The NN optimization of the n-LMF was performed with the TensorFlow 56 library in a local python code. The NN training used input features (see Theory section) obtained with a local version of Turbomole 7.8, based on the scLH23t-mBR-P 20 LH, def2-QZVPPD basis sets, and Turbomole's "universal" auxiliary basis sets for the RI-J approach to the Coulomb integrals, with gridsize 3. The features consisted of the density, the norm of the density gradient, and the kinetic-energy density. Each grid point was processed using a multi-layer perceptron (MLP) with shared weights (see discusion in 2.1 and Figure ). The output layer was employed in eq. 15 to predict the final XC energy density for each atom or molecule in the BH76 and W4-17 data sets. Integration of the predicted XC energy densities was done using Becke's partitioning scheme. The integrated energies were labeled with the reference values obtained from these databases. The mean absolute error (MAE) was calculated for each data set and integrated into the loss function with equal weights for the two sets.