Regularizing Deep Neural Networks with Stochastic Estimators of Hessian Trace

In this paper we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. Hutchinson method is a classical unbiased estimator for the trace of a matrix, but it is very time-consuming on deep learning models. Hence a dropout scheme is proposed to efficiently implements the Hutchinson method. Then we discuss a connection to linear stability of a nonlinear dynamical system and flat/sharp minima. Experiments demonstrate that our method outperforms existing regularizers and data augmentation methods, such as Jacobian, confidence penalty, and label smoothing, cutout and mixup.