  In the presence of noisy or incorrect labels, neural networks have the
undesirable tendency to memorize information about the noise. Standard
regularization techniques such as dropout, weight decay or data augmentation
sometimes help, but do not prevent this behavior. If one considers neural
network weights as random variables that depend on the data and stochasticity
of training, the amount of memorized information can be quantified with the
Shannon mutual information between weights and the vector of all training
labels given inputs, $I(w ; \mathbf{y} \mid \mathbf{x})$. We show that for any
training algorithm, low values of this term correspond to reduction in
memorization of label-noise and better generalization bounds. To obtain these
low values, we propose training algorithms that employ an auxiliary network
that predicts gradients in the final layers of a classifier without accessing
labels. We illustrate the effectiveness of our approach on versions of MNIST,
CIFAR-10, and CIFAR-100 corrupted with various noise models, and on a
large-scale dataset Clothing1M that has noisy labels.
