|
|
--- |
|
|
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> |
|
|
|
