Bibliographic record
Abstract
Abstract The problem of model counting, also known as $$\#\textsf{SAT}$$ # SAT , is to compute the number of models or satisfying assignments of a given Boolean formula F . Model counting is a fundamental problem in computer science with a wide range of applications. In recent years, there has been a growing interest in using hashing-based techniques for approximate model counting that provide $$(\varepsilon , \delta )$$ ( ε , δ ) -guarantees: i.e., the count returned is within a $$(1+\varepsilon )$$ ( 1 + ε ) -factor of the exact count with confidence at least $$1-\delta$$ 1 - δ . While hashing-based techniques attain reasonable scalability for large enough values of $$\delta$$ δ , their scalability is severely impacted for smaller values of $$\delta$$ δ , thereby preventing their adoption in application domains that require estimates with high confidence. The primary contribution of this paper is to address the Achilles heel of hashing-based techniques: we propose a novel approach based on rounding that allows us to achieve a significant reduction in runtime for smaller values of $$\delta$$ δ . The resulting counter, called $$\textsf{ApproxMC6}$$ ApproxMC 6 , achieves a substantial runtime performance improvement over the current state-of-the-art counter, $$\textsf{ApproxMC}$$ ApproxMC . In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows $$\textsf{ApproxMC6}$$ ApproxMC 6 solves 204 more instances than $$\textsf{ApproxMC}$$ ApproxMC , and achieves a $$4\times$$ 4 × speedup over $$\textsf{ApproxMC}$$ ApproxMC .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.035 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.015 | 0.003 |
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".