max-rl/maze_17x17_diverse_1.3m

17x17 Maze with Diverse Paths (1.3M, 16 paths/maze)

This is v2 of the 17x17 maze SFT corpus used in the MaxRL paper. It is designed to make judge_maze_continuous non-trivially different from the binary reward by ensuring path lengths span a wide range per maze, instead of always being shortest.

Why a v2 dataset?

In the original guanning-ai/maze_17x17_1m, every training trajectory is the BFS-shortest path through a perfect Prim-generated maze. As a result, training under a binary "did you reach the goal?" reward already produces near-optimal trajectories, and the continuous reward R = max(0, (UB-L)/(UB-L*)) ends up essentially redundant. We confirmed this empirically: the two rewards yielded nearly identical RL outcomes.

This release fixes that by:

1. Knocking out walls. Every maze starts as a perfect Prim maze and then has K ∈ [5%, 30%] of its inter-cell walls knocked out (uniformly at random per maze). Loops appear, so a single maze admits many distinct simple paths from start to goal.
2. Stratified path harvesting. Per maze we DFS for simple paths of length < UB = 60, with goal-distance pruning. Paths are bucketed by length, kept via reservoir sampling (so the 4 paths per length-bucket are an unbiased uniform sample, not just whatever DFS happened to find first).
3. Diversity-aware selection. From the harvest pool we pick N = 16 paths that (i) are spread across reward R ∈ (0, 1] and (ii) minimize cell-overlap (greedy farthest-point in cell-set space). The 16 paths cover different regions of the maze.

The result is a global continuous-reward distribution that is approximately uniform on (0, 1], and per-prompt reward variance that is non-negligible.

Dataset summary statistics

• Mazes: 1,299,992 kept / 1,300,000 attempted
• SFT-style (path, prompt) pairs: 19,914,711 of target 20,800,000
• Average paths per maze: 15.32 (target 16)
• L* (BFS optimal): min=28, mean=28.3, max=48
• Path length L: min=28, mean=43.6, max=58
• Continuous reward: mean=0.518, std=0.283 (uniform on (0,1] would give ≈0.5 / 0.289 — close match)
• Reward fraction at 0: 0.000; at 1: 0.054
• Per-prompt reward std: median=0.282, mean=0.249
• Per-prompt reward range (max - min): median=0.875

Format

Maze grid: 17×17, walls = 1, paths = 0. Start fixed at (1, 1), goal at (15, 15). Token vocabulary follows the original maze SFT pipeline:

<bos> GRID_START <grid tokens> GRID_END PATH_START <action tokens> DONE <eos>

where grid tokens are WALL, PATH, START, GOAL, NEWLINE and action tokens are UP, DOWN, LEFT, RIGHT. The continuous reward used for both filtering and downstream RL evaluation is

R(L, L*) = max(0, (UB - L) / (UB - L*))   with UB = 60.

Files

File	Rows	Description
main_1.3M.jsonl	1,299,992	Raw build output, 16 paths per maze, full metadata.
train_random.json	1,299,736	SFT-ready, 1 randomly-chosen path per maze.
train_shortest.json	1,299,736	SFT-ready, the lowest-L (≈shortest) path per maze.
test.json	256	256 held-out mazes, shortest path as ground truth.

train_random.json and train_shortest.json use the same 1.3M-256 prompts in the same row order (just with different per-prompt path picks), so SFT runs on the two files with the same seed see prompts in the same order — making them a clean apples-to-apples comparison of "diverse paths" vs "shortest only".

Schema

*.json files (SFT format):

{
  "sequence": "<bos> GRID_START WALL ... GRID_END PATH_START UP DOWN ... DONE <eos>",
  "optimal_path_length": 28,            // BFS shortest L*
  "path_length": 30,                    // L of the path in this row
  "reward_continuous": 0.938,           // (UB - L) / (UB - L*)
  "prompt_id": 12345,                   // unique maze id (== seed)
  "sample_id": 0,                       // index within the maze's 16 paths
  "ub": 60,                             // UB used for reward
  "k_frac": 0.21                        // wall-knockout fraction for this maze
}

main_1.3M.jsonl (one prompt per line, contains all 16 paths):

{
  "prompt_id": 0,
  "grid": [[1,1,1,...], ...],           // 17×17 ints, 1 = wall
  "L_star": 28,
  "k_frac": 0.21,
  "n_knockouts": 11,
  "ub": 60,
  "n_samples": 16,
  "harvest_pool_size": 56,
  "L_std": 9.13,
  "L_min": 28, "L_max": 58,
  "samples": [
    { "sample_id": 0, "L": 30, "reward_continuous": 0.938, "actions": [0,1,2,...] },
    ...
  ]
}

Action ids: 0 = UP, 1 = DOWN, 2 = LEFT, 3 = RIGHT.

Reproducing

The build, conversion, and SFT runs that produced this release live in the maze_v2/ directory of stablegradients/GOS-17X17-Maze:

# Build the raw dataset (~2h on 128 CPU workers).
python maze_v2/src/build_dataset.py \
  --m 1300000 --n 16 --ub 60 --workers 128 \
  --out maze_v2/out/main_1.3M.jsonl

# Split + convert to SFT JSON.
python maze_v2/src/to_sft_json.py \
  --in_path  maze_v2/out/main_1.3M.jsonl \
  --out_train maze_v2/out/sft_data/train_random.json \
  --out_test  maze_v2/out/sft_data/test.json \
  --test_prompts 256 --mode random --seed 0

python maze_v2/src/to_sft_json.py \
  --in_path  maze_v2/out/main_1.3M.jsonl \
  --out_train maze_v2/out/sft_data/train_shortest.json \
  --out_test  maze_v2/out/sft_data/test.json \
  --test_prompts 256 --mode shortest --seed 0

Citation

@misc{tajwar2026maximumlikelihoodreinforcementlearning,
  title={Maximum Likelihood Reinforcement Learning},
  author={Tajwar, Fahim and Zeng, Guanning and Zhou, Yueer and Song, Yuda and Arora, Daman and Jiang, Yiding and Schneider, Jeff and Salakhutdinov, Ruslan and Feng, Haiwen and Zanette, Andrea},
  year={2026},
  eprint={2602.02710},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2602.02710}
}