Graph neural networks stop at predictions: GSD turns message passing into readable formulas and recovers expert descriptors in three systems
Graph neural networks learn structure–property relationships from graphs of atoms and bonds, but those relationships stay in a latent space and are hard to read as scientific rules. Graph symbolic distillation (GSD) first uses a constrained message-passing architecture search to fix how information is transformed, propagated and aggregated, then fits each layer's learned transformation with a sparse symbolic expression while keeping graph connectivity and aggregation. Across halide-perovskite band gaps, molecular hydration free energies and multidentate adsorption on transition-metal surfaces, it rebuilds expert descriptors from elementary node and edge features and yields testable local-geometry, polarity–size and electronic–connectivity relationships.