Review for NeurIPS paper: How to Characterize The Landscape of Overparameterized Convolutional Neural Networks

Additional Feedback: Overall, I have the impression that the paper tries to advocate for the fact that the landscape of convolutional neural networks is convex with respect to the features at each layer. Unless I miss some important details in the paper, I think this claim is not true. Even for finite networks, understanding the convexity of the problem with respect to the features at each layer would require some first understanding of the space of features realizable by the network at every intermediate layer, which is also not treated here. In the main paper, the authors present a theoretical result to support their claim. However, if I understand correct the way their proof works is just by a change of variable where the new variables hide the non-convexity of the system. Thus I believe this cannot be used as a valid argument to say that the whole system is convex with respect to the original distribution of interest.