Teng‐Teng Yao

Teng-Teng Yao, Zheng-Jian Bai, Xiao-Qing Jin et al.

This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by Chen and Chu [SIAM J. Numer. Anal., 33 (1996), pp. 2417--2430]. We provide a Riemannian inexact Gausss-Newton method for solving the least squares inverse eigenvalue problem. The global and local convergence analysis of the proposed method is discussed. Also, a preconditioned conjugate gradient method with an efficient preconditioner is proposed for solving the Riemannian Gauss-Newton equation. Finally, some numerical tests, including an application in the inverse Sturm-Liouville problem, are reported to illustrate the efficiency of the proposed method.

Yaguan Qian, Qiqi Shao, Tengteng Yao et al.

Adversarial training is wildly considered as one of the most effective way to defend against adversarial examples. However, existing adversarial training methods consume unbearable time, due to the fact that they need to generate adversarial examples in the large input space. To speed up adversarial training, we propose a novel adversarial training method that does not need to generate real adversarial examples. By adding perturbations to logits to generate Endogenous Adversarial Examples (EAEs) -- the adversarial examples in the latent space, the time consuming gradient calculation can be avoided. Extensive experiments are conducted on CIFAR-10 and ImageNet, and the results show that comparing to state-of-the-art methods, our EAE adversarial training not only shortens the training time, but also enhances the robustness of the model and has less impact on the accuracy of clean examples than the existing methods.