---
license: cc-by-4.0
task_categories:
  - graph-ml
tags:
  - physics
  - high-energy-physics
  - graph-classification
  - gnn
pretty_name: Graphical Bootstrap Correlator Dataset
size_categories:
  - 100G<n<1T
---

# Graphical Bootstrap Correlator Dataset

This dataset contains large-scale graph-structured data arising from high-order perturbative computations of four-point correlators in planar $\mathcal{N}=4$ super Yang--Mills theory.

The data consists of **denominator graphs (d-graphs)** appearing in the graphical bootstrap formulation of correlators. Each graph is associated with a **binary label** indicating whether it contributes to the correlator at a given perturbative order.

The dataset is designed for **graph classification tasks**, with a focus on generalization across graph sizes and enabling machine learning–assisted reduction of the bootstrap ansatz.

## Scientific Context

In the graphical bootstrap approach, the correlator is expanded over a large set of combinatorial graphs. At high perturbative orders, this set becomes extremely redundant: the vast majority of graphs have vanishing coefficients.

This dataset encodes the binary classification problem:
\[
d_a^{(n)} =
\begin{cases}
0 & \text{if all associated coefficients vanish} \\
1 & \text{otherwise}
\end{cases}
\]

The graph data is derived from:

> Bourjaily et al., *"The 12-loop four-point correlator in planar $\mathcal{N}=4$ SYM"*  
> https://arxiv.org/abs/2503.15593


## Dataset Structure

```
graphical-bootstrap-correlator-dataset/
├── data/
│   ├── den_graph_data_6.npz
│   ├── den_graph_data_7.npz
│   ├── den_graph_data_8.npz
│   ├── den_graph_data_9.npz
│   ├── den_graph_data_10.npz
│   ├── den_graph_data_11.npz
│   ├── den_graph_data_12.npz
│   ├── den_graph_data_12_1.npz
│   │   ...
│   ├── den_graph_data_12_20.npz
│   ├── features_loop_6/
│   ├── features_loop_7/
│   ├── features_loop_8/
│   ├── features_loop_9/
│   ├── features_loop_10/
│   ├── features_loop_11/
│   └── features_loop_12/
├── embeddings/
├── models/
└── rung_rule/
```

Each `den_graph_data_N.npz` file contains all denominator graphs at loop order $N$, together with their binary labels.

For loop 12, both full datasets and split files are provided due to size constraints.

To match the embeddings and model prediction files, the splits den_graph_data_12_1.npz–den_graph_data_12_20.npz must be concatenated in lexicographic (string) order rather than numerical order (e.g. den_graph_data_12_1.npz, den_graph_data_12_10.npz, …).

## Data Format

### Graph data (`.npz` files)

Each `.npz` file stores graph connectivity and labels:

```python
import numpy as np

data = np.load("data/den_graph_data_10.npz", allow_pickle=True)
```

Typical contents include:
- edge indices / adjacency representation
- graph-level labels

Labels are binary:
- `0`: non-contributing graph  
- `1`: contributing graph  

### Pre-computed node features (`features_loop_N/`)

Pre-computed node features are provided for all loop orders (6–12) to facilitate training of GNN models.

| Category   | Features                                                            |
|------------|---------------------------------------------------------------------|
| Spectral   | `eigen_1`–`eigen_3`, `low_eigen_1`–`low_eigen_3`                   |
| Structural | `degree`, `closeness`, `betweenness`, `clustering`, `pagerank`      |
| Graphlet   | `graphlet_3`, `graphlet_4`                                          |
| Distance   | `spd` (shortest-path distances)                                     |



## Models

The `models/` directory contains trained Graph Neural Networks, including:
- GIN (Graph Isomorphism Network)
- GAT (Graph Attention Network)
- Graph Transformer variants

These models are trained to generalize across graph sizes (e.g. $n \rightarrow n+1$).

## Rung Rule Analysis

The `rung_rule/` directory contains data used to study the **rung rule**, a graphical relation linking subsets of contributing graphs across perturbative orders.

## Embeddings

The `embeddings/` directory contains learned graph representations extracted from trained models. These can be used for downstream analysis, such as probing structural information captured by the models.

## License

This dataset is released under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).