TY - GEN
T1 - How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Science
AU - Polat, Can
AU - Serpedin, Erchin
AU - Kurban, Mustafa
AU - Kurban, Hasan
N1 - Publisher Copyright:
© 2026 Owner/Author.
PY - 2026/8/8
Y1 - 2026/8/8
N2 - 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 ∼75,000 crystal-derived nanoparticle structures (33 - 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. Each model is conditioned on the target composition and atom count, isolating geometric extrapolation as the evaluation variable. 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) well-behaved models degrade by ∼13% in global positional error beyond training radii, while divergent models exhibit poor absolute fidelity across scales; local bond fidelity varies sharply across architectures, from negligible degradation to more than 2× error growth; (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 conform to the expected geometric scaling exponent α ≈1/3 whose in-distribution fit accurately predicts out-of-distribution error, making their frontiers quantitatively forecastable. Scaling MatterGen to its published parameter count stabilizes sampling but does not close the extrapolation frontier, while DiffCSP remains unstable even at published scale. These findings establish output scale as a first-class evaluation axis for geometric generative models. The dataset, generation pipeline, and implementations are available at https://github.com/KurbanIntelligenceLab/RADII.
AB - 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 ∼75,000 crystal-derived nanoparticle structures (33 - 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. Each model is conditioned on the target composition and atom count, isolating geometric extrapolation as the evaluation variable. 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) well-behaved models degrade by ∼13% in global positional error beyond training radii, while divergent models exhibit poor absolute fidelity across scales; local bond fidelity varies sharply across architectures, from negligible degradation to more than 2× error growth; (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 conform to the expected geometric scaling exponent α ≈1/3 whose in-distribution fit accurately predicts out-of-distribution error, making their frontiers quantitatively forecastable. Scaling MatterGen to its published parameter count stabilizes sampling but does not close the extrapolation frontier, while DiffCSP remains unstable even at published scale. These findings establish output scale as a first-class evaluation axis for geometric generative models. The dataset, generation pipeline, and implementations are available at https://github.com/KurbanIntelligenceLab/RADII.
KW - benchmark
KW - crystal generation
KW - equivariant architectures
KW - graph neural networks
KW - quantum chemistry
UR - https://www.scopus.com/pages/publications/105051057506
U2 - 10.1145/3770855.3818872
DO - 10.1145/3770855.3818872
M3 - Conference contribution
AN - SCOPUS:105051057506
T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
SP - 11821
EP - 11832
BT - KDD 2026 - Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2
PB - Association for Computing Machinery
T2 - 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1, KDD 2026
Y2 - 9 August 2026 through 13 August 2026
ER -