparsity (λ) correspond to increases the optimal E:I ratio for each performance measure (also see Fig 4A and Fig D in S1 Text). (A) The coding fidelity for a sparse coding models with different sparsity constraints quantified by the normalized reconstruction error. The coding performance is optimized at an E:I ratio of approximately 6.5:1 (in a biophysically plausible range), with values above (below) that number suffering from lack of diversity in the inhibitory (excitatory) cell population. (B) Population Activity Density (1—Population Sparsity) for a sparse coding model (see Methods) is minimized at nearly the same specific optimal E:I ratio as with coding fidelity. (C) Lastly, a metabolic energy consumption measure [45] (see Methods) reveals minimal metabolic energy consumption at nearly the same specific E:I ratio as with coding fidelity and population density.