| --- |
| 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/). |
|
|
