that not all comments are replied here and our replies have to be short due to space, but they'll be fully addressed in a

We appreciate the valuable comments, which urged us to embody explicit connections to practices of learning. We plead a reconsideration based on the improvement, as our contribution is truly innovative and nontrivial. Re: connection to learning, and when Cond.1&2 hold. Fig.1 shows large LR again produces stochasticity as our paper studies. Cond.1&2 use auxiliary random variables to define the needed f Re: weaken isotropic noise assumption?