Reviews: Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks

SUMMARY OF THE PAPER This draft has a combination of good points and grey areas. The problem is of utmost importance and the research questions are clear, but the hypothesis (that neurons receptive fields are organized as low-dimensional manifolds expressed by atlases of locally overlapping charts) is presented as a fact. I'm not sure the normative approach from sociology does apply to neuroscience (see below). The material on the supplementary material provides hints about how to reach a proof but does not provide a proof for theorem 1. It is also said that they can show proof for Eq 9, but I've been unable to find a formal proof in the supplementary material.