Extended Data Fig. 9: Analysis of robustness as a function of network size.

a, The net volume of parameter space that achieves a desired performance threshold (estimated by summing the tolerance across all optimal values of local excitation for a given network size N) increases faster than N2. Computed analytically via Eq. (7) by summing over all optimal values of local excitation (solid black line), and estimated numerically by summing over all values shown in Fig. 4b). The analytic lower bound given in Methods Eq. (16) is shown for comparison (gray dashed line). b, Left: noise robustness increases linearly with network size. Right: the coefficients of the best linear fit vary inversely with the noise variance σ2.