Reviewer 1: Thank you for the insightful analysis and acknowledgement of our effort

Reviewer 1: Thank you for the insightful analysis and acknowledgement of our effort. The model is clearly expressive enough as training and test accuracy are near-perfect. We did not intend to make this impression that over-fitting is new or surprising for these datasets. In Sec 2.2 and Theorem 2.1, we rigorously showed the existence of a perfect accuracy For example, compare P@k and PSP@k of PfastreXML and FastXML in T able 3 and T able 4. We Note that near-orthogonality is condition No. 5 mentioned in Theorem 2.1 for the existence of a perfect XMC repository and we have verified its correctness and we will release it in the final version. We are happy to provide more details if this is a point of concern.