Title: Generalisation dynamics of online learning in over-parameterised neural networks,
Abstract: Deep neural networks achieve stellar generalisation on a variety of problems,
despite often being large enough to easily fit all their training data. Here we
study the generalisation dynamics of two-layer neural networks in a
teacher-student setup, where one network, the student, is trained using
stochastic gradient descent (SGD) on data generated by another network, called
the teacher. We show how for this problem, the dynamics of SGD are captured by
a set of differential equations. In particular, we demonstrate analytically
that the generalisation error of the student increases linearly with the
network size, with other relevant parameters held constant. Our results
indicate that achieving good generalisation in neural networks depends on the
interplay of at least the algorithm, its learning rate, the model architecture,
and the data set.