A General Theory of Additive State Space Abstractions
Bibliographic record
Abstract
Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubik's Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)-TopSpin puzzle and by three orders of magnitude over state of the art methods for the 17-Pancake puzzle. We also derive a way of testing if the heuristic value returned by additive abstractions is provably too low and show that the use of this test can reduce search time for the 15-puzzle and TopSpin by roughly a factor of two.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".