Geometric Integration for Neural Control Variates

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dc.contributor.authorMeister, Danielen_US
dc.contributor.authorHarada, Takahiroen_US
dc.contributor.editorChristie, Marcen_US
dc.contributor.editorPietroni, Nicoen_US
dc.contributor.editorWang, Yu-Shuenen_US
dc.date.accessioned2025-10-07T05:03:43Z
dc.date.available2025-10-07T05:03:43Z
dc.date.issued2025
dc.description.abstractControl 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 approximators 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.en_US
dc.description.number7
dc.description.sectionheadersLighting & Rendering
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume44
dc.identifier.doi10.1111/cgf.70275
dc.identifier.issn1467-8659
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.70275
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70275
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleGeometric Integration for Neural Control Variatesen_US
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