  We study the dynamics of supervised learning in layered neural networks, in
the regime where the size $p$ of the training set is proportional to the number
$N$ of inputs. Here the local fields are no longer described by Gaussian
probability distributions and the learning dynamics is of a spin-glass nature,
with the composition of the training set playing the role of quenched disorder.
We show how dynamical replica theory can be used to predict the evolution of
macroscopic observables, including the two relevant performance measures
(training error and generalization error), incorporating the old formalism
developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a
special case. For simplicity we restrict ourselves in this paper to
single-layer networks and realizable tasks.
