High-Dimensional Distribution Generation Through Deep Neural Networks. (arXiv:2107.12466v3 [cs.LG] UPDATED)

We show that every $d$-dimensional probability distribution of bounded
support can be generated through deep ReLU networks out of a $1$-dimensional
uniform input distribution. What is more, this is possible without incurring a
cost - in terms of approximation error measured in Wasserstein-distance -
relative to generating the $d$-dimensional target distribution from $d$
independent random variables. This is enabled by a vast generalization of the
space-filling approach discovered in (Bailey & Telgarsky, 2018). The
construction we propose elicits the importance …

arxiv distribution generation networks neural networks