---
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>