Input Hessian Regularization of Neural Networks
This addresses the problem of adversarial vulnerability in neural networks, offering an incremental improvement in regularization methods.
The paper tackled the computational challenge of regularizing the input Hessian in neural networks to improve robustness, proposing an efficient algorithm that increased robustness over input gradient regularization on MNIST and FMNIST datasets.
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.