论文标题
建设性通用的高维分销通过深层relu网络生成
Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networks
论文作者
论文摘要
我们提出了一个明确的深神经网络构建，该构建将均匀分布的一维噪声转换为任意接近任何二维Lipschitz-连续目标分布的近似值。我们设计的关键要素是对（Bailey＆Telgarsky，2018）中发现的锯齿功能的“空间填充”属性的概括。我们在神经网络构建中引起了深度的重要性 - 在驱动目标分布与网络实现的近似值之间的瓦斯汀距离中的重要性。概述了任意维度的输出分布的扩展。最后，我们表明拟议的构造不会产生成本 - 就瓦斯坦斯坦距离所测得的错误而言 - 相对于从$ d $ d $独立的随机变量产生$ d $二维的目标分布。
We present an explicit deep neural network construction that transforms uniformly distributed one-dimensional noise into an arbitrarily close approximation of any two-dimensional Lipschitz-continuous target distribution. The key ingredient of our design is a generalization of the "space-filling" property of sawtooth functions discovered in (Bailey & Telgarsky, 2018). We elicit the importance of depth - in our neural network construction - in driving the Wasserstein distance between the target distribution and the approximation realized by the network to zero. An extension to output distributions of arbitrary dimension is outlined. Finally, we show that the proposed construction does not incur a cost - in terms of error measured in Wasserstein-distance - relative to generating $d$-dimensional target distributions from $d$ independent random variables.
