This is a well-written paper addressing an important and timely problem. The authors rebuttal was well done, and managed to answer lingering doubts of the reviewers. The consensus among the reviewers after the rebuttal was that the paper be accepted. Adding another point to the reviewers' comments: One remaining issue in my opinion, and a limitation of the results, is that the assumption in theorem 1 that G has real eigenvalues is far more restrictive than it seems: a system with only teal eigenvalues cannot capture many interesting physical dynamics; for example any system whose response has any kind of oscillation needs complex eigenvalues. So extension to nonsymmetric G is needed and I strongly encouraged the authors to pursue it for the work to be more useful; the later work of Hazan manages to do this for the wave filter approach. Still, the results have enough novelty to be published and will contribute to NeurIPS community.