Optimal depth-first strategies for and-or trees
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Bibliographic record
Abstract
A probabilistic boolean expression (PBE) consists of a boolean expression over a set of boolean variables, each with a corresponding cost and probability value that indicates respectively the cost of determining a variable's value and the probability that the value is true. Given a PBE, a resolution strategy is a sequential testing algorithm that determines the value of the expression, where each test is a query of the value of one variable. A strategy is optimal if its expected cost is minimum, over all possible strategies. The minimum cost resolution strategy problem (MRSP) is to find an optimal strategy of a given PBE. As MRSP is NP-hard in general, we consider the restricted case in which each variable occurs exactly once; the corresponding expressions are sometimes called and-or trees, since they have a tree representation in which internal nodes correspond to (boolean) operators and leaf nodes correspond to variables. We further assume that variables are independent, and focus on a depth-first algorithm, dfa, that orders subexpressions within subtrees based on probability/cost ratios. Our main results are that dfa produces optimal strategies for and-or trees with depth 1 or 2, but can be very bad for and-or trees with depth 3 or more.
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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