My summary of the paper: The paper proves that if you have two distributions that you want to ensure you cannot distinguish linearly (i.e a logistic regression will fail to achieve better than chance score), then one way to do this is to make sure they have the same mean. Previous work has done similar stuff (https://arxiv.org/abs/2212.04273), but without proving optimality.
then one way to do this is to make sure they have the same mean
Yep, although we actually go a bit further than that and show that making the means equal is necessary, at least if you want your method to work for general convex loss functions.
My summary of the paper: The paper proves that if you have two distributions that you want to ensure you cannot distinguish linearly (i.e a logistic regression will fail to achieve better than chance score), then one way to do this is to make sure they have the same mean. Previous work has done similar stuff (https://arxiv.org/abs/2212.04273), but without proving optimality.
Yep, although we actually go a bit further than that and show that making the means equal is necessary, at least if you want your method to work for general convex loss functions.