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Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers

This repository contains the code and models necessary to replicate the results of our recent paper:

Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers
Hadi Salman, Greg Yang, Jerry Li, Huan Zhang, Pengchuan Zhang, Ilya Razenshteyn, Sebastien Bubeck
Blog post:

Our paper outperforms all existing provably L2-robust classifiers by a significant margin on ImageNet and CIFAR-10, establishing the state-of-the-art for provable L2-defenses.

Note: the models corresponding to the best certified accuracy for each of the radii in the above tables can be found here. Also, for the clean accuracies corresponding to these models, see Tables 16 and 17 in the paper.

Overview of the Repository

Our code is based on the open source code of Cohen et al (2019). The major content of our repo are:

  • code/ contains the code for our experiments.
  • data/ contains the log data from our experiments.
  • analysis/ contains the plots and tables, based on the contents of data/, that are shown in our paper.

Let us dive into the files in code/:

  1. the main code to adversarially train smoothed classifiers.
  2. the original training code of Cohen et al (2019) using Gaussian noise data augmentation.
  3. Given a pretrained smoothed classifier, returns a certified L2-radius for each data point in a given dataset using the algorithm of Cohen et al (2019).
  4. Given a pretrained smoothed classifier, predicts the class of each data point in a given dataset.
  5. an entry point for specifying which model architecture to use per dataset (Resnet-50 for ImageNet, Resnet-110 for CIFAR-10).
  6. contains our PGD and DDN attacks for smoothed classifiers (referred to as SmoothAdvPGD and SmoothAdvDDN in the paper).

Getting started

  1. git clone

  2. Install dependencies:

conda create -n smoothing-adversarial python=3.6
conda activate smoothing-adversarial
conda install numpy matplotlib pandas seaborn
pip install setGPU
conda install pytorch torchvision cudatoolkit=10.0 -c pytorch # for Linux
  1. Download our trained models from here. Then move the downloaded models.tar.gz into the root directory of this repo. Run tar -xzvf models.tar.gz to extract the models.

  2. If you want to run ImageNet experiments, obtain a copy of ImageNet and preprocess the val directory to look like the train directory by running this script. Finally, set the environment variable IMAGENET_DIR to the directory where ImageNet is located.

  3. Let us try to certify the robustness of one of our adversarially trained CIFAR-10 models.

python code/ cifar10 $model 0.12 $output --skip 20 --batch 400

Check the results in certification_output. You should get similar to these results.


Let us train a smoothed resnet110 CIFAR-10 classifier using SmoothAdv-ersarial training (see our paper), certify its robustness, and attack it.

Adversarial training

  • Train the model via 10 step (smooth) PGD adversarial training with ε=64/255, σ=0.12, and m_train=2
python code/ cifar10 cifar_resnet110 model_output_dir --batch 256 --noise 0.12 --gpu 0 --lr_step_size 50 --epochs 150 --adv-training --attack PGD --num-steps 10 --epsilon 64 --train-multi-noise --num-noise-vec 2 --warmup 10

For a faster result, start from an ImageNet pretrained model and fine-tune for only 30 epochs! We are open-sourceing 16 ImageNet pretrained models (see the imagenet32 folder here) that are trained using our code. Use the one with the desired ε and σ as shown below

python code/ cifar10 cifar_resnet110 model_output_dir --batch 256 --noise 0.12 --gpu 0 --lr 0.001 --epochs 30 --adv-training --attack PGD --num-steps 10 --epsilon 64 --train-multi-noise --num-noise-vec 2 --resume --pretrained-model pretrained_models/imagenet32/PGD_2steps/eps_64/imagenet32/resnet110/noise_0.12/checkpoint.pth.tar

If you even cannot wait for fine-tuning to finish, dont worry! We have a fine-tuned model ready for you. Simply set


and contiue with the example!


  • Certify the trained model on CIFAR-10 test set using σ=0.12
python code/ cifar10 $model_output_dir/checkpoint.pth.tar 0.12 certification_output --batch 400 --alpha 0.001 --N0 100 --N 100000

will load the base classifier saved at $model_output_dir/checkpoint.pth.tar, smooth it using noise level σ=0.12, and certify every image from the cifar10 test set with parameters N0=100, N=100000 and alpha=0.001.

Visualize robustness plots

Repeating the above two steps (Training and Certification) for σ=0.12, 0.25, 0.5, and 1.0 allows you to generate the below plot. Simply run:

python code/

This generate the below plot using our certification results. Modify the paths inside to point to your certification_output in order to plot your results.


