Wave represents QC systems accurately with a local variable model, while convolution requires global variables. (A) Graph-based deep learning methods can be used to learn an atom-local variable model of quantum chemistry. This intermediate representation can then be decoded to a quantum measurement. Wave is an atom-local variable model, while MPNN-G, which includes a global variable, is a mixed local variable model. (B) Removing the global variable from MPNN-G (MPNN) results in substantially higher error on total energy and (C) polarizability. Both methods exhibit higher error than Wave. (D) Increase in total energy error of MPNN vs MPNN-G. MPNN exhibits a statistically significant increase in error for all molecules, but substantially larger error increases for large molecules. Statistical tests were performed by paired t-test. *: p < 0.05, ***: p < 0.001.