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Adversarial Training Without Input Gradients via Low-Rank Householder Expansions

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

This work concerns adversarial training against the small-norm adversarial examples that arise from the inherent input instability of a trained deep neural network. Examples in this class are small as measured in the relative $\ell^2$-norm, and therefore lie in the neighborhood of the input on which the model acts approximately linearly, the regime in which the perturbation remains imperceptible. We first show that such examples can be computed directly from the trained network parameters, without input gradient iterations, by means of a linearization called the low-rank Householder expansion

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