C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation
Existing generative models for materials lack systematic evaluation in cross-scale generalization—from infinite periodic crystals to finite nanostructures—and struggle to capture surface effects and size-dependent geometric distortions. This work proposes the C2NP benchmark, which establishes the first systematic generative tasks bridging bulk crystals and nanoparticles: (i) generating nanoparticles of specified radii from unit cells, and (ii) inferring bulk lattice parameters and space groups from given nanoparticles. Leveraging a dataset of over 170,000 DFT-relaxed nanoparticles, the benchmark introduces size-based interpolation and extrapolation splits to assess geometric invariance across scales. Experiments reveal that while mainstream generative models achieve low training losses, they fail catastrophically under distributional shifts, exhibiting large lattice recovery errors and near-zero joint accuracy in structure–symmetry prediction, exposing their reliance on template memorization rather than physically grounded, scalable generalization.