For the Mg case in Fig. (c,top), all energy densities integrate to nearly the same correlation energy by Eq. 1. However, the correlation energies from our GES and LES models differ dramatically when tested for transferability. The first such test is shown in Fig. ), where we see major differences in accuracy when applied to stretching the BH diatomic system along its dissociation curve. The LES-based model closely follows the e κMP2 c (r) (proxy) reference result, while the GES-based model is not sufficiently accurate even at equilibrium and breaks down completely as the bond is stretched. In Fig. more diatomic systems are shown, where we again see dramatic improvements of LES-based curves over their GES counterparts, displaying in some systems even unphysical discontinuities. These cases clearly demonstrate the crucial transferability advantages of LES-based models, expanding one GES energy data point to thousands. Furthermore, we observe another crucial difference between GES-and LES-based learning: when LES is used as the loss function, the learning process is much smoother and it has a much faster convergence with respect to learning steps (epochs) compared to GES (see Fig. in the SI). Now we take a closer look at the learning process of the ML2 neural network using LES. In Fig. , the absolute error in e ML2 c (r) based on LES as a function of distance is shown for several epochs in the He atom case as one of the ML2's training points. We observe how this pointwise improvement in e ML2 c (r) is transferred epoch by epoch to correlation energies for the LiH diatomic system along its dissociation curve (absolute errors become lower with larger epochs) in Fig. . In contrast to that, the GES based model yields no improvements of the transferability from atoms as the learning process progresses (see Fig. in the SI exposing poor transferability to diatomic systems, especially at large distances even at large epochs).