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README.md

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----
-license: mit
----
+---
+license: mit
+language:
+- en
+pretty_name: Metamath Proof Graphs
+size_categories:
+- 10K<n<100K
+task_categories:
+- graph-ml
+tags:
+- graphs
+- gnn
+- theorem-proving
+- reasoning
+- metamath
+- pytorch-geometric
+---
+
+# Metamath Proof Graphs
+
+Graph-structured representations of Metamath theorem proofs designed for reasoning-focused Graph Neural Networks.  
+Each example contains node features, directed edges, and theorem labels suitable for proof-step prediction and symbolic reasoning research.
+
+## Dataset Summary
+
+This dataset converts Metamath’s human-verified formal proofs into directed graphs:
+
+- **Nodes** represent logical statements (proof steps or hypotheses)
+- **Edges** represent inference dependencies
+- **Node features** are 512-dimensional Universal Sentence Encoder embeddings
+- **Labels** represent the proven theorem, normalized into a compact integer space
+
+Ideal for research on GNN-based symbolic reasoning, proof-step prediction, and theorem classification.
+
+## Dataset Structure
+
+Each proof instance includes:
+
+- **Proof Graph** — logical inference steps represented as a directed graph  
+- **Statement Graph** — hypotheses and conclusion as a compact graph  
+- **Node Features** — 512-dimensional USE embeddings  
+- **Label** — integer id for the target theorem (with UNK handling below)
+
+## Label Normalization (UNK)
+
+To reduce extreme class imbalance:
+
+- Labels appearing **five times or fewer** are mapped to a single `UNK` class  
+- Remaining labels are reindexed into a **dense, contiguous integer space**  
+- A reverse mapping is provided for converting predictions back to theorem names
+
+## Label Mapping
+
+Each theorem label is mapped to an integer via a fixed index derived from the Metamath label list.  
+A reverse index is included for interpretability.
+
+## Node Embeddings
+
+Node representations use **Universal Sentence Encoder (USE v4)**:
+
+- 512-dimensional embeddings  
+- Computed once during preprocessing  
+- Applied to both proof-step nodes and statement-graph nodes  
+
+## Data Splits
+
+A fixed-seed 80/10/10 split is used in reference experiments:
+
+| Split | Examples |
+|-------|----------|
+| Train | ~8,000 |
+| Validation | ~1,000 |
+| Test | ~1,000 |
+
+## Dataset Size (approx.)
+
+- **10,000** proof graphs  
+- **50–200** nodes per graph  
+- **512-dimensional** node features  
+- **~829** normalized labels (including `UNK`)  
+
+## Example Data Structure
+
+```json
+{
+  "x": [...],           // Node features [num_nodes, 512]
+  "edge_index": [...],  // Directed edges (COO format)
+  "graph_features": [...],
+  "label": 42
+}
+```
+
+## Intended Use
+
+Designed for:
+
+- Proof-step prediction  
+- Symbolic reasoning research  
+- Theorem classification tasks  
+- Benchmarking GNN architectures (GIN, GAT, Graph Transformers)
+
+Not intended for:
+
+- End-to-end automated theorem proving  
+- Non-graph ML tasks without graph conversion  
+
+## Usage
+
+### Hugging Face Datasets
+
+```python
+from datasets import load_dataset
+ds = load_dataset("jableable/metamath-proof-graphs")
+sample = ds["train"][0]
+```
+
+### PyTorch Geometric (loader included)
+
+```python
+from proofgraphs import ProofDataset
+dataset = ProofDataset(root="data/")
+```
+
+## Limitations
+
+- USE embeddings are fixed; domain-specific encoders may yield better performance  
+- Some theorem classes remain imbalanced even after `UNK` grouping  
+- The dataset targets step-level reasoning, not full theorem proving  
+- Logical structure is encoded via graph topology + text embeddings, not explicit grammar
+
+## Baseline Performance
+
+**Reference GNN (GIN, 3 layers):**
+- **Top-5 Accuracy:** 70 percent  
+- (Link to training code to be added)
+
+## Dataset Creation
+
+### Source
+
+Derived from the public-domain **Metamath** proof database.  
+Graph extraction, embedding generation, normalization, and preprocessing were performed by the dataset author.
+
+### Preprocessing (brief)
+
+1. Convert proofs to directed graphs  
+2. Generate USE embeddings for each node  
+3. Normalize labels and collapse rare ones into `UNK`  
+4. Reindex labels contiguously  
+5. Generate fixed-seed train/val/test splits  
+
+Scripts are provided in the repository.
+
+### Acknowledgments
+
+This dataset builds on earlier code and extraction work developed in collaboration with Hongyi Shen and Evgeniya Lagoda.  
+Their contributions to the initial graph-processing pipeline informed the final dataset.  
+All packaging, normalization, and Hugging Face dataset preparation were performed by the dataset author.
+
+## Citation
+
+If you use this dataset, please cite:
+
+```bibtex
+@misc{able2025proofgraphs,
+  author       = {Able, Jared},
+  title        = {Metamath Proof Graphs Dataset},
+  year         = {2025},
+  publisher    = {Hugging Face},
+  howpublished = {\url{https://huggingface.co/datasets/jableable/metamath-proof-graphs}}
+}
+```
+
+## Contact
+
+For questions or issues, please open an issue on the GitHub repo.