---
license: cc-by-4.0
language:
- en
pretty_name: RADII
size_categories:
- 10K<n<100K
task_categories:
- other
tags:
- materials-science
- crystal-structures
- generative-models
- benchmark
- kdd-2026
- nanoparticles
configs:
- config_name: default
  data_files:
  - split: train
    path: train.parquet
  - split: id_test
    path: id_test.parquet
  - split: ood_test
    path: ood_test.parquet
---

# 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](https://github.com/KurbanIntelligenceLab/RADII) (MIT)
- **Archival DOI:** [10.5281/zenodo.20431021](https://doi.org/10.5281/zenodo.20431021) (CC-BY-4.0)

## Quick start

```bash
pip install datasets
```

```python
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:

```python
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`)

```python
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`):

```python
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

```bibtex
@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](https://doi.org/10.5281/zenodo.20431021)
for the archival record terms. Accompanying code is MIT-licensed at the GitHub repo.