Residuals of (a) the VSF emulator predictions and (b) the density profile emulator predictions on the test set show that both are highly accurate. The blue and gray bands indicate 68% and 95% of predictions on the test set, and the black line shows the deviation of 1σ as derived from the covariance estimate. For clarity we denote $\frac{\mathrm{d}{n}_{\mathrm{v}}}{\mathrm{d}ln{r}_{\mathrm{v}}}[h^3{\mathrm{Mpc}}^{-3}]$ as VSF and Δ denotes the difference of its prediction with respect to the measurement from the corresponding box. As defined in the main body, each profile (here binned by r_v into quartiles) spans from 0.3 × r_v to 2.7 × r_v.