DeepDefense: Robust Learning via Layer-Wise Gradient-Feature Alignment

Deep neural networks are known to be vulnerable to adversarial perturbations, which are small, carefully crafted inputs that lead to incorrect predictions. In this paper, we propose DeepDefense, a novel defense framework that applies Gradient-Feature Alignment (GFA) regularization across multiple layers to suppress adversarial vulnerability. By aligning input gradients with internal feature representations, DeepDefense promotes a smoother loss landscape in tangential space, also known as feature space, thereby reducing the model's sensitivity to adversarial noise. We provide insights into how adversarial perturbations can be decomposed into radial and tangential components and demonstrate that alignment suppresses loss variation in tangential space, where most attacks are effective. Empirically, our method achieves significant improvements in robustness against both gradient-based and optimization-based attacks. For example, on CIFAR-10, CNN models trained with DeepDefense outperform standard adversarial training by up to 15.2 percent under APGD attacks and 24.7 percent under FGSM attacks. Against optimization-based attacks such as DeepFool and EADEN, DeepDefense requires perturbation magnitudes that are 20 to 30 times larger to cause misclassification, indicating stronger decision boundaries and a flatter loss landscape. Our approach is architecture-agnostic, simple to implement, and highly effective, offering a promising direction for improving the adversarial robustness of deep learning models.