  In a recently published paper [1], it is shown that deep neural networks
(DNNs) with random Gaussian weights preserve the metric structure of the data,
with the property that the distance shrinks more when the angle between the two
data points is smaller. We agree that the random projection setup considered in
[1] preserves distances with a high probability. But as far as we are
concerned, the relation between the angle of the data points and the output
distances is quite the opposite, i.e., smaller angles result in a weaker
distance shrinkage. This leads us to conclude that Theorem 3 and Figure 5 in
[1] are not accurate. Hence the usage of random Gaussian weights in DNNs cannot
provide an ability of universal classification or treating in-class and
out-of-class data separately. Consequently, the behavior of networks consisting
of random Gaussian weights only is not useful to explain how DNNs achieve
state-of-art results in a large variety of problems.
