Title: Towards fast and effective single-step adversarial training. Abstract: Recently, Wong et al. (2020) showed adversarial training with single-step FGSM leads  to  a  characteristic  failure  mode  named catastrophic  overfitting (CO),  in which  a  model  becomes  suddenly  vulnerable  to  multi-step  attacks.   Moreover, they showed adding a random perturbation prior to FGSM (RS-FGSM) seemed to be sufficient to prevent CO. However, Andriushchenko & Flammarion (2020) observed that RS-FGSM still leads to CO for larger perturbations and argue that the  only  contribution  of  the  random  step  is  to  reduce  the  magnitude  of  the  attacks.  They suggest a regularizer (GradAlign) that avoids CO but is significantly more expensive than RS-FGSM. In this work,  we methodically revisit the role of noise and clipping in single-step adversarial training.  Contrary to previous intuitions, we find that not clipping the perturbation around the clean sample and using a stronger noise is highly effective in avoiding CO for large perturbation radii,  despite leading to an increase in the magnitude of the attacks.   Based on these observations, we propose a method called Noise-FGSM (N-FGSM), which attacks noise-augmented samples directly using a single-step. Empirical analyses on a large suite of experiments show that N-FGSM is able to match or surpass the performance of GradAlign while achieving a 3x speed-up.