jgalego/knot2vec
Feature Extraction • 4.97M • Updated • 186
Datasets:
name stringlengths 3 8 | pd listlengths 3 64 |
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... |
End of preview. Expand in Data Studio
knot2vec-diagrams
Every prime knot up to 13 crossings, with invariants, and about 620,000 diagrams of them tangled by random Reidemeister moves. Built to train and evaluate jgalego/knot2vec. Part of Weird2Vec, embedding models for data nobody embeds.
What is a knot diagram? A knot is a closed loop in space. Drawn on paper it becomes a diagram: a curve with crossings, each marked over or under. The same knot has infinitely many diagrams, related by Reidemeister moves. Here each diagram is a PD code: one list of four edge labels per crossing.
🗂️ Configs
knots
12,965 rows, one per prime knot in KnotInfo, in a single train split.
| Column | Meaning |
|---|---|
name |
KnotInfo name, e.g. 3_1 (trefoil), 11n_34 (Conway knot) |
crossing_number |
Crossings in a minimal diagram |
pd |
KnotInfo's minimal diagram, relabelled the way SnapPy writes PD codes |
braid |
KnotInfo's braid word |
signature |
Knot signature |
determinant |
Knot determinant |
volume |
Hyperbolic volume; 0 for knots that are not hyperbolic, such as torus knots |
seen |
false for the 10% of knots held out of training |
diagrams
| Split | Rows | Contents |
|---|---|---|
train |
571,781 | For each seen knot, its minimal diagram and 48 tangled ones |
test |
51,860 | For every knot, seen or not, 4 tangled diagrams |
Each row has the knot's name and the diagram's pd. Join on name to get the invariants.
🧶 How the diagrams were made
SnapPy's backtrack applies 2–40 random Reidemeister moves, which tend to add crossings; half the time simplify("basic") then tidies the result. Diagrams over 64 crossings are drawn again. The random seed is set per knot, so a rebuild gives the same rows.
🚀 Usage
import snappy
from datasets import load_dataset
knots = load_dataset("jgalego/knot2vec-diagrams", "knots", split="train")
test = load_dataset("jgalego/knot2vec-diagrams", "diagrams", split="test")
print(knots[0])
diagram = test.filter(lambda d: d["name"] == "11n_34")[0]
link = snappy.Link(diagram["pd"])
print(diagram["name"], len(link.crossings), "crossings")
print(link.exterior().identify())
To rebuild a small sample (100 knots) into out/data/:
uv run https://huggingface.co/jgalego/knot2vec/resolve/main/knot2vec.py data --limit 100
📜 Source and license
Knots, minimal diagrams and invariants come from KnotInfo through the database_knotinfo package (GPL-3.0), so this dataset is GPL-3.0 too. Please cite KnotInfo if you use it:
- Livingston, C., & Moore, A. H. (2026). KnotInfo: Table of knot invariants. https://knotinfo.org
- Culler, M., Dunfield, N. M., Goerner, M., & Weeks, J. R. SnapPy, a computer program for studying the geometry and topology of 3-manifolds. https://snappy.computop.org
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Models trained or fine-tuned on jgalego/knot2vec-diagrams