Early Stopping by Gradient Disparity

Validation-based early-stopping methods are one of the most popular techniques used to avoid over-training deep neural networks. They require to set aside a reliable unbiased validation set, which can be expensive in applications offering limited amounts of data. In this paper, we propose to use \emph{gradient disparity}, which we define as the $\ell_2$ norm distance between the gradient vectors of two batches drawn from the training set. It comes from a probabilistic upper bound on the difference between the classification errors over a given batch, when the network is trained on this batch and when the network is trained on another batch of points sampled from the same dataset. We empirically show that gradient disparity is a very promising early-stopping criterion when data is limited, because it uses all the training samples during training. Furthermore, we show in a wide range of experimental settings that gradient disparity is not only strongly related to the usual generalization error between the training and test sets, but that it is also much more informative about the level of label noise.