We thank the reviewers for their comments, and are very glad to see that all reviewers appreciate the novel and interesting

They also raise some great points and criticisms, which we respond to below. All reviewers want more experiments, though R1 "understands that the focus of the paper B, E, the nontrivial proof of Prop.8, etc.) and accompanied them with We can show how CI changes with W, as suggested by R1. We can run the experiments on more domains (probably in the appendix, as we want the main text to focus on theory). We have tried many methods to stablize training and documented the working tricks in F.2. We are considering changing "confidence interval" to "value interval" to avoid this issue.