Korf's Conjecture and the Future of Abstraction-Based Heuristics
Why this work is in the frame
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Bibliographic record
Abstract
In his 1997 paper on solving Rubik’s Cube optimally using IDA * and pattern database heuristics (PDBs), Rich Korf conjectured that there was an inverse relationship between the size of a PDB and the amount of time required for IDA * to solve a problem instance on average. In the current paper, I examine the implications of this relationship, in particular how it limits the ability of abstraction-based heuristic methods, such as PDBs, to scale to larger problems. My overall conclusion is that abstraction will play an important, but auxiliary role in heuristic search systems of the future, in contrast to the primary role it played in Korf’s Rubik’s Cube work and in much work since. m 1+log(m)
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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 | 0.000 | 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 | 0.000 |
| 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 it