We propose to use deep neural networks for generating samples in Monte Carlo
integration. Our work is based on non-linear independent components estimation
(NICE), which we extend in numerous ways to improve performance and enable its
application to integration problems. First, we introduce piecewise-polynomial
coupling transforms that greatly increase the modeling power of individual
coupling layers. Second, we propose to preprocess the inputs of neural networks
using one-blob encoding, which stimulates localization of computation and
improves inference. Third, we derive a gradient-descent-based optimization for
the KL and the $\chi^2$ divergence for the specific application of Monte Carlo
integration with unnormalized stochastic estimates of the target distribution.
Our approach enables fast and accurate inference and efficient sample
generation independently of the dimensionality of the integration domain. We
show its benefits on generating natural images and in two applications to
light-transport simulation: first, we demonstrate learning of joint
path-sampling densities in the primary sample space and importance sampling of
multi-dimensional path prefixes thereof. Second, we use our technique to
extract conditional directional densities driven by the product of incident
illumination and the BSDF in the rendering equation, and we leverage the
densities for path guiding. In all applications, our approach yields on-par or
higher performance than competing techniques at equal sample count.

本文介绍了基于深度神经网络的非线性独立分量估计（NICE）用于 Monte Carlo 积分中样本生成的应用，并介绍了分段多项式耦合变换、一块编码、基于梯度下降的 KL 和 χ2 散度优化等提高模型性能的改进方案。通过应用于生成自然图像以及在光传输模拟中的两种应用，证明了该方法在不同维度积分领域下具有快速、准确、高性能等特点。

神经重要性采样

Neural Importance Sampling

Estimating the number of eigenvalues located in a given interval of a large
sparse Hermitian matrix is an important problem in certain applications and it
is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often
an exact count is not necessary and methods based on stochastic estimates can
be utilized to yield rough approximations. This paper examines a number of
techniques tailored to this specific task. It reviews standard approaches and
explores new ones based on polynomial and rational approximation filtering
combined with a stochastic procedure.

文章探讨了基于多项式和有理逼近过滤器结合随机过程的方法，用于估计大型稀疏埃尔米特矩阵中所在给定区间的特征值数量的问题。