Composable Crystals: Controllable Materials Discovery via Concept Learning

Existing methods for de novo crystal generation largely produce complete crystal structures, either through stochastic sampling or under predefined structural constraints, providing limited mechanisms for explicitly structuring how the crystal space is explored. In this work, we introduce a concept-based compositional framework that represents crystal generation as the recombination of learned structural units. We learn a discrete vocabulary of local crystal concepts using a vector-quantized variational autoencoder, where each concept represents a recurring local atomic environment. Unlike predefined structural attributes, these concepts are automatically discovered from data, and multiple concepts can coexist and be recombined within a single crystal. Moreover, the learned concepts exhibit interpretable patterns in both local atomic environments and global crystal symmetries, and empirically transfer across crystal datasets. We further introduce a composition generator to produce novel concept combinations and refine it using high-quality samples. The resulting concept compositions guide downstream crystal generation toward structural combinations beyond those observed in the training data. Experiments on MP-20 and Alex-MP-20 show that concept composition improves the V.S.U.N. score of the base generative model by 53.2% and 51.7%, respectively, with the main gain arising from increased novelty.