# Neural Sequence Transformation

Published in *Computer Graphics Forum; Pacific Graphics Conference 2021*, 2021

Recommended citation: Mukherjee, Sabyasachi; Mukherjee, Sayan; Hua, Binh-Son; Umetani, Nobuyuki and Meister, Daniel. "Neural Sequence Transformation." *Computer Graphics Forum* (Wiley), Volume 40, Issue 7, Pages 131-140 (2021). __https://doi.org/10.1111/cgf.14407__

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 $O(\sqrt n)$, 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.

DOI: 10.1111/cgf.14407