Adversarial Training Without Input Gradients via Low-Rank Householder Expansions

The paper introduces a method for adversarial training that avoids computing input gradients by using a low‑rank Householder expansion (LRHE) to directly generate small‑norm adversarial examples from a network’s parameters. This approach requires only forward passes and standard back‑propagation, eliminating the inner maximization loop and reducing computational cost to roughly 2.8 PGD steps per epoch. The resulting models achieve comparable robustness to multi‑step PGD training for small relative ε budgets, demonstrating the feasibility of gradient‑free adversarial training.

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