Bibliographic record
Abstract
Model counting is task of counting the number of satisfying assignments of a Boolean formula. Since counting is intractable in general, most applications use $(\varepsilon, \delta)$-approximations, where the output is within a $(1+\varepsilon)$-factor of the count with probability at least $1-\delta$. Many demanding applications make thousands of counting queries, and the state-of-the-art approximate counter, ApproxMC, makes hundreds of calls to SAT solvers to answer a single approximate counting query. The sheer number of SAT calls, poses a significant challenge to the existing approaches. In this work, we propose an approximation scheme, RealMC, that is tailored to such demanding applications with low time limits. Compared to ApproxMC, RealMC makes 14$\times$ fewer SAT calls while providing the same guarantees as ApproxMC in the constant-factor regime. In an evaluation over 2,247 instances, RealMC solved 271 more and achieved a $2\times$ speedup against ApproxMC.
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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 | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 0.004 |
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".