Bibliographic record
Abstract
Crosswords puzzles continue to be a popular form of entertainment. In Artificial Intelligence (AI), crosswords can be represented as a constraint problem, and attacked with a combinatorial search algorithm. In combinatorial search, the branching factor can play a crucial role on the search space size and thus on the search effort. We introduce tiered state expansion, a completeness-preserving technique to reduce the branching factor. In problems where the successors of a state correspond to the values in the domain of a state variable selected for instantiation, the domain is partitioned into two subsets called tiers. The instantiation of the two tiers is performed at different times, with tier 1 first and tier 2 in a subsequent state. Before a tier-2 instantiation occurs, its set of applicable values can shrink substantially due to constraint propagation, with a corresponding reduction of the branching factor. We apply tiered state expansion to a constraint optimization problem modeled on the Romanian Crosswords Competition, empirically demonstrating a substantial improvement. Tiered state expansion allows finding a full solution, with an average CPU time of up to 1.2 minutes, to many puzzles that would otherwise time out after 4 hours.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".