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Neural Sequence Transformation

Publication ,  Journal Article
Mukherjee, S; Hua, BS; Umetani, N; Meister, D
Published in: Computer Graphics Forum
October 1, 2021

Monte Carlo integration is a technique for numerically estimating a definite integral by stochastically sampling its integrand. These samples can be averaged to make an improved estimate, and the progressive estimates form a sequence that converges to the integral value on the limit. Unfortunately, the sequence of Monte Carlo estimates converges at a rate of O(), where n denotes the sample count, effectively slowing down as more samples are drawn. To overcome this, we can apply sequence transformation, which transforms one converging sequence into another with the goal of accelerating the rate of convergence. However, analytically finding such a transformation for Monte Carlo estimates can be challenging, due to both the stochastic nature of the sequence, and the complexity of the integrand. In this paper, we propose to leverage neural networks to learn sequence transformations that improve the convergence of the progressive estimates of Monte Carlo integration. We demonstrate the effectiveness of our method on several canonical 1D integration problems as well as applications in light transport simulation.

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Published In

Computer Graphics Forum

DOI

EISSN

1467-8659

ISSN

0167-7055

Publication Date

October 1, 2021

Volume

40

Issue

7

Start / End Page

131 / 140

Related Subject Headings

  • Software Engineering
  • 4607 Graphics, augmented reality and games
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Mukherjee, S., Hua, B. S., Umetani, N., & Meister, D. (2021). Neural Sequence Transformation. Computer Graphics Forum, 40(7), 131–140. https://doi.org/10.1111/cgf.14407
Mukherjee, S., B. S. Hua, N. Umetani, and D. Meister. “Neural Sequence Transformation.” Computer Graphics Forum 40, no. 7 (October 1, 2021): 131–40. https://doi.org/10.1111/cgf.14407.
Mukherjee S, Hua BS, Umetani N, Meister D. Neural Sequence Transformation. Computer Graphics Forum. 2021 Oct 1;40(7):131–40.
Mukherjee, S., et al. “Neural Sequence Transformation.” Computer Graphics Forum, vol. 40, no. 7, Oct. 2021, pp. 131–40. Scopus, doi:10.1111/cgf.14407.
Mukherjee S, Hua BS, Umetani N, Meister D. Neural Sequence Transformation. Computer Graphics Forum. 2021 Oct 1;40(7):131–140.
Journal cover image

Published In

Computer Graphics Forum

DOI

EISSN

1467-8659

ISSN

0167-7055

Publication Date

October 1, 2021

Volume

40

Issue

7

Start / End Page

131 / 140

Related Subject Headings

  • Software Engineering
  • 4607 Graphics, augmented reality and games
  • 0801 Artificial Intelligence and Image Processing