Update README.md

README.md

@@ -12,33 +12,64 @@ tags:
 size_categories:
 - 10K<n<100K
 dataset_summary: >
-  A graph-based dataset of the first 10,000 Metamath proofs, including
-  CodeBERT node embeddings, DAG structure, 3,358 labels after rare-label
-  collapsing, conclusion masking, and fixed train/val/test splits.
+  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 hosts a single PyTorch Geometric dataset file used for the TAG-DS TopoBench challenge.
+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 database.
 
 ## Contents
 
 - **`data.pt`**  
-  A preprocessed graph dataset containing:
-  - `data` — collated PyG `Data` object storing all node features, edges, and labels  
-  - `slices` — indexing information for reconstructing individual graphs  
+  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 Summary
+---
+
+## 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  
 
-- Contains the **first 10,000 proofs** from the ~45,000-theorem Metamath database  
-- Each example is a **directed acyclic graph** (DAG)  
-- **Node features:** 768-dimensional CodeBERT embeddings of Metamath statements  
-- **Labels:** the theorem required to justify each node (axioms and assumptions share a fixed label); there are 3,557 distinct labels after collapsing rare ones (<=5 occurrences in train set) into UNK
-- **Conclusion masking:** the conclusion node’s embedding is zeroed out so the model must predict the final logical step directly from the graph structure and the other nodes  
-- **All theorem statements** (not just proofs) are included in training, since the model must treat theorems themselves as prior knowledge  
-- Under the Metamath proof language, any theorem used to justify a step always has an index <= the theorem being proved. So a later theorem never appears in an earlier proof
+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