Engineering an Efficient Probabilistic Exact Model Counter
Bibliographic record
Abstract
Abstract Given a formula F , the problem of model counting, also known as #SAT, is to compute the number of satisfying assignments of F . While model counting has emerged as a crucial primitive in diverse domains from quantitative information flow analysis to neural network verification, scalability remains a fundamental challenge despite advances in both exact and approximate counting techniques. We present $$\textsf{Ganak2}$$ Ganak 2 , a novel framework that achieves substantial performance improvements through three key technical innovations: (1) refined residual formula processing incorporating SAT-specific techniques while maintaining seamless state transitions, (2) dual independent set framework maintaining distinct SAT-eligibility and decision sets, and (3) chronological backtracking specifically adapted to model counting. Our empirical evaluation on 1600 previous model counting competition instances demonstrates that $$\textsf{Ganak2}$$ Ganak 2 successfully computes counts for 1121 instances within the one hour time limit, compared to 1032 instances by the prior state of the art approach, representing an 8.7% improvement. This progress is especially remarkable considering the extensive development and refinement of model counting tools over the years, driven by yearly competitive evaluation in the field.
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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 | 0.005 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".