We start our response with Reviewer # 3, since some of the comments made there are inaccurate

Neural Information Processing Systems 

We thank all the reviewers for their insightful comments and suggestions that will all be incorporated in the final version. We start our response with Reviewer #3, since some of the comments made there are inaccurate. The other critique is we make strong assumptions. In fact, our assumptions are common and often weaker than literature. We therefore think that it is a good starting point for developing the theory.