  We consider the dynamics of gradient descent (GD) in overparameterized single
hidden layer neural networks with a squared loss function. Recently, it has
been shown that, under some conditions, the parameter values obtained using GD
achieve zero training error and generalize well if the initial conditions are
chosen appropriately. Here, through a Lyapunov analysis, we show that the
dynamics of neural network weights under GD converge to a point which is close
to the minimum norm solution subject to the condition that there is no training
error when using the linear approximation to the neural network. To illustrate
the application of this result, we show that the GD converges to a prediction
function that generalizes well, thereby providing an alternative proof of the
generalization results in Arora et al. (2019).

Machine Learning