Reviews: How Many Samples are Needed to Estimate a Convolutional Neural Network?

The authors consider the number of samples needed to achieve an error epsilon in the context of learning an m-dimensional convolutional filter as well as one followed by a linear projection. This is motivated by a desire to rigorously understand the empirical success of CNNs. This paper seems technically correct, yet I believe the setting is very far from real CNNs to the point where it's not clear if the results will be impactful. The authors only consider a linear convolution layer, which corresponds to a wiener filtering-like operation according to their model, for removing noise for estimating the label. My concern is the motivation, the novelty and the assumptions.