Learning to Slide: Cross-Size Graph Neural Heuristics for Optimal Puzzle Solving
Why this work is in the frame
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Bibliographic record
Abstract
Heuristic techniques such as A* and IDA* with Manhattan distance or linear conflict as heuristics fall short for larger sliding-tile puzzles. This is quite unfortunate as the sliding-tile puzzle is often used as a heuristic search benchmark. We introduce PuzzleGNN, a size-adaptive graph neural network that learns cross-size heuristics for puzzles ranging from 3× 3 to 7 × 7. By encapsulating tiles and adjacencies as graph nodes and edges and embedding the board size into the model, PuzzleGNN functions as a predictor of optimal step counts for puzzles. After being trained on solutions generated by IDA*, PuzzleGNN achieved R2 ≥ 0.85 within its trained range, performing 10 to 30 times faster in inference compared to A*, and excelling on mid-sized boards with a mean absolute error (MAE) of 0.62 on 6 × 6. Nonetheless, while generalizing PuzzleGNN to unseen configurations remains challenging, a promising approach is to fuse neural and admissible heuristics as a means to achieving optimal, scalable search in combinatorial domains.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it