  Recent evidence has shown the existence of a so-called double-descent and
even triple-descent behavior for the generalization error of deep-learning
models. This important phenomenon commonly appears in implemented neural
network architectures, and also seems to emerge in epoch-wise curves during the
training process. A recent line of research has highlighted that random matrix
tools can be used to obtain precise analytical asymptotics of the
generalization (and training) errors of the random feature model. In this
contribution, we analyze the whole temporal behavior of the generalization and
training errors under gradient flow for the random feature model. We show that
in the asymptotic limit of large system size the full time-evolution path of
both errors can be calculated analytically. This allows us to observe how the
double and triple descents develop over time, if and when early stopping is an
option, and also observe time-wise descent structures. Our techniques are based
on Cauchy complex integral representations of the errors together with recent
random matrix methods based on linear pencils.
