Conditional distributions of true given reconstructed field values. Top-left panel: conditional distribution of true densities for a given reconstructed density $1+\hat{\delta }=0.36$ (marked by the vertical dotted line) for NN (blue) and WF (orange) in the validation mocks. The conditional mean true values and the 68% most likely true values are shown as vertical dashed lines and shaded ares, respectively. Top-right panel: same for the peculiar velocity components for a given reconstructed velocity component of $\hat{\mathit{v}}=267\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. Bottom row: same for $1+\hat{\delta }=3.16$ and a component of $\hat{\mathit{v}}=534\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$.