For the manipulation and labeling of the collected pre-training set, we used the Python Materials Genomics (pymatgen) library . In particular, for the APC task, the crystal structures were represented as graphs, where disconnected sub-graphs were considered as isolated molecules, for the SEP task the space groups of the crystals were first identified and subsequently were mapped to their corresponding symmetry elements. For the remaining tasks the label generation was straightforward using pymatgen. Before being inputted into the model, the crystals were converted into the P 1 space group to ensure the feasibility of subsequent SEP and APC tasks during pre-training phase. For the persistence image generation, we used MoleculeTDA to compute persistence images with a resolution of 50 × 50 and a spread of 0.15, consistent with previous studies . For the t-SNE embedding, we used a perplexity parameter of 50, due to the large size of the pre-training dataset.