arXiv subjects

Lijia Yu

Publications and source records attributed to Lijia Yu.

21 records · Page 2Linked to original sources

arXiv2022

Adversarial Parameter Attack on Deep Neural Networks

In this paper, a new parameter perturbation attack on DNNs, called adversarial parameter attack, is proposed, in which small perturbations to the parameters of the DNN are made such that the accuracy of the attacked DNN does not decrease much, but its robustness becomes much lower. The adversarial parameter attack is stronger than previous parameter perturbation attacks in that the attack is more difficult to be recognized by users and the attacked DNN gives a wrong label for any modified sample input with high probability. The existence of adversarial parameters is proved. For a DNN $F_Θ$ with the parameter set $Θ$ satisfying certain conditions, it is shown that if the depth of the DNN is sufficiently large, then there exists an adversarial parameter set $Θ_a$ for $Θ$ such that the accuracy of $F_{Θ_a}$ is equal to that of $F_Θ$, but the robustness measure of $F_{Θ_a}$ is smaller than any given bound. An effective training algorithm is given to compute adversarial parameters and numerical experiments are used to demonstrate that the algorithms are effective to produce high quality adversarial parameters.

cs.LG↗

arXiv2022

Robust and Information-theoretically Safe Bias Classifier against Adversarial Attacks

In this paper, the bias classifier is introduced, that is, the bias part of a DNN with Relu as the activation function is used as a classifier. The work is motivated by the fact that the bias part is a piecewise constant function with zero gradient and hence cannot be directly attacked by gradient-based methods to generate adversaries, such as FGSM. The existence of the bias classifier is proved and an effective training method for the bias classifier is given. It is proved that by adding a proper random first-degree part to the bias classifier, an information-theoretically safe classifier against the original-model gradient attack is obtained in the sense that the attack will generate a totally random attacking direction. This seems to be the first time that the concept of information-theoretically safe classifier is proposed. Several attack methods for the bias classifier are proposed and numerical experiments are used to show that the bias classifier is more robust than DNNs with similar size against these attacks in most cases.

cs.LG↗

arXiv2020

Improve the Robustness and Accuracy of Deep Neural Network with $L_{2,\infty}$ Normalization

In this paper, the robustness and accuracy of the deep neural network (DNN) was enhanced by introducing the $L_{2,\infty}$ normalization of the weight matrices of the DNN with Relu as the activation function. It is proved that the $L_{2,\infty}$ normalization leads to large dihedral angles between two adjacent faces of the polyhedron graph of the DNN function and hence smoother DNN functions, which reduces over-fitting. A measure is proposed for the robustness of a classification DNN, which is the average radius of the maximal robust spheres with the sample data as centers. A lower bound for the robustness measure is given in terms of the $L_{2,\infty}$ norm. Finally, an upper bound for the Rademacher complexity of DNN with $L_{2,\infty}$ normalization is given. An algorithm is given to train a DNN with the $L_{2,\infty}$ normalization and experimental results are used to show that the $L_{2,\infty}$ normalization is effective to improve the robustness and accuracy.

stat.ML↗