This paper investigates the ability of generative networks to convert their
input noise distributions into other distributions. Firstly, we demonstrate a
construction that allows ReLU networks to increase the dimensionality of their
noise distribution by implementing a "space-filling" function based on iterated
tent maps. We show this construction is optimal by analyzing the number of
affine pieces in functions computed by multivariate ReLU networks. Secondly, we
provide efficient ways (using polylog $(1/\epsilon)$ nodes) for networks to
pass between univariate uniform and normal distributions, using a Taylor series
approximation and a binary search gadget for computing function inverses.
Lastly, we indicate how high dimensional distributions can be efficiently
transformed into low dimensional distributions.

本文研究了基于生成网络将其输入噪声分布转换为其他分布的能力，提出通过实现一个基于迭代帐篷映射的 “填充空间” 函数来增加 ReLU 网络的噪声分布维数，使用泰勒级数逼近和二分搜索工具来计算函数反，从而提供了通过少量节点快速传递单变量均匀和正态分布的有效方法，最后指出了将高维分布有效转换为低维分布的方法。