We thank all the reviewers for their time and effort to evaluate our paper

We thank all the reviewers for their time and effort to evaluate our paper. We will discuss the assumptions in the context of the SDE in Eq. 4, which is our main The boundedness assumption requires the solutions to the SDE to be'non-explosive' in the sense that for On the other hand, in Thm.S3, we already proved a bound which does not require H4, but This assumption is common in statistics (see [Bra83]) but hard to verify in practice. We agree that Prop.1 can be difficult to grasp at a first sight; hence, we provided BN is not fully understood. Our main focus is the relationship between generalization and intrinsic dimensionality. Relationship between BN and dimensionality is an interesting future direction which would complement our work.