LM-cut and Operator Counting Heuristics for Optimal Numeric Planning with Simple Conditions
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Bibliographic record
Abstract
We consider optimal numeric planning with numeric conditions consisting of linear expressions of numeric state variables and actions that increase or decrease numeric state variables by constant quantities. We build on previous research to introduce a new variant of the numeric hmax heuristic based on the delete-relaxed version of such planning tasks. Although our hmax heuristic is inadmissible, it yields a numeric version of the classical LM-cut heuristic which is admissible. Further, we prove that our LM-cut heuristic neither dominates nor is dominated by the existing numeric heuristic hmax(hbd). We show that admissibility also holds when integrating the numeric cuts into the operator-counting (OC) heuristic producing an admissible numeric version of the OC heuristic. Through experiments, we demonstrate that both these heuristics compete favorably with the state-of-the-art heuristics: in particular, while sometimes expanding more nodes than other heuristics, numeric OC solves 19 more problem instances than the next closest heuristic.
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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 | 0.001 | 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