AICY

Overview

CYTransformer is a transformer that generates Fine, Regular, Star Triangulations (FRSTs) of 4‑dimensional reflexive polytopes — the combinatorial data behind smooth Calabi-Yau threefolds — and verifies each generated triangulation is a genuine FRST in real time. You can run a trained model, or train your own. It is the reference implementation for arXiv:2507.03732 and the first software component of AICY.

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Install

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

This gives you three commands: cyt-prepare, cyt-train, cyt-infer.

Generate FRSTs (with a trained model)

You need a weights file (e.g. model.pt) and an input polytope file. A small example, examples/polytopes.json, ships with the repo.

cyt-infer --checkpoint model.pt --polys examples/polytopes.json --num-per-poly 100

The model generates candidate triangulations for each polytope and verifies each one as a real FRST on the spot:

FRST validation: 87/100 candidates are FRSTs (87.0%)

It also saves a boolean *_is_frst.npy mask flagging which candidates are genuine FRSTs. The encoding is read from the checkpoint, so you never specify it. (Add --no-validate to skip the FRST check.)

Train your own model

The repo ships ready‑to‑train datasets of favorable reflexive polytopes, already split into train/val/test: datasets/9+1/ (h^1,1 = 5) and datasets/10+1/ (h^1,1 = 6).

1. Train (a GPU is recommended):

cyt-train --config configs/train_9+1.yaml      # or configs/train_10+1.yaml for h11 = 6

2. Watch it learn. The log shows train/val loss and, every monitoring step, the live FRST generation rate — the fraction of the model's generated triangulations that are genuine FRSTs. Checkpoints are written to Checkpoints/<folder>/<exp>/chkpt-<step>.

3. Use the trained model:

cyt-infer --checkpoint Checkpoints/9+1/run/chkpt-399999 --polys examples/polytopes.json

• The shipped configs are the paper‑scale model (~119M params: d_model=512, 16 heads, 16 layers, ~400k steps) and want a GPU. For a quick CPU sanity run, lower model.d_model, model.num_layers and training.n_steps.
• To continue from a checkpoint, set job.continued_training: true.
• To train on your own data, make split files with cyt-prepare and point the job.*_file_* paths at them.

Data generation (optional)

The scripts in generation/ produce polytope data and require a CYTools install:

# Generate FRSTs for any Kreuzer-Skarke polytope:
python generation/fetch_polytopes.py --h11 5 --n 100 --out polys.json
cyt-infer --checkpoint model.pt --polys polys.json

# Build a fresh training dataset:
python generation/make_dataset.py --n_vertices 9 --upper_bound 2000 \
    --folder data_raw --polys_file data_raw/polys.json --triangs_file data_raw/triangs.json

Data format

Plain JSON:

• Polytopes: a list of [POLYID, DRESVERTS], where DRESVERTS is "{{x,y,z,w},{...},...}" of resolved vertices.
• Triangulations: a list of [POLYID, TRIANG], where TRIANG is "{{i,j,k,l,m},...}" of simplex vertex indices.

FRST verification

Every candidate is verified as a genuine FRST by checking it is valid (a true triangulation of the polytope, via pycddlib) and satisfies the Fine, Regular, and Star conditions — Regular being the substantive test (a linear program asking whether a height function exists whose lower hull is exactly this triangulation). These combine in is_frst, whose verdicts match CYTools on a labeled set with full agreement.

Repository layout

cytransformer/        # the model + training/inference + FRST verifier
  models  args  dataset  utilities  inference  train  config  data_prep
  cli/         prepare_data  train  infer
  validation/  frst  regularity  check_valid
datasets/             # ready-to-train data: 9+1 (h11=5), 10+1 (h11=6)
generation/           # optional tools that make polytope data (need CYTools)
configs/  examples/  tests/  dev/

Full details, including how to cite, are on the GitHub repository and the Cite page.