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Record W4415077200 · doi:10.1111/cgf.70275

Geometric Integration for Neural Control Variates

2025· article· en· W4415077200 on OpenAlex
Daniel Meister, Takahiro Harada

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

VenueComputer Graphics Forum · 2025
Typearticle
Languageen
FieldEngineering
TopicAdvanced Numerical Analysis Techniques
Canadian institutionsAdvanced Micro Devices (Canada)
Fundersnot available
KeywordsControl variatesNumerical integrationArtificial neural networkMonte Carlo methodPiecewise linear functionPerceptronPiecewiseQuasi-Monte Carlo methodMonte Carlo integration

Abstract

fetched live from OpenAlex

Abstract Control variates are a variance‐reduction technique for Monte Carlo integration. The principle involves approximating the integrand by a function that can be analytically integrated, and integrating using the Monte Carlo method only the residual difference between the integrand and the approximation, to obtain an unbiased estimate. Neural networks are universal approx‐imators that could potentially be used as a control variate. However, the challenge lies in the analytic integration, which is not possible in general. In this manuscript, we study one of the simplest neural network models, the multilayered perceptron (MLP) with continuous piecewise linear activation functions, and its possible analytic integration. We propose an integration method based on integration domain subdivision, employing techniques from computational geometry to solve this problem in 2D. We demonstrate that an MLP can be used as a control variate in combination with our integration method, showing applications in the light transport simulation.

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)0.000
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: none
Teacher disagreement score0.967
Threshold uncertainty score0.505

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.006
GPT teacher head0.234
Teacher spread0.229 · 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