brozonoyer/gram-graph-coloring

GRAM Graph Coloring Dataset

A replication of the Graph Coloring dataset from Generative Recursive Reasoning Models (GRAM) (Baek et al., ICLR 2026 Workshop on AI with Recursive Self-Improvement), Appendix E.1.2.

Repository: Generate, Verify, Upload

# Setup
python -m venv venv-graph-coloring && source venv-graph-coloring/bin/activate  # or: venv-graph-coloring\Scripts\activate on Windows
pip install -r requirements.txt

# Generate (use salloc for parallel: salloc --cpus-per-task=16 --mem=8G --time=2:00:00)
python generate_dataset.py -o gram_graphcoloring_dataset.json

# Verify
python verify_dataset.py gram_graphcoloring_dataset.json

# Upload to HuggingFace (after: hf auth login)
python upload_to_hub.py gram_graphcoloring_dataset.json brozonoyer/gram-graph-coloring

Dataset Summary

This is the 3-coloring variant of the Graph Coloring problem: given a graph, assign one of 3 colors to each node so that no two adjacent nodes share the same color. The dataset is designed for evaluating recursive reasoning models on constraint satisfaction tasks with multiple valid solutions.

Split	8-vertex	10-vertex	Total
Train	7,002	13,465	20,467
Test	255	192	447
Total	7,257	13,657	20,914

Dataset Description

Generation Procedure

1. Generate graphs using the Erdős–Rényi random graph model (GNN-GCP pipeline, Lemos et al., 2019)
2. Retain only 3-colorable graphs
3. Enumerate all valid 3-colorings and retain only canonical forms (eliminate redundancy under color permutation)
4. The adjacency matrix (upper triangle) is the input
5. One canonical coloring is the target label

Parameters (per GRAM Appendix E.1.2)

Graph Size	Edge Probability (p)
8 vertices	0.4 (default)
10 vertices	0.35 (default)

Data Format

• Input: Upper triangle of adjacency matrix (excluding diagonal), flattened; length = n(n-1)/2
• Output: Sequence of length n, each position = color for node
• Vocabulary: 0 = pad, 1 = no edge, 2 = edge; colors 3, 4, 5 for red, blue, green
• Split: By unique input graph (no data leakage)

Data Fields

Field	Type	Description
input	list[int]	Flattened upper triangle (length n(n-1)/2), values in {1, 2}
target	list[int]	Valid 3-coloring (length n), values in {3, 4, 5}
n	int	Number of vertices (8 or 10)
num_solutions	int	Count of canonical valid colorings for this graph
instance_id	str	Hash of input (for deduplication)
split	str	"train" or "test"
config	str	"8-vertex" or "10-vertex"

Uses

Direct Use

• Training and evaluating recursive reasoning models (e.g., GRAM, HRM, TRM)
• Benchmarking constraint satisfaction and multi-solution reasoning
• Research on latent-space reasoning and generative recursion

Out-of-Scope Use

• Not intended for k-coloring with k ≠ 3
• Not suitable for tasks requiring natural language input/output

Dataset Structure

The dataset contains two splits (train, test) with instances from both 8-vertex and 10-vertex graphs. Each instance has a unique instance_id; the split ensures no input pattern appears in both train and test.

Loading the Dataset

from datasets import load_dataset

# Load full dataset (train + test)
dataset = load_dataset("brozonoyer/gram-graph-coloring")

# Access splits
train = dataset["train"]
test = dataset["test"]

# Filter by graph size
train_8 = train.filter(lambda x: x["config"] == "8-vertex")
train_10 = train.filter(lambda x: x["config"] == "10-vertex")

# Example instance
example = train[0]
print("Input length:", len(example["input"]))  # 28 for 8-vertex, 45 for 10-vertex
print("Target length:", len(example["target"]))  # 8 or 10
print("Num solutions:", example["num_solutions"])

Note: The GRAM model prepends 16 puzzle embedding tokens at training time. This dataset stores only the raw graph; add those tokens when training GRAM-compatible models.

Dataset Creation

• Curation rationale: Exact replication of GRAM Appendix E.1.2 for reproducibility
• Generation: Erdős–Rényi graphs, 3-colorability check, backtracking enumeration, canonicalization
• Split: Fixed target sizes (7,002/255 for 8-vertex, 13,465/192 for 10-vertex) with seed 42

Citation

BibTeX:

@inproceedings{baek2026gram,
  title={Generative Recursive Reasoning Models},
  author={Baek, Junyeob and Jo, Mingyu and Kim, Minsu and Bengio, Yoshua and Ahn, Sungjin},
  booktitle={ICLR 2026 Workshop on AI with Recursive Self-Improvement},
  year={2026}
}

Paper: OpenReview

License

CC-BY-4.0 (matching the GRAM paper)