AICY hosts the data and models behind CYTransformer — a transformer that generates Fine, Regular, Star Triangulations (FRSTs) of reflexive polytopes, the combinatorial data of smooth Calabi-Yau threefolds. The training datasets and the pretrained weights are both openly available.
Get the datasetsTraining datasets
Favorable 4-dimensional reflexive polytopes paired with reference FRSTs, pre-split into train / validation / test. These are the datasets behind the CYTransformer paper.
| Config | h1,1 | Train | Val | Test | Size |
|---|---|---|---|---|---|
| 9 + 1 | 5 | 3,897 / 45,416 | 500 / 5,763 | 500 / 5,535 | 20 MB |
| 10 + 1 | 6 | 14,608 / 513,973 | 1,000 / 36,213 | 1,000 / 34,095 | 242 MB |
| 11 + 1 | 7 | 42,221 / 5,266,151 | 3,000 / 347,784 | 3,000 / 376,398 | 2.88 GB |
| 12 + 1 | 8 | 7,425 / 3,751,111 | 1,000 / 503,231 | 1,000 / 488,398 | 2.60 GB |
| 13 + 1 | 9 | 16,727 / 4,386,161 | 1,000 / 260,805 | 1,000 / 258,880 | 3.03 GB |
| 14 + 1 | 10 | 16,486 / 4,815,210 | 1,000 / 291,089 | 1,000 / 291,313 | 3.72 GB |
Train, validation and test columns read polytopes / pairs, where a pair is one polytope together with one of its triangulations. Splits are per polytope, so no polytope appears in more than one split. Configurations 9+1 through 12+1 enumerate triangulations exhaustively; 13+1 and 14+1 use a fast sampler capped at 300 triangulations per polytope.
Data format
Every record is plain JSON. A polytope is [POLYID, DRESVERTS] and a triangulation
is [POLYID, TRIANG], with row i of the polytope file pairing with row
i of the triangulation file. A polytope is given by its vertices in
Z4; a triangulation by its 4-simplices, each a list of indices into
those vertices.
| polys | [3081, "{{0,1,0,0},{1,0,0,0},{-3,-2,-1,-1},…}"] |
|---|---|
| triangs | [3081, "{{0,1,2,5},{0,1,2,8},{0,1,3,4},…}"] |
The files are already split, so they feed cyt-train directly with no
preparation step. Generated with CYTools from the Kreuzer-Skarke
database.
Pretrained weights
Trained CYTransformer models are available across h1,1 = 5 to 10 — download them and generate FRSTs directly with the software.
Browse the modelsModel-generated FRSTs
Coming soon — new FRSTs generated by CYTransformer and automatically validated, a growing catalog of Calabi-Yau data.