Comments on “Deep Neural Networks With Random Gaussian Weights: A Universal Classification Strategy?”
In a recently published paper (Giryes et al., 2016), 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 (Giryes et al., 2016) 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 (Giryes et al., 2016) 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.