  This paper explores the generalization loss of linear regression in variably
parameterized families of models, both under-parameterized and
over-parameterized. We show that the generalization curve can have an arbitrary
number of peaks, and moreover, locations of those peaks can be explicitly
controlled. Our results highlight the fact that both classical U-shaped
generalization curve and the recently observed double descent curve are not
intrinsic properties of the model family. Instead, their emergence is due to
the interaction between the properties of the data and the inductive biases of
learning algorithms.
