CYTransformer generates Fine, Regular, Star Triangulations (FRSTs) of favorable 4-dimensional reflexive polytopes — the combinatorial data of smooth Calabi-Yau threefolds. These are the trained models from the paper, free to download and run.
Get the weightsCheckpoints
One model per polytope size. Nvert is written as vertices + origin:
9+1 is 9 polytope vertices plus the origin, i.e. 10 lattice points. The models are
not interchangeable — the vocabulary and sequence length grow with the
number of vertices, so each file loads only into its own configuration.
| Checkpoint | h1,1 | Nvert | Step | Vocab | Params | Val loss |
|---|---|---|---|---|---|---|
chkpt_9+1 | 5 | 9+1 | 1,120,108 | 129 | 118.9 M | 2.203 |
chkpt_10+1 | 6 | 10+1 | 1,019,736 | 213 | 119.0 M | 2.416 |
chkpt_11+1 | 7 | 11+1 | 861,838 | 333 | 119.1 M | 2.575 |
chkpt_12+1 | 8 | 12+1 | 1,438,540 | 498 | 119.3 M | 2.829 |
chkpt_14+1 | 10 | 14+1 | 1,218,169 | 1,004 | 119.8 M | 2.971 |
Each checkpoint is about 1.4 GB and stores the model, optimizer and scheduler state together with its full training and validation history, so training can be resumed or inspected. Losses are read from the curves inside each checkpoint.
Architecture
Identical across every configuration: 16 encoder and 16 decoder layers, embedding
dimension 512, 16 attention heads, feed-forward hidden dimension 2048, dropout 0.1
— about 119 million parameters. Only the target vocabulary,
C(vertices, 4) + 3, and the maximum sequence length change with polytope size.
Trained with Adam at learning rate 5×10-5 with exponential decay.
Using a model
Install the software, then fetch a checkpoint and generate:
pip install -e .
python -c "from huggingface_hub import hf_hub_download; \
print(hf_hub_download('jhtyip/cytransformer-frst-models','chkpt_9+1'))"
cyt-infer --checkpoint <path> --polys examples/polytopes.json --num-per-poly 100
Every candidate is verified as a genuine FRST in real time — fine, star, valid and regular. CYTools is not required: verification uses an exact rational intersection test plus a linear program for regularity, cross-checked against CYTools on a labeled set with full agreement.
Triangulations are generated as an unordered set of simplices, so the same FRST can be emitted in different simplex orders. Canonicalise before counting distinct results.
Training data
The training datasets for this work are published alongside these models — the full catalog, with formats and download links, is on the Data page.
Browse the datasets