Automatically generated lower bounds for search
Why this work is in the frame
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Bibliographic record
Abstract
Heuristic search algorithms (eg. A* and IDA*) with accurate lower bounds can solve impressively large problems optimally. Most lower bounds, such as the well known Manhattan Distance heuristic for the sliding-tile puzzles or the Assignment Problem lower bound for the Asymmetric Traveling Salesman problem, are the products of human ingenuity and insight. An alternative approach to obtain lower bounds is to precalculate shortest distances in an abstraction of the original search space which is derived automatically and store the bounds in pattern databases (look-up tables). This latter technique, based on the ideas of Culberson and Schaeffer, gained popularity when Korf for the first time solved random instances of Rubik's Cube using pattern databases. While researchers were pushing for solving larger and larger problems, the fact that there exist a very large number of abstract spaces that can provide lower bounds was overlooked. This thesis fills this gap in research by investigating the search performance of lower bounds derived from abstractions. We also use the results of this analysis to automatically derive high performance pattern databases. First, we establish a very predictable trade-off between search speed and the number of entries in the pattern database. Second, we derive simple statistics that can predict the search performance of pattern databases without performing actual searches in the original state space. Using these results, we derive high performance pattern databases to search for macro-operators and to solve challenging instances of the well known Sequential Ordering Problem (SOP). Macro-search is a good candidate to showcase automatically derived lower bounds since there are many search spaces and each needs a different lower bound. The SOP is an NP-hard optimization problem. We were able to solve an unsolved instance from the TSPLIB. This required a greedy search in the space of abstractions to find a sufficiently accurate lower bound and several novel enhancements to the basic branch and bound algorithm.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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