Explaining the Saliency Map Sparsity of Adversarially-Trained Neural Networks
The paper investigates why saliency maps from adversarially-trained neural networks are sparse—meaning they highlight only a few important image regions. It uses theoretical tools to show that adversarial training effectively selects a classifier with minimal gradients and a small Barron norm. This implies adversarial training implicitly enforces an $\ell_1$ regularization, leading to sharper, more focused saliency maps compared to naturally trained models.