We stressed in section 2.3 that our GNN model only predicts the magnitudes but not the phases (signs) of the ATCs. In this work, we simply assigned to our predicted ATC magnitudes the phases predicted by DFT. This shortcoming is less serious than it first appears. We found that ATC phase could be computed accurately using very simple functionals and basis sets, and moreover that the signs could be obtained after terminating the self-consistent loop after 5 iterations. This enables the phase to be computed with a time decrease of between 3 to 11 times that of calculating the fully converged ATC, which is equivalent to a few minutes to run on a 32core high performance computing machine (see Supplementary Information S3 for further information). We did find however that there was a potential for incorrectly predicting the phase using the unconverged ATC calculation between 10 % to 20 %. While it is beyond the scope of this paper to explain why ATC phases can be obtained at these low computational costs, we point out that similar phenomena has been observed in the statistical mechanics literature, where it is known that the phase of the wave functions of the Heisenberg spin model converge considerably faster than the wave functions themselves. However, while it is possible to obtain ATC phase using cheap DFT calculations, it is hardly desirable from a machine-learning perspective, in which predictions should be obtainable within milliseconds. Further work will therefore need to address the sign problem properly, either with a machine-learned model or with a simple physicsbased model.