Q-NET：一个神经代理的低维积分网络
Q-NET: A Network for Low-Dimensional Integrals of Neural Proxies
摘要：
许多应用需要计算多维函数的积分。一个普遍和流行的程序是通过平均函数的多个评估来估计积分。通常，函数的每次求值都需要昂贵的计算。如果需要重复计算，则使用\emph{proxy}或true函数的代理函数非常有用。如果它的积分是解析已知的，并且可以实际计算，则代理函数甚至更有用。我们建议使用一个通用而简单的人工神经网络类- sigmoidal通用逼近器-作为代理的功能，其积分需要估计。我们设计了一个家庭的固定网络，我们称之为Q-NET，操作的参数训练的代理计算精确积分的输入域的\emph{any subset of dimensions}。我们确定的输入空间的积分可以重新计算，而无需重新计算的被积函数或重新训练的代理转换。我们强调这个计划的好处，如逆渲染，生成程序噪声，可视化和模拟的几个应用程序。提议的代理在以下情况下很有吸引力：维度较低（$<10$ D）;积分的估计需要与采样策略解耦;使用稀疏、自适应采样;边缘函数需要以函数形式已知;或者当强大的单指令多数据/线程（SIMD/SIMT）管道可用于计算时。
英文摘要：
Many applications require the calculation of integrals of multidimensional functions. A general and popular procedure is to estimate integrals by averaging multiple evaluations of the function. Often, each evaluation of the function entails costly computations. The use of a \emph{proxy} or surrogate for the true function is useful if repeated evaluations are necessary. The proxy is even more useful if its integral is known analytically and can be calculated practically. We propose the use of a versatile yet simple class of artificial neural networks -- sigmoidal universal approximators -- as a proxy for functions whose integrals need to be estimated. We design a family of fixed networks, which we call Q-NETs, that operate on parameters of a trained proxy to calculate exact integrals over \emph{any subset of dimensions} of the input domain. We identify transformations to the input space for which integrals may be recalculated without resampling the integrand or retraining the proxy. We highlight the benefits of this scheme for a few applications such as inverse rendering, generation of procedural noise, visualization and simulation. The proposed proxy is appealing in the following contexts: the dimensionality is low ($<10$D); the estimation of integrals needs to be decoupled from the sampling strategy; sparse, adaptive sampling is used; marginal functions need to be known in functional form; or when powerful Single Instruction Multiple Data/Thread (SIMD/SIMT) pipelines are available for computation.
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