variances that are not crazy gradient descent converges to an epsilon global minimizer as long as the loss is convex your learning rate is small roughly speaking or works for any model so when you're sufficiently over privatized you get an epsilon approximate global minimizer of the training loss let me sketch a proof of why this could be true of course when you're over parametrized looking at the parameters is not a great idea they're not identifiable there's permutations and all sorts of other invariances that come out that the