find our responses to your comments below. 2 Reviewer # 1: 3 Thank you for the positive comments on the novelty of our idea and insightful questions for further improvement

We would like to thank all three reviewers for acknowledging our contributions and providing valuable feedback. Thank you for the positive comments on the novelty of our idea and insightful questions for further improvement. We first characterize the solutions of DEAN. Other choices for the energy objective will be left to future works. Rejection rates for d = 1 (left) and d = 3 .