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Record W6929021048 · doi:10.48448/mvcq-4k93

Towards Real-Time Approximate Counting

2025· other· en· W6929021048 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueUnderline Science Inc. · 2025
Typeother
Languageen
Field
Topic
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsCounting problemSpeedupTask (project management)Counting processBoolean functionTrue quantified Boolean formula

Abstract

fetched live from OpenAlex

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.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.070
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0020.003
Science and technology studies0.0000.002
Scholarly communication0.0000.000
Open science0.0020.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0050.014

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.

Opus teacher head0.017
GPT teacher head0.297
Teacher spread0.280 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Quick stats

Citations0
Published2025
Admission routes1
Has abstractyes

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