How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Science

TL;DR

This paper introduces RADII, a comprehensive benchmark to measure and analyze the extrapolation limits of graph generative models in materials science, revealing diverse failure modes and scaling behaviors across architectures.

Contribution

It systematically characterizes the extrapolation frontier of graph generative models for nanoparticle structures using RADII, providing diagnostics and scaling laws to predict out-of-distribution performance.

Findings

Models degrade by ~13% in positional error beyond training radii.

Local bond fidelity varies widely across architectures.

Power-law scaling predicts out-of-distribution errors.

Abstract

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 $\alpha \approx 1/3$ 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.