PIPs were first used as inputs to Gaussian Process Regression (GPR) by some of us. That approach, referred to as PIP-GP, was assessed against direct PIPs representations for molecules ranging in size from H 3 O + to the 10-atom formic acid dimer. Linear PIP regression generally outperformed the non-linear PIP-GPR, both in terms of precision and speed. Very recently this approach was used to develop a ∆-ML PES for several chemical reactions. using a recently reported approach. One issue with using PIP or FIs as inputs either NN or GPR is that it grows rapidly with the size of the molecule and symmetry. And it has been noted that the fitting precision does depend on the number of PIPs and FIs "FIs up to degree 5 or 6 provide adequate accuracy for use in the fitting process." For a 10-atom molecules with symmetry A 4 B 4 C 2 there are 1153 FIs for degree 5. Clearly evaluating these just as inputs to a NN, which typically has two-hidden layers and tens of neurons per layer would be a large overhead in the cpu effort.