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Record W4412347816 · doi:10.1007/s10703-025-00481-6

Rounding meets approximate model counting

2025· article· en· W4412347816 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

VenueFormal Methods in System Design · 2025
Typearticle
Languageen
FieldComputer Science
TopicMachine Learning and Algorithms
Canadian institutionsUniversity of Toronto
FundersNational Supercomputing Centre SingaporeMinistry of Education, IndiaMinistry of Education - SingaporeNational Research Foundation SingaporeNational Research Foundation
KeywordsRoundingMathematicsComputer scienceOperating system

Abstract

fetched live from OpenAlex

Abstract The problem of model counting, also known as $$\#\textsf{SAT}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>#</mml:mo> <mml:mi>SAT</mml:mi> </mml:mrow> </mml:math> , 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 $$(\varepsilon , \delta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>,</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -guarantees: i.e., the count returned is within a $$(1+\varepsilon )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -factor of the exact count with confidence at least $$1-\delta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:math> . While hashing-based techniques attain reasonable scalability for large enough values of $$\delta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> , their scalability is severely impacted for smaller values of $$\delta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> , 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 $$\delta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> . The resulting counter, called $$\textsf{ApproxMC6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ApproxMC</mml:mi> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> , achieves a substantial runtime performance improvement over the current state-of-the-art counter, $$\textsf{ApproxMC}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ApproxMC</mml:mi> </mml:math> . In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows $$\textsf{ApproxMC6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ApproxMC</mml:mi> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> solves 204 more instances than $$\textsf{ApproxMC}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ApproxMC</mml:mi> </mml:math> , and achieves a $$4\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> speedup over $$\textsf{ApproxMC}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ApproxMC</mml:mi> </mml:math> .

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)0.010
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.760
Threshold uncertainty score0.681

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0100.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.048
GPT teacher head0.374
Teacher spread0.326 · 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