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license: mit
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- en
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pretty_name: Metamath Proof Graphs
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size_categories:
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- 10K<n<100K
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task_categories:
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- graph-ml
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tags:
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- graphs
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- gnn
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- theorem-proving
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- reasoning
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- metamath
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- pytorch-geometric
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- split: train
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path: data/train-*
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- split: validation
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path: data/validation-*
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- split: test
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path: data/test-*
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- config_name: raw
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data_files:
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- split: train
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path: raw/train-*
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- split: validation
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path: raw/validation-*
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- split: test
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path: raw/test-*
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dataset_info:
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- config_name: default
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features:
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- name: theorem_index
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dtype: int64
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- name: theorem_label
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dtype: string
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- name: graph_type
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dtype: string
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- name: nodes
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list:
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- name: label
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dtype: string
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- name: node_index
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dtype: int64
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- name: num
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dtype: int64
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- name: statement
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dtype: string
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- name: edge_index
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list:
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list: int64
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- name: edge_attr
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list:
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list: int64
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splits:
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- name: train
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num_bytes: 496594530
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num_examples: 76489
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- name: validation
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num_bytes: 27586060
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num_examples: 4249
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- name: test
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num_bytes: 27592552
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num_examples: 4250
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download_size: 92724290
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dataset_size: 551773142
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- config_name: raw
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features:
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- name: theorem_index
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dtype: int64
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- name: theorem_label
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dtype: string
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- name: graph_type
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dtype: string
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- name: nodes
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list:
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- name: label
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dtype: string
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- name: node_index
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dtype: int64
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- name: num
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dtype: int64
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- name: statement
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dtype: string
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- name: edge_index
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list:
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list: int64
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- name: edge_attr
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list:
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list: int64
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splits:
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- name: train
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num_bytes: 496594530
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num_examples: 76489
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- name: validation
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num_bytes: 27586060
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num_examples: 4249
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- name: test
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num_bytes: 27592552
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num_examples: 4250
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download_size: 92724290
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dataset_size: 551773142
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---
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# Metamath Proof Graphs
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Graph-structured representations of Metamath theorem proofs designed for reasoning-focused Graph Neural Networks.
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Each example contains node features, directed edges, and theorem labels suitable for proof-step prediction and symbolic reasoning research.
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## Dataset Summary
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This dataset converts Metamath’s human-verified formal proofs into directed graphs:
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- **Nodes** represent logical statements (proof steps or hypotheses)
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- **Edges** represent inference dependencies
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- **Node features** are 512-dimensional Universal Sentence Encoder embeddings
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- **Labels** represent the proven theorem, normalized into a compact integer space
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Ideal for research on GNN-based symbolic reasoning, proof-step prediction, and theorem classification.
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## Dataset Structure
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Each proof instance includes:
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- **Proof Graph** — logical inference steps represented as a directed graph
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- **Statement Graph** — hypotheses and conclusion as a compact graph
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- **Node Features** — 512-dimensional USE embeddings
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- **Label** — integer id for the target theorem (with UNK handling below)
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## Label Normalization (UNK)
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To reduce extreme class imbalance:
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- Labels appearing **five times or fewer** are mapped to a single `UNK` class
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- Remaining labels are reindexed into a **dense, contiguous integer space**
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- A reverse mapping is provided for converting predictions back to theorem names
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## Label Mapping
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Each theorem label is mapped to an integer via a fixed index derived from the Metamath label list.
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A reverse index is included for interpretability.
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## Node Embeddings
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Node representations use **Universal Sentence Encoder (USE v4)**:
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- 512-dimensional embeddings
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- Computed once during preprocessing
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- Applied to both proof-step nodes and statement-graph nodes
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## Data Splits
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A fixed-seed 80/10/10 split is used in reference experiments:
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| Split | Examples |
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|-------|----------|
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| Train | ~8,000 |
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| Validation | ~1,000 |
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| Test | ~1,000 |
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## Dataset Size (approx.)
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- **50–200** nodes per graph
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- **512-dimensional** node features
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- **~829** normalized labels (including `UNK`)
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##
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```
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##
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Designed for:
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- Proof-step prediction
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- Symbolic reasoning research
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- Theorem classification tasks
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- Benchmarking GNN architectures (GIN, GAT, Graph Transformers)
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Not intended for:
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- End-to-end automated theorem proving
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- Non-graph ML tasks without graph conversion
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## Usage
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### Hugging Face Datasets
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```python
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ds = load_dataset("jableable/metamath-proof-graphs")
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sample = ds["train"][0]
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```
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### PyTorch Geometric (loader included)
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```python
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from proofgraphs import ProofDataset
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dataset = ProofDataset(root="data/")
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```
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## Limitations
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- USE embeddings are fixed; domain-specific encoders may yield better performance
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- Some theorem classes remain imbalanced even after `UNK` grouping
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- The dataset targets step-level reasoning, not full theorem proving
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- Logical structure is encoded via graph topology + text embeddings, not explicit grammar
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## Baseline Performance
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**Reference GNN (GIN, 3 layers):**
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- **Top-5 Accuracy:** 70 percent
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- (Link to training code to be added)
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## Dataset Creation
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### Source
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Derived from the public-domain **Metamath** proof database.
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Graph extraction, embedding generation, normalization, and preprocessing were performed by the dataset author.
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### Preprocessing (brief)
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1. Convert proofs to directed graphs
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2. Generate USE embeddings for each node
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3. Normalize labels and collapse rare ones into `UNK`
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4. Reindex labels contiguously
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5. Generate fixed-seed train/val/test splits
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Scripts are provided in the repository.
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### Acknowledgments
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This dataset builds on earlier code and extraction work developed in collaboration with Hongyi Shen and Evgeniya Lagoda.
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Their contributions to the initial graph-processing pipeline informed the final dataset.
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All packaging, normalization, and Hugging Face dataset preparation were performed by the dataset author.
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## Citation
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If you use this dataset, please cite:
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```bibtex
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@misc{able2025proofgraphs,
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author = {Able, Jared},
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title = {Metamath Proof Graphs Dataset},
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year = {2025},
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publisher = {Hugging Face},
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howpublished = {\url{https://huggingface.co/datasets/jableable/metamath-proof-graphs}}
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}
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```
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---
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license: mit
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pretty_name: Metamath Proof Graphs (10k)
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task_categories:
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- graph-ml
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tags:
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- graphs
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- gnn
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- metamath
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- pytorch-geometric
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- topobench
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size_categories:
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- 10K<n<100K
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---
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# Metamath Proof Graphs (10k)
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This repository hosts a single PyTorch Geometric dataset file used for the TAG-DS TopoBench challenge.
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## Contents
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- `data.pt`
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A serialized object with the following keys:
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- `data` (PyG `Data` object with collated node features, edges and labels)
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- `slices` (index information for reconstructing individual graphs)
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- `train_idx` (tensor of graph indices for training)
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- `val_idx` (tensor of graph indices for validation)
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- `test_idx` (tensor of graph indices for testing)
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## Basic usage
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```python
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import torch
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obj = torch.load("data.pt", weights_only=False)
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data = obj["data"]
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slices = obj["slices"]
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train_idx = obj["train_idx"]
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val_idx = obj["val_idx"]
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test_idx = obj["test_idx"]
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