| --- |
| license: mit |
| pretty_name: Metamath Proof Graphs (10k) |
| task_categories: |
| - graph-ml |
| tags: |
| - graphs |
| - gnn |
| - metamath |
| - pytorch-geometric |
| - topobench |
| size_categories: |
| - 10K<n<100K |
| dataset_summary: > |
| A graph-based dataset of 10,000 Metamath theorems and their 10,000 |
| corresponding proof DAGs, including CodeBERT node embeddings, |
| conclusion masking, rare-label collapsing, and fixed train/val/test splits. |
| --- |
| |
| # Metamath Proof Graphs (10k) |
|
|
| This repository provides a PyTorch Geometric dataset designed for the TAG-DS TopoBench challenge. |
| It contains **20,000 graphs total:** 10,000 theorem-only DAGs and 10,000 full proof DAGs drawn from the first 10k theorems in the Metamath [1] database. |
|
|
| ## Contents |
|
|
| - **`data.pt`** |
| A preprocessed PyG dataset containing: |
| - `data` — global collated storage of all nodes, edges, and labels |
| - `slices` — pointers for reconstructing individual graphs |
| - `train_idx`, `val_idx`, `test_idx` — fixed graph-level splits |
|
|
| --- |
|
|
| ## Dataset Structure |
|
|
| ### **1. Theorem Graphs (indices 0–9,999)** |
| Each theorem is represented as a small DAG consisting only of: |
| - its hypothesis nodes |
| - its conclusion node |
| - **no proof steps** |
|
|
| These encode the *statement only*, not the derivation. |
|
|
| ### **2. Proof Graphs (indices 10,000–19,999)** |
| For each of the same theorems, the full proof DAG is included, containing: |
| - hypothesis nodes |
| - intermediate proof steps |
| - the same conclusion node |
|
|
| Thus each theorem appears **twice**: |
| 1. once as a theorem-only graph |
| 2. once as the complete proof of that theorem |
|
|
| This pairing enables: |
| - learning from theorem statements |
| - evaluating on masked proof conclusions |
| - consistent label space across both halves |
|
|
| --- |
|
|
| ## Additional Details |
|
|
| - Total graphs: **20,000** |
| - Node embeddings: **768-dimensional CodeBERT** vectors |
| - Graph type: **directed acyclic graphs (DAGs)** |
| - Label space: **3,557 justification labels**, where all labels with <5 training occurrences are collapsed into `UNK` |
| - **Conclusion masking:** the conclusion node’s embedding is zeroed out; the model must infer its label from the structure and other nodes |
| - **Monotonicity constraint:** in Metamath, proofs only use theorems with index <= the current theorem, so later theorems never appear in earlier graphs |
| - Theorem-only graphs are included in training as prior knowledge for downstream proof prediction. |
|
|
| --- |
|
|
| ## Basic Usage |
|
|
| ```python |
| import torch |
| |
| obj = torch.load("data.pt", weights_only=False) |
| |
| data = obj["data"] |
| slices = obj["slices"] |
| train_idx = obj["train_idx"] |
| val_idx = obj["val_idx"] |
| test_idx = obj["test_idx"] |
| ``` |
|
|
| --- |
|
|
| ## Acknowledgements |
|
|
| Thanks to the Erdős Institute for providing the project-based, collaborative |
| environment where key components of the preprocessing pipeline were first |
| developed. |
|
|
| --- |
|
|
| ## References |
| [1] Metamath Official Site — <https://us.metamath.org/index.html> |
|
|
