  Over-parameterized deep neural networks (DNNs) with sufficient capacity to
memorize random noise can achieve excellent generalization performance,
challenging the bias-variance trade-off in classical learning theory. Recent
studies claimed that DNNs first learn simple patterns and then memorize noise;
some other works showed a phenomenon that DNNs have a spectral bias to learn
target functions from low to high frequencies during training. However, we show
that the monotonicity of the learning bias does not always hold: under the
experimental setup of deep double descent, the high-frequency components of
DNNs diminish in the late stage of training, leading to the second descent of
the test error. Besides, we find that the spectrum of DNNs can be applied to
indicating the second descent of the test error, even though it is calculated
from the training set only.
