Checklist 1. For all authors (a)

Do the main claims made in the abstract and introduction accurately reflect the paper's Did you discuss any potential negative societal impacts of your work? Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Y es] See Appendix Did you specify all the training details (e.g., data splits, hyperparameters, how they Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? Did you include the total amount of compute and the type of resources used (e.g., type Did you include any new assets either in the supplemental material or as a URL? [Y es] Did you discuss whether and how consent was obtained from people whose data you're Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? If you used crowdsourcing or conducted research with human subjects... (a) Proposition 4. F orΓ H and domains S, T we have: T This is a mild assumption that can hold in practice. We prove the first inequality for example and others follow similarly.