Reviewer 1: The regularized version of the FR problem is a geodesically convex optimization problem over the feasible

We would like to thank all referees for their appreciation of our results and the useful feedback. The KL divergence (confined to the subspace of Gaussian distributions) is not induced by any Riemannian metric. We propose to elaborate on these connections in the introduction. As we pointed out in our response to Rev. 1, solving the KL problem (12) using Theorem 3.2 takes Because (12) is non-convex, the gradient descent algorithm cannot guarantee to converge to global minimum of (12). Thank you also for your minor suggestions, which we plan to address in the revised version of the manuscript.