Developing Hessian-free second-order adversarial examples for adversarial training

• Autorzy: Qian, Yaguan , Zhang, Liangjian , Wang, Yuqi , Ji, Boyuan , Yao, Tengteng , Wang, Bin
• Języki publikacji: EN

Abstrakty

EN

Recent studies show that deep neural networks (DNNs) are extremely vulnerable to elaborately designed adversarial examples. Adversarial training, which uses adversarial examples as training data, has been proven to be one of the most effective methods of defense against adversarial attacks. However, most existing adversarial training methods use adversarial examples relying on first-order gradients, which perform poorly against second-order adversarial attacks and make it difficult to further improve the robustness of the model. In contrast to first-order gradients, second-order gradients provide a more accurate approximation of the loss landscape relative to natural examples. Therefore, our work focuses on constructing second-order adversarial examples and utilizing them for training DNNs. However, second-order optimization involves computing the Hessian inverse, which typically consumes considerable time. To address this issue, we propose an approximation method that transforms the problem into optimization within the Krylov subspace. Compared with the Euclidean space, the Krylov subspace method typically does not require storing the entire matrix. It only needs to store vectors and intermediate results, avoiding explicitly calculating the complete Hessian matrix. We approximate the adversarial direction by a linear combination of Hessian-vector products in the Krylov subspace to reduce the computation cost. Because of the non-symmetrical Hessian matrix, we use the generalized minimum residual to search for an approximate polynomial solution of the matrix. Our method efficiently reduces computational complexity and accelerates the training process. Extensive experiments conducted on the MNIST, CIFAR-10, and ImageNet-100 datasets demonstrate that our adversarial learning using second-order adversarial samples outperforms other first-order methods, leading to improved model robustness against various attacks.

Słowa kluczowe

PL

uczenie maszynowe; przestrzeń Kryłowa; sieć neuronowa głęboka

EN

adversarial example; adversarial machine learning; Krylov subspace; deep neural network

• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2024
• Tom: Vol. 34, no. 3
• Strony: 425--438
• Opis fizyczny: Bibliogr. 47 poz., rys., tab., wykr.

Twórcy

autor

Qian, Yaguan

• College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China,

autor

Zhang, Liangjian

• College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China,

autor

Wang, Yuqi

• College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China,

autor

Ji, Boyuan

• College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China,

autor

Yao, Tengteng

• College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China,

autor

Wang, Bin

• Zhejiang Key Laboratory of Artificial Intelligence of Things (AIoT) Network and Data Security, Hangzhou 310052, China,

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Identyfikatory

DOI

10.61822/amcs-2024-0030