Input Hessian Regularization of Neural Networks
Abstract
Regularizing the input gradient has shown to be effective in promoting the robustness of neural networks. The regularization of the input's Hessian is therefore a natural next step. A key challenge here is the computational complexity. Computing the Hessian of inputs is computationally infeasible. In this paper we propose an efficient algorithm to train deep neural networks with Hessian operator-norm regularization. We analyze the approach theoretically and prove that the Hessian operator norm relates to the ability of a neural network to withstand an adversarial attack. We give a preliminary experimental evaluation on the MNIST and FMNIST datasets, which demonstrates that the new regularizer can, indeed, be feasible and, furthermore, that it increases the robustness of neural networks over input gradient regularization.
Cite
@article{arxiv.2009.06571,
title = {Input Hessian Regularization of Neural Networks},
author = {Waleed Mustafa and Robert A. Vandermeulen and Marius Kloft},
journal= {arXiv preprint arXiv:2009.06571},
year = {2020}
}
Comments
Workshop on "Beyond first-order methods in ML systems" at the 37th International Conference on Machine Learning, Vienna, Austria, 2020