Datasets:
license: mit
task_categories:
- other
tags:
- physics
- string-theory
- calabi-yau
- algebraic-geometry
- triangulation
size_categories:
- 10M<n<100M
CYTransformer — FRST training datasets
Favorable 4-dimensional reflexive polytopes paired with Fine, Regular, Star Triangulations (FRSTs) — the combinatorial data behind smooth Calabi–Yau threefolds — pre-split into train / validation / test.
These are the datasets behind "Transforming Calabi–Yau Constructions: Generating New Calabi–Yau Manifolds with Transformers" (arXiv:2507.03732), released for AICY.
Code: github.com/jhtyip/cytransformer · Weights: jhtyip/cytransformer-frst-models
Contents
One folder per configuration. 9+1 means 9 polytope vertices plus the origin; the paper's
Nvert counts the origin, so folder 9+1 is the paper's Nvert = 10.
| Folder | h1,1 | Train | Val | Test | Size | Sampling |
|---|---|---|---|---|---|---|
9+1 |
5 | 3,897 / 45,416 | 500 / 5,763 | 500 / 5,535 | 20 MB | exhaustive |
10+1 |
6 | 14,608 / 513,973 | 1,000 / 36,213 | 1,000 / 34,095 | 242 MB | exhaustive |
11+1 |
7 | 42,221 / 5,266,151 | 3,000 / 347,784 | 3,000 / 376,398 | 2.88 GB | exhaustive |
12+1 |
8 | 7,425 / 3,751,111 | 1,000 / 503,231 | 1,000 / 488,398 | 2.60 GB | exhaustive |
13+1 |
9 | 16,727 / 4,386,161 | 1,000 / 260,805 | 1,000 / 258,880 | 3.03 GB | fast sampler, ≤300 per polytope |
14+1 |
10 | 16,486 / 4,815,210 | 1,000 / 291,089 | 1,000 / 291,313 | 3.72 GB | fast sampler, ≤300 per polytope |
Train / val / test columns are polytopes / pairs. Every count above was measured from the files, not taken from filenames. Splits are per-polytope, so no polytope appears in more than one split.
Format
Six files per folder — {polys,triangs}_{train,val,test} — as plain JSON lists of
[POLYID, STRING] records. Row i of the polys file pairs with row i of the triangs file, so a
polytope is repeated once per triangulation.
polys: [3081, "{{0,1,0,0},{1,0,0,0},{-3,-2,-1,-1},{0,0,0,1},{0,0,1,0},{-2,0,-1,0},{-1,0,1,-1},{-1,1,0,0},{-2,-1,0,-1}}"]
triangs: [3081, "{{0,1,2,5},{0,1,2,8},{0,1,3,4},{0,1,3,5},{0,1,4,6},{0,1,6,8},{0,2,5,8},...}"]
A polytope is its list of vertices in ℤ⁴ (DRESVERTS). A triangulation is its list of
4-simplices, each given as indices into that vertex list. Polytopes are favorable — vertex count
equals lattice-point count minus the origin.
Because each polytope is duplicated once per triangulation, these files compress extremely well (the polys files by more than 100×).
Usage
from huggingface_hub import hf_hub_download
p = hf_hub_download("jhtyip/cytransformer-frst-datasets", "9+1/9+1_polys_train.json", repo_type="dataset")
t = hf_hub_download("jhtyip/cytransformer-frst-datasets", "9+1/9+1_triangs_train.json", repo_type="dataset")
They feed cyt-train directly — the files are already split, so no preparation step is needed.
Provenance
Generated with CYTools from the Kreuzer–Skarke database. Configurations
9+1–12+1 enumerate triangulations exhaustively; 13+1 and 14+1 use a fast sampler capped at
300 triangulations per polytope, since exhaustive enumeration is infeasible at that size.
Published filenames drop the polytope counts that appeared in the original working filenames — those counts referred to scan ranges and configured limits rather than file contents, and did not match the data. The measured counts are in the table above.
Citation
@article{Yip:2025hon,
author = {Yip, Jacky H. T. and Arnal, Charles and Charton, Fran\c{c}ois and Shiu, Gary},
title = {Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers},
journal = {arXiv e-prints},
eprint = {2507.03732},
year = {2025},
doi = {10.48550/arXiv.2507.03732}
}
MIT licensed. Department of Physics, University of Wisconsin–Madison.