Review for NeurIPS paper: Optimizing Neural Networks via Koopman Operator Theory

This paper provides a new perspective on neural network training based on Koopman operator theory (KOT). The paper received mixed reviews (top 50% - marginally above, reject, marginally above - accept, marginally below). On the positive side, and despite KOT being very old, the new perspective has a lot of potential: since the KOT is linear, if one can find (or approximate) eigenfunctions, one could compute and analyze training dynamics more easily and make optimization more efficient. On the negative side, the paper is a first step, and needs further development and experimental evaluation to demonstrate the value. Some reviewers also expressed the paper lacks clarity.