As e MP2 c (r) by Eq. 1 integrates to the MP2 correlation energy, it can be easily argued that it is not a sufficiently good proxy reference to train ML energy densities given general MP2 limitations , particularly for small orbital-gap systems . To address this, we apply Head-Gordon's κ-regulizaration (κ ≥ 0) to e MP2 c (r) of Eq. 5 by regularizing its partial MP2 doubles amplitudes, (r) for the NeAr system as κ increases (plotted is the interaction correlation energy density calculated as the difference between the total system and that of the individual atoms).