  • Predict the classes of CIFAR-10 test set using σ=0.12
python code/ cifar10 $model_output_dir/checkpoint.pth.tar 0.12 prediction_output_dir --batch 400 --N 1000 alpha=0.001

will load the base classifier saved at $model_output_dir/checkpoint.pth.tar, smooth it using noise level σ=0.12, and classify every image from the cifar10 test set with parameters N=1000 and alpha=0.001.

Empirical attack

  • Attacking the trained model using SmoothAdvPGD with ε=64/255 or 127/255 or 255/255, T=20 steps, m_test=32, and σ=0.12. Then predicts the classes of the resulting adversarial examples. The flag --visualize-examples saves the first 1000 adversarial examples in the prediction_output_dir.
python code/ cifar10 $model_output_dir/checkpoint.pth.tar 0.12 prediction_output_dir --batch 400 --N 1000 --attack PGD --epsilon 64 --num-steps 20 --num-noise-vec 32 --visualize-examples 

python code/ cifar10 $model_output_dir/checkpoint.pth.tar 0.12 prediction_output_dir --batch 400 --N 1000 --attack PGD --epsilon 127 --num-steps 20 --num-noise-vec 32 --visualize-examples 

python code/ cifar10 $model_output_dir/checkpoint.pth.tar 0.12 prediction_output_dir --batch 400 --N 1000 --attack PGD --epsilon 255 --num-steps 20 --num-noise-vec 32 --visualize-examples 

Replicate our tables and figures

We provide code to generate all the tables and results of our paper. Simply run

python code/

This code reads from data/ i.e. the logs that were generated when we certifiied our trained models, and automatically generates the tables and figures that we present in the paper.

Below are example plots from our paper which you will be able to replicate by running the above code.

Download our pretrained models

You can download our trained models here. These contain all our provably robust models (that achieve SOTA for provably L2-robust image classification on CIFAR-10 and ImageNet) that we present in our paper.

The downloaded folder contains three subfolders: imagenet, imagenet32, and cifar10. Each of these contains subfolders with different hyperparameters for training imagenet, downscaled imagenet(32x32), and cifar10 classifiers respectively.

For example:

  • pretrained_models/cifar10/ contains PGD_2steps/, PGD_4steps/, DDN_2steps/ ..... corresponding to different attacks.
    • PGD_2steps/ contatins:
      • eps_64/, eps_127/, eps_255/, eps_512/, correpsonding to models trained with various ε (maximum allowed L2-perturbation).
      • jobs.yaml file that has the exact commands we used to train the models in PGD_2steps/ e.g.
- name: eps_64/cifar10/resnet110/noise_0.12
  sku: G1
  sku_count: 1
  - python code/ cifar10 cifar_resnet110 ./ --batch 256 --noise 0.12 --gpu
    0 --lr_step_size 50 --epochs 150 --adv-training --attack PGD --epsilon 64 --num-steps
    2 --resume --warmup 10
  id: application_1556605998994_2048
  results_dir: /mnt/_output/pt-results/2019-05-02/application_1556605998994_2048
  submit_args: {}
  tags: []
  type: bash

You should focus on the - name: and command: lines of every jobs.yaml as they reflect our experiments and their correpsonding commands. (Ignore the rest of the details which are specific to our job scheduling system).

Very Important Make sure to use the right data normalization layer if you want to use our trained models.

Below is the mapping betweem our trained models and the corresponding normalization layer that we used during training.

imagenet32/ --> NormalizeLayer
cifar10/finetune_cifar_from_imagenetPGD2steps/ --> NormalizeLayer
cifar10/self_training/ --> NormalizeLayer

imagenet/--> InputCenterLayer
cifar10/"everythingelse"/ --> InputCenterLayer

For NormalizeLayer, unomment get_normalize_layer and comment out get_input_center_layer

For InputCenterLayer, uncomment get_input_center_layer and comment out get_normalize_layer

Note that if you want to train your own models, it doesn't matter which layer you use for training (both will give very similar results) as longs as you use the same layer when doing prediciton or certification. Check this issue for more details.


We would like to thank Zico Kolter, Jeremy Cohen, Elan Rosenfeld, Aleksander Madry, Andrew Ilyas, Dimitris Tsipras, Shibani Santurkar, Jacob Steinhardt for comments and discussions.


If you have any question, or if anything of the above is not working, don't hestitate to contact us! We are more than happy to help!

  • Hadi Salman (hadi dot salman at microsoft dot com)
  • Greg Yang (gregyang at microsoft dot com)
  • Jerry Li (jerrl at microsoft dot com)
  • Ilya Razenshteyn (ilyaraz at microsoft dot com)


Code for our NeurIPS 2019 *spotlight* "Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers"





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