This is the code for the paper "Understanding Generalization in Adversarial Training via the Bias-Variance Decomposition".

• Python
• Pytorch (1.3.1)
• CUDA
• numpy

There are 4 folders, cifar10, cifar100, 2d, and logistic_regression. First cd into the directory.

To run the L-infinity adversarial training with eps=8.0 on the CIFAR10 dataset saved to folder model_Linf_eps8, run

python train_adv.py --norm l_inf --fname model_Linf_eps8 --epsilon 8 --width-factor 10

• norm: l_p norm for adversarial attack.
• width-factor: width-factor of the WideResNet-28.
• epochs: how many epochs for training.
• fname: specify the name of the folder for saving logs and checkpoints.

To evaluate the standard (squared loss) bias-variance on the above model model_Linf_eps8 on epoch 200, run

python eval_adv_bv_mse.py  --fname model_Linf_eps8 --resume 200 --attack none

To evaluate the adversarial (squared loss) bias-variance on the above model model_Linf_eps8 on epoch 200 with perturbation size eps=6, run

python eval_adv_bv_mse.py  --fname model_Linf_eps8 --resume 200 --attack pgd --epsilon 6 

To evaluate the standard (cross-entropy) bias-variance on the above model model_Linf_eps8 on epoch 200, run

python eval_adv_bv_kl.py  --fname model_Linf_eps8 --resume 200 --attack none

• fname: specify the name of the folder for evaluation.
• resume: specify the epoch of the train models for evaluation.
• attack: attack method for evaluation.
• epsilon: perturbation radius of the adversarial attack.

The results (including bias and variance) will be save in 'bv_mse_log_epoch{}_eps{}.txt'.format(resume, epsilon) (for mse)/bv_kl_log_epoch{}_eps{}.txt'.format(resume, epsilon)(for cross-entropy), in the folder fname.

The log file includes the following,

To run the L-infinity adversarial training with eps=8.0 on the CIFAR100 dataset saved to folder model_Linf_eps8, run

python train_adv.py --norm l_inf --fname model_Linf_eps8 --epsilon 8

To evaluate the standard (squared loss) bias-variance on the above model model_Linf_eps8 on epoch 200, run

python eval_adv_bv_mse.py  --fname model_Linf_eps8 --resume 200 --attack none

To reproduce the 2D box example results, run 2d_bv.ipynb.

To reproduce the logistic_regression results, run logistic_regression.ipynb.

For more experimental and technical details, please check our paper.

@article{yu2021understanding,
  title={Understanding Generalization in Adversarial Training via the Bias-Variance Decomposition},
  author={Yaodong Yu and Zitong Yang and Edgar Dobriban and Jacob Steinhardt and Yi Ma},
  journal={arXiv preprint arXiv:2103.09947},
  year={2021}
}