  Deep neural networks are known to exhibit a `double descent' behavior as the
number of parameters increases. Recently, it has also been shown that an
`epochwise double descent' effect exists in which the generalization error
initially drops, then rises, and finally drops again with increasing training
time. This presents a practical problem in that the amount of time required for
training is long, and early stopping based on validation performance may result
in suboptimal generalization. In this work we develop an analytically tractable
model of epochwise double descent that allows us to characterise theoretically
when this effect is likely to occur. This model is based on the hypothesis that
the training data contains features that are slow to learn but informative. We
then show experimentally that deep neural networks behave similarly to our
theoretical model. Our findings indicate that epochwise double descent requires
a critical amount of noise to occur, but above a second critical noise level
early stopping remains effective. Using insights from theory, we give two
methods by which epochwise double descent can be removed: one that removes slow
to learn features from the input and reduces generalization performance, and
another that instead modifies the training dynamics and matches or exceeds the
generalization performance of standard training. Taken together, our results
suggest a new picture of how epochwise double descent emerges from the
interplay between the dynamics of training and noise in the training data.
