> why would SGD put the right things in the right bucket?

Think of it as a best fit curve and exceptions to that curve. The noise is essentially this set of exceptions that move points away from where they would otherwise fall on the curve.

Gradient descent wants to be able to make the smallest change that moves the most data points towards the curve. To do this it learns an arrangement where it can change, say, one parameter and have a bunch of points move at once. What does this correspond to? The big common patterns shared by many data points.

Most of the capacity gets soaked up modelling these sorts of common patterns, and after they have been learned the model starts adding exceptions that allow individual points to deviate from the curve.

Because they’re exceptions, they must not impact neighbouring points, or at least only ones within a very short distance from them. Otherwise they’re now driving the error higher by impacting more points than they should. So you end up with very narrow ranges of features that are able to trigger different sorts of noise.

How narrow they are is shaped by the training data, they’re exactly as narrow as needed not to raise the error, so assuming the total population has the same distribution, they don’t get hit. Much.

At least, that’s what I take away from it.