To All Reviewers: We thank all reviews for your insightful feedback and your appreciation of our MCR 2 formulation

We will incorporate suggestions on minor corrections, references, footnotes, and presentations in the final version. This work aims to introduce a new objective (i.e., MCR Compare with OLE: " 1). It is not clear why a larger . . . Does the OLE type loss have the same property as Theorem 1? 3). The authors should show more comparison . . . We will make these connections more clear in the final version; 2). Q2: Gaussian assumption of data: "I have a concern whether the rate distortion function . . . to be self-contained.