Review for NeurIPS paper: Understanding Approximate Fisher Information for Fast Convergence of Natural Gradient Descent in Wide Neural Networks

Additional Feedback: Line 1: Change to "Natural Gradient Descent..." Line 10, 11: "the function space" should just be "function space" Line 15: it might be worth pointing out here and/or in the intro that a special kind of data preprocessing (the "Forster transform") is required to get this result for K-FAC in general Line 16, 46: "under some assumptions"/"under specific conditions" should perhaps be replaced with "under some approximating assumptions". AFAIK the "gradient independence assumption" doesn't have any rigorous justification and might not even be true in practice. Line 69: "New insights and perspectives on the natural gradient method" also argues that the empirical Fisher is a poor substitute for the "true" one. Line 71: first quotation make is backwards Line 79: delete "firing" here Line 88: "We normalize each sample by" should be "We normalize each sample so that" Line 90: "we overview" should be "we give an overview of" Line 116: Although the use of damping in the context of NTK theory can be explained this way, damping has a larger role in second order optimization in general (where NTK theory doesn't necessarily apply). The way you are describing it though, it sounds like you are saying its use is fully explained by this theory, and I would suggest you change this.