Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Dimensional Distribution Generation Through Deep Neural Networks   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 of network depth in driving the
Wasserstein distance between the target distribution and its neural network
approximation to zero. Finally, we find that, for histogram target
distributions, the number of bits needed to encode the corresponding generative
network equals the fundamental limit for encoding probability distributions as
dictated by quantization theory.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con