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To ensure that our experiments perform fair comparison with previous work, we mainly adopt the public codes from TRADES, and make some modifications on them to run the trials.

• Train PGD-AT

python train_adv_cifar10.py --loss=pgd

Here we activate the HE operation and set the scale s and margin m.

• Train PGD-AT + HE:

python train_adv_cifar10.py --loss=pgd_he --s=10.0 --m=0.2 --wd 5e-4

• Train TRADES + HE:

python train_adv_cifar10.py --loss=trades_he --beta=6.0 --s=15.0 --m=0.2

• Train ALP + HE:

python train_adv_cifar10.py --loss=alp_he --beta=0.5 --s=20.0 --m=0.3

Our pre-trained models for CIFAR-10 WideResNets (in width factor 20 and 10) are available, including PGD+HE-wide20 and PGD+HE-wide10. We find that our HE mechanism is more suitable for the PGD-AT framework, since its principled formula is more aligned with our analysis.

To evaluate the performance of the trained models under the PGD attacks (default PGD-20), the running command is

  $ python pgd_attack_cifar10.py

We also evaluate a reliable attack, named AutoAttack, the running command is

  $ python test_autoattack.py --model-path=$CHECKPOINT_PATH$ --use_FNandWN --widen_factor=20

To evaluate the performance of the general robustness, we also test on the CIFAR-10-C datasets by Hendrycks & Dietterich (ICLR 2019). The running command is

  $ python general_attack_cifar10.py