We thank the reviewers for their kind comments and for their consensus view that our theoretical results on TV modulus

We are also thankful for the reviewers' concrete suggestions on improving the draft, We agree with the reviewers that our proposed estimators are not computationally efficient. We work in the high-temperature regime i.e., We agree with the reviewer that our estimator doesn't recover the true model even in Model Width as relaxed parameter . We thank the reviewer for raising this subtle issue.