RADII: Radius-Resolved Benchmark of Nanoparticle Structures

RADII measures where graph generative models start to fail as the structures they generate grow larger. Radius is treated as a continuous scaling knob from in-distribution to out-of-distribution; the dataset spans 10 materials and 25 radii with leakage-free splits.

• Paper: How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Science — KDD '26
• Code (models, trainer, generation pipeline): github.com/KurbanIntelligenceLab/RADII (MIT)
• Archival DOI: 10.5281/zenodo.20431021 (CC-BY-4.0)

Quick start

pip install datasets

from datasets import load_dataset

ds = load_dataset("KurbanIntelligenceLab/RADII", split="train").with_format("torch")
print(ds.features, len(ds), ds[0]["material"], ds[0]["num_atoms"])

That's it — no trust_remote_code, no Zenodo download, no regeneration.

Splits

Split	Size	Radii (Å)
train	48,000	15 values: 8–10, 12, 14, 16, 18, 20, 22–28
id_test	13,500	6 values: 11, 13, 15, 17, 19, 21 (interleaved, unseen orientations)
ood_test	13,480	4 values: 6, 7, 29, 30 (strictly outside training range)

OOD test structures are ~59% smaller and ~24% larger than the smallest and largest training structures (atom counts 33–11,298 vs train 81–9,148).

Materials (10)

Ag, Au, CH₃NH₃PbI₃, Fe₂O₃, MoS₂, PbS, SnO₂, SrTiO₃, TiO₂, ZnO.

Schema (per row)

Column	Type	Notes
material	str	One of the 10 above
radius	int	Truncation radius in Å
rot_idx	int	Orientation index
split	str	train, id_test, or ood_test
num_atoms	int	Length of pos/z
pos	list[list[float32]]	num_atoms × 3 atomic coordinates
z	list[int8]	num_atoms atomic numbers
cell_matrix	list[list[float32]]	3 × 3 lattice vectors of the parent unit cell
cell_pos	list[list[float32]]	Unit-cell basis positions (per-material)
cell_z	list[int8]	Unit-cell basis atomic numbers

Analysis recipes (per-radius, per-material, cross-split)

The metadata columns are first-class, so slicing and grouping are one-liners:

from datasets import load_dataset

# All three splits at once
ds_all = load_dataset("KurbanIntelligenceLab/RADII")

# Per-radius slice — every train sample at R=12
r12 = ds_all["train"].filter(lambda x: x["radius"] == 12)

# Per-material grouping
materials = ds_all["train"].unique("material")  # ['Ag', 'Au', ...]
ag_ood    = ds_all["ood_test"].filter(lambda x: x["material"] == "Ag")

# Cross-split: atom counts by radius
import pandas as pd
for split in ("train", "id_test", "ood_test"):
    df = ds_all[split].select_columns(["radius", "num_atoms"]).to_pandas()
    print(split, df.groupby("radius")["num_atoms"].agg(["mean", "min", "max"]))

# Atom-count envelope check (replicates the paper's 59% / 24% statistic)
train_min, train_max = ds_all["train"]["num_atoms"], ds_all["train"]["num_atoms"]
print("train atom-count range:", min(train_min), "to", max(train_max))
print("OOD  atom-count range:", min(ds_all["ood_test"]["num_atoms"]),
      "to", max(ds_all["ood_test"]["num_atoms"]))

PyTorch collate (variable-length pos/z)

import torch
from torch.utils.data import DataLoader

def collate(batch):
    return {
        "pos":         [torch.as_tensor(b["pos"]) for b in batch],
        "z":           [torch.as_tensor(b["z"])   for b in batch],
        "cell_matrix": torch.stack([torch.as_tensor(b["cell_matrix"]) for b in batch]),
        "material":    [b["material"] for b in batch],
        "radius":      torch.tensor([b["radius"] for b in batch]),
    }

loader = DataLoader(ds, batch_size=32, shuffle=True, collate_fn=collate)

For PyTorch Geometric, the pos/z lists drop straight into torch_geometric.data.Batch.from_data_list(...).

Models

The 5 baselines from the paper (ADiT, CDVAE, DiffCSP, FlowMM, MatterGen) live in the GitHub repo's radii.models namespace and follow the standard HuggingFace model interface (PyTorchModelHubMixin):

from radii.models import ADiTUnitCell
from radii.train_config import ModelConfig

m = ADiTUnitCell(**ModelConfig.ADiT.to_dict())
m.save_pretrained("./my_adit")
m2 = ADiTUnitCell.from_pretrained("./my_adit")
# m.push_to_hub("my-username/my-radii-adit") also works

See the GitHub README for training (python -m radii.train --model adit) and override flags (--epochs, --lr, --from-checkpoint, --eval-only).

Citation

@article{polat2026far,
  title   = {How Far Can You Grow? Characterizing the Extrapolation Frontier of Graph Generative Models for Materials Science},
  author  = {Polat, Can and Serpedin, Erchin and Kurban, Mustafa and Kurban, Hasan},
  journal = {arXiv preprint arXiv:2602.09309},
  year    = {2026}
}

License

CC-BY-4.0. See 10.5281/zenodo.20431021 for the archival record terms. Accompanying code is MIT-licensed at the GitHub repo.