brozonoyer/gram-n-queens

GRAM N-Queens Dataset

A replication of the N-Queens dataset from Generative Recursive Reasoning Models (GRAM) (Baek et al., ICLR 2026 Workshop on AI with Recursive Self-Improvement), Appendix E.1.1.

Dataset Summary

This is a partial-completion variant of the N-Queens problem: given a chessboard with some queens already placed, complete the configuration so that no two queens attack each other. The dataset is designed for evaluating recursive reasoning models on constraint satisfaction tasks with multiple valid solutions.

Split	8×8	10×10	Total
Train	4,375	36,907	41,282
Test	773	6,513	7,286
Total	5,148	43,420	48,568

Dataset Description

Generation Procedure

1. Start from a complete valid N-Queens solution
2. Remove k queens from the board
3. The remaining partial configuration is the input
4. The original complete board is the target label

Parameters (per GRAM Appendix E.1.1)

Board Size	Queens Removed (k)
8×8	5, 6, 7
10×10	7, 8, 9

Data Format

• Input/Output: N×N board flattened row-major into a 1D sequence of length N²
• Vocabulary: 0 = pad, 1 = empty cell, 2 = queen
• Split: 85% train / 15% test by unique input configuration (no data leakage)

Data Fields

Field	Type	Description
input	list[int]	Partial board (length N²), values in {0, 1, 2}
target	list[int]	Complete solution, same format
n	int	Board size (8 or 10)
k_removed	int	Number of queens removed (5–7 or 7–9)
num_solutions	int	Count of valid completions for this partial
instance_id	str	Hash of input (for deduplication)
split	str	"train" or "test"
config	str	"8x8" or "10x10"

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 standard (empty-board) N-Queens solving
• Not suitable for tasks requiring natural language input/output

Dataset Structure

The dataset contains two splits (train, test) with instances from both 8×8 and 10×10 boards. 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-n-queens")

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

# Filter by board size
train_8x8 = train.filter(lambda x: x["config"] == "8x8")
train_10x10 = train.filter(lambda x: x["config"] == "10x10")

# Example instance
example = train[0]
print("Input shape:", len(example["input"]))  # 64 for 8×8, 100 for 10×10
print("Num solutions:", example["num_solutions"])

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

Dataset Creation

• Curation rationale: Exact replication of GRAM Appendix E.1.1 for reproducibility
• Generation: Backtracking enumeration of N-Queens solutions, partial removal, completion counting
• Split: 85:15 by unique input with fixed seed (42) for reproducibility

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)