Hessian regularization of deep neural networks: A novel approach based on stochastic estimators of Hessian trace.

[Display omitted] • Connecting Hessian trace with a generalization error bound. • Flat minima of loss landscape and stability analysis in dynamical systems. • Efficient Hessian trace regularization algorithm with Dropout. • Performance comparison on vision and language tasks. 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. We explain its benefits in finding flat minima and avoiding Lyapunov stability in dynamical systems. We adopt the Hutchinson method as a classical unbiased estimator for the trace of a matrix and further accelerate its calculation using a Dropout scheme. Experiments demonstrate that our method outperforms existing regularizers and data augmentation methods, such as Jacobian, Confidence Penalty, Label Smoothing, Cutout, and Mixup. The code is available at https://github.com/Dean-lyc/Hessian-Regularization. [ABSTRACT FROM AUTHOR]