Strictly speaking, our framework requires the use of KS orbitals, as we build here models for correlation energy in KS DFT theory. Yet, for practical purposes, we use here Hartree-Fock (HF) orbitals and density to calculate all energy terms and input features for our NNs, to prevent uncontrolled error cancellation of functional-and density-driven errors when building datadriven DFAs 39,81-83 . An alternative theoretical foundation for our correlation energy models, built on top of HF orbitals, is provided by the Møller-Plesset adiabatic connection framework , where approximations for the correlation energy in HF theory are constructed using the same orbitals.