Efficient local linearity regularization to overcome catastrophic overfitting

TL;DR

This paper introduces ELLE, a computationally efficient regularization method that effectively prevents catastrophic overfitting in single-step adversarial training by enforcing local linearity without double backpropagation.

Contribution

The paper proposes ELLE, a novel regularization term linked to loss curvature, which mitigates catastrophic overfitting efficiently in adversarial training, outperforming previous methods.

Findings

ELLE prevents catastrophic overfitting in various adversarial training regimes.

ELLE is computationally cheaper than previous regularization methods.

Adaptive ELLE (ELLE-A) improves performance in large perturbation settings.

Abstract

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly with respect to the input, this is however lost in single-step AT. To address CO in single-step AT, several methods have been proposed to enforce local linearity of the loss via regularization. However, these regularization terms considerably slow down training due to Double Backpropagation. Instead, in this work, we introduce a regularization term, called ELLE, to mitigate CO effectively and efficiently in classical AT evaluations, as well as some more difficult regimes, e.g., large adversarial perturbations and long training schedules. Our regularization term can be theoretically linked to curvature of the loss function and is computationally cheaper than previous methods by avoiding Double Backpropagation. Our thorough experimental validation demonstrates that our work does not suffer from CO, even in challenging settings where previous works suffer from it. We also notice that adapting our regularization parameter during training (ELLE-A) greatly improves the performance, specially in large $\epsilon$ setups. Our implementation is available in https://github.com/LIONS-EPFL/ELLE .