Learning Hierarchical Representations of Metal–Organic Frameworks with Coupled Euclidean and Hyperbolic Geometry

Learning representations of structured materials requires combining local geometry with connectivity across chemical building units. Metal–organic frameworks (MOFs) make this challenge explicit: their properties depend on both atomic environments and the organization of metal-containing units and organic linkers. We introduce , a graph representation model that couples Euclidean and hyperbolic geometry. A Euclidean branch encodes periodic local interactions, while a Lorentz branch processes an atomic covalent graph enriched with building-block features. Graph-level attention combines the two representations for property prediction. Building blocks augment atom features rather than define a separate coarse-grained graph. Across the reported hMOF and CoRE MOF adsorption benchmarks, achieves the lowest MAE among the evaluated models; additional comparisons cover MOF-specific architectures, repeated training runs, and accessible surface area. Geometric diagnostics show lower normalized hyperbolicity than degree-matched rewired controls and better graph-distance preservation for the evaluated Lorentz encoder. However, hyperbolicity has little association with per-structure prediction gains. These findings support coupled geometry as a useful inductive bias for MOF pore-related properties, while separating geometric motivation from claims about the causes of predictive improvement.