How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Science
This addresses a critical issue for nanomaterial design by providing a benchmark to evaluate and predict the scaling limits of generative models, though it is incremental in improving evaluation methods rather than proposing new models.
The paper tackles the problem of generative models for crystalline materials becoming unreliable beyond a critical structure size, introducing RADII to systematically measure this extrapolation frontier and finding that models degrade by ~13% in global positional error beyond training radii, with local bond fidelity varying widely.
Every generative model for crystalline materials harbors a critical structure size beyond which its outputs quietly become unreliable -- we call this the extrapolation frontier. Despite its direct consequences for nanomaterial design, this frontier has never been systematically measured. We introduce RADII, a radius-resolved benchmark of ${\sim}$75,000 nanoparticle structures (55-11,298 atoms) that treats radius as a continuous scaling knob to trace generation quality from in-distribution to out-of-distribution regimes under leakage-free splits. RADII provides frontier-specific diagnostics: per-radius error profiles pinpoint each architecture's scaling ceiling, surface-interior decomposition tests whether failures originate at boundaries or in bulk, and cross-metric failure sequencing reveals which aspect of structural fidelity breaks first. Benchmarking five state-of-the-art architectures, we find that: (i) all models degrade by ${\sim}13\%$ in global positional error beyond training radii, yet local bond fidelity diverges wildly across architectures -- from near-zero to over $2\times$ collapse; (ii) no two architectures share the same failure sequence, revealing the frontier as a multi-dimensional surface shaped by model family; and (iii) well-behaved models obey a power-law scaling exponent $α\approx 1/3$ whose in-distribution fit accurately predicts out-of-distribution error, making their frontiers quantitatively forecastable. These findings establish output scale as a first-class evaluation axis for geometric generative models. The dataset and code are available at https://github.com/KurbanIntelligenceLab/RADII.