Wavelet scattering networks for stable classification in adversarial settings

Abstract

Deep neural networks achieve impressive performance in image and speech recognition, yet they are sensitive to small input perturbations known as adversarial examples that can cause critical misclassifications. This vulnerability motivates classification systems that are inherently stable and robust. In this work, we first demonstrate the susceptibility of conventional convolutional neural networks (CNNs) to adversarial attacks generated via the Fast Gradient Sign Method (FGSM) on the MNIST dataset. We then propose an alternative based on the wavelet scattering transform, which provides translation-invariant and deformation-stable representations through predefined wavelet filters. The scattering network outputs are subsequently used as features for a downstream classifier. Experiments on the full MNIST test set (10,000 samples) show that CNN accuracy deteriorates drastically as the perturbation magnitude ε increases under FGSM attacks, while the scattering-based model preserves significantly higher accuracy across the tested range. Although our proposed technique has only been tested using the MNIST dataset under FGSM attacks, the results obtained can thus lay down a great basis for future studies in evaluating the method's generalizability across more complicated datasets and various types of attacks.