cytransformer-frst-models

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), and the first released weights for AICY.

Code: github.com/jhtyip/cytransformer · Data: 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.

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

Naming. N_vert 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_vert = 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

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

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

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

@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.