---
license: mit
library_name: pytorch
tags:
  - physics
  - string-theory
  - calabi-yau
  - algebraic-geometry
  - triangulation
  - transformer
datasets:
  - jhtyip/cytransformer-frst-datasets
---

# CYTransformer — trained weights

Encoder–decoder transformers that generate **Fine, Regular, Star Triangulations (FRSTs)** of
4-dimensional reflexive polytopes — the combinatorial data behind smooth Calabi–Yau threefolds.

These are the trained models from *"Transforming Calabi–Yau Constructions: Generating New
Calabi–Yau Manifolds with Transformers"* ([arXiv:2507.03732](https://arxiv.org/abs/2507.03732)),
and the first released weights for [**AICY**](https://aicy.physics.wisc.edu).

Code: [github.com/jhtyip/cytransformer](https://github.com/jhtyip/cytransformer) ·
Data: [jhtyip/cytransformer-frst-datasets](https://huggingface.co/datasets/jhtyip/cytransformer-frst-datasets)

## Checkpoints

One model per polytope size. They are **not interchangeable** — vocabulary and sequence length
grow with the number of vertices, so each file loads only into its own configuration.

| File | h<sup>1,1</sup> | N<sub>vert</sub> | Step | Vocab | Max simplices | Params | Train loss | Val loss |
|---|---|---|---|---|---|---|---|---|
| `chkpt_9+1`  | 5  | 9+1  | 1,120,108 | 129   | 30 | 118.9 M | 2.170 | **2.203** |
| `chkpt_10+1` | 6  | 10+1 | 1,019,736 | 213   | 35 | 119.0 M | 2.389 | **2.416** |
| `chkpt_11+1` | 7  | 11+1 | 861,838   | 333   | 45 | 119.1 M | 2.579 | **2.575** |
| `chkpt_12+1` | 8  | 12+1 | 1,438,540 | 498   | 55 | 119.3 M | 2.757 | **2.829** |
| `chkpt_14+1` | 10 | 14+1 | 1,218,169 | 1,004 | 65 | 119.8 M | 2.985 | **2.971** |

Losses are read from the curves stored inside each checkpoint, not from external logs.

**Naming.** N<sub>vert</sub> is written as *vertices + origin*: `9+1` is 9 polytope vertices plus
the origin, i.e. 10 lattice points, which is the paper's N<sub>vert</sub> = 10.

## Architecture

Identical across all configurations: **16 encoder + 16 decoder layers, d_model 512, 16 attention
heads, FFN hidden 2048 (4×), dropout 0.1** — roughly 119 M parameters. Only the target vocabulary
(`C(vertices, 4) + 3`) and maximum sequence length vary. Trained with Adam
(lr 5e-5, β = (0.9, 0.98), ε = 1e-9) and exponential decay.

Each checkpoint carries `model_state_dict`, `optimizer_state_dict`, `scheduler_state_dict`,
`n_vertices`, `last_step`, `hyperparams`, and the full `loss` / `validation` histories, so training
can be resumed or inspected.

## Usage

```bash
git clone https://github.com/jhtyip/cytransformer && cd cytransformer
pip install -e .
```

```python
from huggingface_hub import hf_hub_download
ckpt = hf_hub_download("jhtyip/cytransformer-frst-models", "chkpt_9+1")
```

```bash
cyt-infer --checkpoint "$ckpt" --polys examples/polytopes.json --num-per-poly 100
```

Every generated 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
(pycddlib) plus a linear program for regularity (SciPy), cross-checked against CYTools on a labeled
set with full agreement.

Input polytopes are `[POLYID, DRESVERTS]` records; see the dataset repository for the format.

## Notes

Generated triangulations are emitted as an unordered set of simplices, so the same FRST can appear
in different simplex orders. **Canonicalise before counting distinct results** — otherwise
duplicates are counted as new triangulations.

## Citation

```bibtex
@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.