Despite the success of the MPAC's functionals, they currently rely on a global interpolation of the correlation energy along the MPAC , without access to a local, pointwise e c (r) . Defining MPAC correlation energy densities would enable improving the accuracy of the MPAC functionals by transitioning from global to local 4 (i.e., pointwise) MPAC interpolation. This, in turn, motivates the need for a well-defined e c (r) within the wavefunction framework. Additionally, in the context where functionals for E c are constructed from HF-density-based features -machine learning (ML) has emerged as a powerful tool training machine learning (ML) models of e c (r). The study demonstrated that training an ML model using LES enables generalization from atoms to molecules. In contrast, GES treats each system as a single energy data point, limiting transferability across systems. Thus, a well-founded e c (r) is crucial for advancing both traditional and ML-based methods mapping HF-density-based features to E c .