Explaining the Saliency Map Sparsity of Adversarially-Trained Neural Networks

arXiv:2610.10666 · cs.LG, math.OC, stat.ML · Submitted 2026-10-07 · Read on arXiv

cs.LG, math.OC, stat.ML

Submitted: 2026-10-07

Updated: 2026-10-07

Code: https://github.com/MadryLab/cifar10_challenge

Terminology

• Adversarial Training — 47× in this paper · explained in 1 episode
• Sparsity — 32× in this paper · explained in 4 episodes
• Regularization — 30× in this paper · explained in 3 episodes
• Accuracy — 19× in this paper · explained in 1 episode
• Robustness — 17× in this paper · explained in 5 episodes
• Loss Function — 11× in this paper · explained in 2 episodes
• Generalization — 10× in this paper · explained in 13 episodes
• Generalization Bounds — 9× in this paper · explained in 2 episodes
• Activation Function — 8× in this paper · explained in 1 episode
• Adversarial Robustness — 8× in this paper · explained in 3 episodes
• Interpretability — 7× in this paper · explained in 15 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Generative AI — 2× in this paper · explained in 2 episodes
• Homogeneity — 2× in this paper · explained in 2 episodes
• Projected Gradient Descent — 2× in this paper
• Adam — 1× in this paper · explained in 2 episodes
• Adversarial Attacks — 1× in this paper · explained in 1 episode
• Adversarial Examples — 1× in this paper · explained in 2 episodes
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Explainable AI (XAI) — 1× in this paper · explained in 7 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalizability — 1× in this paper · explained in 6 episodes

Sources

• A Remark on the Anisotropic Outer Minkowski content
• Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
• SmoothGrad: removing noise by adding noise

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