Hybridizing expert descriptors and learned embeddings yields transferable Mat2Vec-^* element representations

Element representations bridge chemical identity and machine-learning models for materials prediction, but handcrafted descriptors, corpus-derived embeddings, and supervised embeddings are typically treated as separate choices. Here we show that handcrafted and supervised representations encode complementary chemical information and that supervised element geometry can be distilled into reusable element tables (Mat2Vec-^*). Across eight structure-based MatBench regression tasks, controlled CGCNN and MEGNet benchmarks span 2,240 models over representation mixtures and latent dimensions. The top-performing models define rotation-invariant cosine-distance relations from which we reconstruct Mat2Vec-^*. In composition-only model (CrabNet), these tables replace or augment corpus-derived Mat2Vec, with most configurations improving performance across all four MatBench composition tasks. On the Matbench Discovery WBM benchmark, Mat2Vec-^* features further reduce errors for several modern structure-based predictors through lightweight residual correction. Together, these results establish Mat2Vec-^* as a compact, transferable supervised chemical prior for materials prediction.