Wavelet Regularization Benefits Adversarial Training

Adversarial training methods are state-of-the-art (SOTA) empirical defense methods against adversarial examples. Many regularization methods have been proven to be effective with the combination of adversarial training. Nevertheless, such regularization methods are implemented in the time domain. Since adversarial vulnerability can be regarded as a high-frequency phenomenon, it is essential to regulate the adversarially-trained neural network models in the frequency domain. Faced with these challenges, we make a theoretical analysis on the regularization property of wavelets which can enhance adversarial training. We propose a wavelet regularization method based on the Haar wavelet decomposition which is named Wavelet Average Pooling. This wavelet regularization module is integrated into the wide residual neural network so that a new WideWaveletResNet model is formed. On the datasets of CIFAR-10 and CIFAR-100, our proposed Adversarial Wavelet Training method realizes considerable robustness under different types of attacks. It verifies the assumption that our wavelet regularization method can enhance adversarial robustness especially in the deep wide neural networks. The visualization experiments of the Frequency Principle (F-Principle) and interpretability are implemented to show the effectiveness of our method. A detailed comparison based on different wavelet base functions is presented. The code is available at the repository: \url{https://github.com/momo1986/AdversarialWaveletTraining}.

On Procedural Adversarial Noise Attack And Defense

Deep Neural Networks (DNNs) are vulnerable to adversarial examples which would inveigle neural networks to make prediction errors with small perturbations on the input images. Researchers have been devoted to promoting the research on the universal adversarial perturbations (UAPs) which are gradient-free and have little prior knowledge on data distributions. Procedural adversarial noise attack is a data-free universal perturbation generation method. In this paper, we propose two universal adversarial perturbation (UAP) generation methods based on procedural noise functions: Simplex noise and Worley noise. In our framework, the shading which disturbs visual classification is generated with rendering technology. Without changing the semantic representations, the adversarial examples generated via our methods show superior performance on the attack.