In Fig. (r) completely misses the shape of the reference. But, can we, solely based on this observation, conclude that LES is better than GES? We need to be careful here, as these correlation energy densities are not observables even within our physically sound gauge (see Sec. II B). Instead, they are used here to enhance energy training data efficiency in ML of DFAs, expanding from one to thousands of energy datapoints per system. Thus, what ultimately matters for judging the quality of GES vs. LES training are the integrated correlation energies (Eq. 1) once we go outside of the training set.