Comments on "Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?"
This is an incremental critique that questions the theoretical foundations of using random weights to understand deep learning performance, relevant for researchers in neural network theory.
The authors challenge a previous claim that deep neural networks with random Gaussian weights preserve metric structure in a way that enables universal classification, arguing instead that the relationship between data angles and distance shrinkage is opposite, rendering such networks ineffective for explaining DNN success.
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.