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

Model, sample, and epoch-wise descents: exact solution of gradient flow in the random feature model