We thank all the reviewers for their insightful comments, suggestions, and references

Neural Information Processing Systems 

We thank all the reviewers for their insightful comments, suggestions, and references. Novelty of tandem loss: it is not new, but we were not aware of the prior work, we thank Reviewer 2 for bringing it up. While most of the computed bounds are non-vacuous, they look to be not that tight. Also a discussion of potential ways to obtain tighter bond values, or whether there is a fundamental limitation. We provide some discussion in Sections 3.2 and 4.4.

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