RADII: how far can a generative model grow a crystal before it breaks?

Radius as a scaling knob

RADII is a radius-resolved benchmark of roughly 75,000 crystal-derived nanoparticle structures, ranging from 33 to 11,298 atoms. By treating particle radius as a continuous knob, it traces generation quality smoothly from in-distribution sizes into out-of-distribution territory, under leakage-free data splits. Each model is conditioned on composition and atom count, so geometric extrapolation — and nothing else — is what gets measured.

Diagnostics, not just scores

Beyond a leaderboard number, RADII ships frontier-specific diagnostics: per-radius error profiles pinpoint each architecture's scaling ceiling; a surface–interior decomposition tests whether failures start at particle boundaries or in the bulk; and cross-metric failure sequencing reveals which aspect of structural fidelity breaks first as structures grow.

What we found across five architectures

Benchmarking five state-of-the-art graph generative models produced three headline findings. First, well-behaved models degrade by about 13% in global positional error beyond their training radii, while divergent models are unreliable at every scale — and local bond fidelity varies from negligible degradation to more than 2× error growth depending on architecture. Second, no two architectures share the same failure sequence: the frontier is a multi-dimensional surface shaped by model family. Third, well-behaved models follow the expected geometric scaling exponent α ≈ 1/3, which makes their out-of-distribution error quantitatively forecastable from in-distribution fits alone.

A sobering detail: scaling MatterGen to its published parameter count stabilizes sampling but does not close the frontier, and DiffCSP remains unstable even at published scale. Output size, the paper argues, deserves to be a first-class evaluation axis for geometric generative models.

Applications & economic impact

Generative models are moving into the design loop for batteries, catalysts, coatings, and drug-delivery nanoparticles — domains where a failed synthesis run costs real lab time, materials, and months of iteration. RADII changes the economics of that loop:

• Trust before synthesis — teams can determine whether a model is reliable at their production particle size before committing wet-lab resources, instead of discovering failure after the fact.
• Forecastable risk — because well-behaved models follow the α ≈ 1/3 scaling law, out-of-distribution error becomes predictable arithmetic rather than a gamble.
• Smarter compute spend — the MatterGen result shows that buying more parameters does not buy extrapolation; budgets are better directed at data coverage and architecture choice.

Go deeper

Full paper: Download the PDF — complete benchmark design, diagnostics, and per-architecture results.

Dataset, pipeline & code: github.com/KurbanIntelligenceLab/RADII

To appear in the Proceedings of KDD '26 (August 9–13, 2026), DOI 10.1145/3770855.3818872.