Robustness Cannot be Reduced to Regularization: Studying Adversarial Training Beyond the Linear Case
The vulnerability of ML models to adversarial examples has recently emerged as a major concern. While adversarial training is one of the most effective countermeasures to this issue, its high computational cost remains an obstacle to practical deployment. Recent progress in reducing this cost has relied, in the case of linear models, on a formal equivalence between the adversarial risk and a simpler form of regularized risk. This enabled significantly more efficient training procedures, which naturally raises the question of whether such an equivalence can be extended beyond linear models. In this work, we formally show that no such equivalence is possible for two-layer networks. Our proo...
| Authors | David A. R. Robin, Rafael Pinot, Yann Chevaleyre |
|---|---|
| Primary category | cs.LG |
| Published | 19 June 2026 |
| Last updated at source | 19 June 2026 |
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