Problem Difficulty and the Phase Transition in Heuristic Search
Why this work is in the frame
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Bibliographic record
Abstract
In the recent years, there has been significant work on the difficulty of heuristic search problems, identifying different problem instance characteristics that can have a significant impact on search effort. Phase transitions in the solubility of random problem instances have proved useful in the study of problem difficulty for other classes of computational problems, notably SAT and CSP, and it has been shown that the hardest problems typically occur during this rapid transition. In this work, we perform the first empirical investigation of the phase transition phenomena for heuristic search. We establish the existence of a rapid transition in the solubility of an abstract model of heuristic search problems and show that, for greedy best first search, the hardest instances are associated with the phase transition region. We then perform a novel investigation of the behavior of heuristics of different strength across the solubility spectrum. Finally, we demonstrate that the behavior of our abstract model carries over to commonly used benchmark problems including the Pancake Problem, Grid Navigation, TopSpin, and the Towers of Hanoi. An interesting deviation is observed and explained in the Sliding Puzzle.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.003 | 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 it