All proposed model variants are built in Tensorflow and Keras (), built upon the framework provided by the MEGNET library . LiCOMPGNN's design, hyperparameters and training process was refined on Materials Project 2018 Formation Energy dataset and ported over to other tasks. Two model widths (64 and 256) were tested for LiCOMPGNN. All COMPGNN models have an additional warm-up training stage at higher learning rate under mean-square-error loss before changing to the target meanabsolute-error metric, a scheme that was found empirically to boost both accuracy and generalisability. The models were trained for a maximum of 1,000 epochs using the Adam optimizer using exponential moving averaging of weights and a learning rate reduction on plateau strategy using the validation MAE metric. For coGN, default hyperparameters and training schemes were used as reported in for a maximum of 1,000 epochs. For all remaining competitors we report scores from . Detailed training configurations are reported in the Supplementary Information in Supplementary Table .