Not a stupid question at all, but one problem is that the boundaries of a zero-train-loss region are not well characterized and evaluating the validation loss e

Not a stupid question at all, but one problem is that the boundaries of a zero-train-loss region are not well characterized and evaluating the validation loss even at a single point is computationally expensive. The centroid of one of these regions might not even be inside it (eg. donut shape but in higher dimensions) Interesting discussion though -- probably worth a few papers if someone were to investigate further.