  Understanding the learning dynamics of neural networks is one of the key
issues for the improvement of optimization algorithms as well as for the
theoretical comprehension of why deep neural nets work so well today. In this
paper, we introduce a random matrix-based framework to analyze the learning
dynamics of a single-layer linear network on a binary classification problem,
for data of simultaneously large dimension and size, trained by gradient
descent. Our results provide rich insights into common questions in neural
nets, such as overfitting, early stopping and the initialization of training,
thereby opening the door for future studies of more elaborate structures and
models appearing in today's neural networks.
