The graphs in the validation set were used to evaluate the top-K (K " 1, 5) similarity scores against the embedded vectors of texts that describe the space groups and the local atomic environments. Note that there are multiple, a non-constant number of local atomic environments each crystal; we thus counted the top-K retrieval as correct if at least one of the local atomic environments is included in the list of the ground truths. In evaluating the local atomic environments, the metric that counts the cases of "at least one of them is included" as correct may be biased; however, this metric seems not to deviate from the qualitative analysis through Table -5. Note that, we also observed cases where retrieved concepts do not exactly match the list, but are still considered reasonable in their meanings of geometry.