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

arXiv: https://arxiv.org/abs/2602.09309 · HTML: https://mlsanity.com/paper/2602.09309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 77 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry](https://mlsanity.com/paper/2502.06485/) (2025)
- [Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materials](https://mlsanity.com/paper/2306.09375/) (2023)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation](https://mlsanity.com/paper/2601.19076/) (2026)

## Built on by (most cited first, 1 of 1)

- [Physics as the label for measuring and correcting materials reasoning in multimodal models](https://mlsanity.com/paper/2609.12181/) (2026)

## Abstract (arXiv)

Every generative model for crystalline materials harbors a critical structure size beyond which its outputs become unreliable; we call this the extrapolation frontier. Despite its 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, tracing generation quality from in- to out-of-distribution under leakage-free splits. Each model is conditioned on 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 separates boundary from bulk failures, and cross-metric 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 show poor fidelity across scales, with local bond fidelity ranging from negligible degradation to over 2x error growth; (ii) no two architectures share a failure sequence, revealing the frontier as a multi-dimensional surface shaped by model family; and (iii) well-behaved models follow the expected geometric scaling exponent alpha ~ 1/3, whose in-distribution fit predicts out-of-distribution error, making frontiers forecastable. Scaling MatterGen to its published parameter count stabilizes sampling but does not close the frontier, while DiffCSP remains unstable at published scale. These findings establish output scale as a first-class evaluation axis for geometric generative models. Code and data: https://github.com/KurbanIntelligenceLab/RADII.