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Examples

We provide many examples of using our auto_LiRPA library, including robustness verification and certified robust training for fairly complicated networks and specifications. Please first install required libraries to run the examples:

cd examples
pip install -r requirements.txt

Basic Bound Computation and Robustness Verification of Neural Networks

We provide a very simple tutorial for auto_LiRPA at examples/vision/simple_verification.py. This script is self-contained. It loads a simple CNN model and compute the guaranteed lower and upper bounds using LiRPA for each output neuron under a L infinity perturbation.

cd examples/vision
python simple_verification.py

In this example, we compute lower and upper bounds of neural network outputs under input perturbations with a few different methods: IBP, CROWN-IBP, CROWN (backward) and optimized-CROWN (α-CROWN). For the adversarially trained network in this demonstration, IBP usually provides a very loose bound. CROWN can provide a reasonably tight bound almost instantly, and the tightest bounds can be obtained using α-CROWN within a few seconds.

Basic Certified Adversarial Defense Training

We provide a simple example of certified training. By default it uses CROWN-IBP to train a certifiably robust model:

cd examples/vision
python simple_training.py

The default model is a small ResNet model for MNIST, used in Wong et al. 2018. You should get less than 10% verified error (at Linf eps=0.3) after training.

We also provide an L0-norm option in simple_training.py and an example to use L0-norm certified training to train an MLP model. The IBP bounds for L0-norm is provided in Chiang et al., but here we also use the tighter backward mode perturbation analysis for L0-norm which is the first time in literature.

cd examples/vision
python simple_training.py --model mlp_3layer --norm 0 --eps 1

For CIFAR-10, we provided some sample models in examples/vision/models: e.g., cnn_7layer_bn, DenseNet, ResNet18, ResNeXt. For example, to train a ResNeXt model on CIFAR, use:

python cifar_training.py --batch_size 256 --model ResNeXt_cifar

See a list of supported models here. This command uses multi-GPUs by default. You probably need to reduce batch size if you have only 1 GPU. The CIFAR training implementation includes loss fusion, a technique that can greatly reduce training time and memory usage of LiRPA based certified defense.

Pretrained models for CIFAR-10: We released our CIFAR-10 certified defense models here. To compute verified error, please run:

python cifar_training.py --verify  --model cnn_7layer_bn --load saved_models/cnn_7layer_bn_cifar --eps 0.03137254901961

More example of CIFAR-10 training can be found in doc/paper.md.

Certified Adversarial Defense on Downscaled ImageNet and TinyImageNet with Loss Fusion

Loss fusion is essential for certified training on Tiny-ImageNet (200 classes) or downscaled ImageNet (1000 classes) using LiRPA based bounds (e.g., CROWN-IBP). This technique leads to ~50X speeding up on training time and also greatly reduces memory usage.

First, we need to prepare the data, for Tiny-ImageNet:

cd examples/vision/data/tinyImageNet
bash tinyimagenet_download.sh

To train the WideResNet model on Tiny-Imagenet:

cd examples/vision
python tinyimagenet_training.py --batch_size 100 --model wide_resnet_imagenet64

For downscaled ImageNet, please download raw images (Train and Val, 64x64, npz format) from Image-Net.org, under the "Download downsampled image data (32x32, 64x64)" section, to example/vision/data/ImageNet64/raw_data, decompress them and then run data preprocessing:

cd examples/vision/data/ImageNet64
python imagenet_data_loader.py

To train the WideResNet model on downscaled Imagenet:

cd examples/vision
python imagenet_training.py --batch_size 100 --model wide_resnet_imagenet64_1000class

Pretrained models for ImageNet: We released our certified defense models (trained with loss fusion) for Tiny-Imagenet and downscaled Imagenet. To evaluate the clean error and verified error:

# This is the model saved path.
MODEL=saved_models/wide_resnet_imagenet64_1000	
# Run evaluation.
python imagenet_training.py --verify --model wide_resnet_imagenet64_1000class --load $MODEL --eps 0.003921568627451

See more details in paper.md for these examples.

Certified Adversarial Defense Training for LSTM on MNIST

In examples/sequence, we have an example of training a certifiably robust LSTM on MNIST, where an input image is perturbed within an Lp-ball and sliced to several pieces each regarded as an input frame. To run the example:

cd examples/sequence
python train.py

Certifiably Robust Language Classifier with Transformer and LSTM

In examples/language, we show that our framework can support perturbation specification of word substitution, beyond Lp-ball perturbation. We perform certified training for Transformer and LSTM on a sentiment classification task.

First, download data and extract them to examples/language/data:

cd examples/language
wget http://download.huan-zhang.com/datasets/language/data_language.tar.gz
tar xvf data_language.tar.gz

We use $DIR to represent the directory for storing checkpoints. Then, to train a robust Transformer:

python train.py --dir=$DIR --robust --method=IBP+backward_train --train
python train.py --load=$DIR/ckpt_25 --robust --method=IBP+backward # for verification

And to train a robust LSTM:

python train.py --dir=$DIR --model=lstm --lr=1e-3 --robust --method=IBP+backward_train --dropout=0.5 --train
python train.py --model=lstm --load=$DIR/ckpt_25 --robust --method=IBP+backward # for verification

Pretrained models for Transformer/LSTM: We provide our certified defense models for Transformer and LSTM. To directly evaluate them:

# Download and evaluate our trained Transformer
wget http://web.cs.ucla.edu/~zshi/files/auto_LiRPA/trained/ckpt_transformer
python train.py --load=ckpt_transformer --robust --method=IBP+backward
# Download and evaluate our trained LSTM
wget http://web.cs.ucla.edu/~zshi/files/auto_LiRPA/trained/ckpt_lstm
python train.py --model=lstm --load=ckpt_lstm --robust --method=IBP+backward

Certified Robustness against Model Weight Perturbations and Certified Defense

In our paper (Xu et al. 2020), we provide an example for training a robust network under weight perturbations by applying LiRPA bounds on network weights rather than data inputs. Importantly, because our algorithm considers general computational graphs, and model weights are also inputs of a computational graph, LiRPA bounds can be naturally applied on model weights, immediately enabling robustness certification and certified defense against model weight perturbations. This also allows us to obtain a network that has a "flat" optimization landscape (a small change in weight parameters does not change the loss too much).

The run robustness verification and certified defense for model weight perturbations, run the following code example:

cd examples/vision
python weight_perturbation_training.py --norm 2 --bound_type CROWN-IBP

By default it uses the CROWN-IBP bound to efficiently bound model outputs under model weight perturbations, and the training process is reasonably fast. Other bound types such as the full backward (CROWN) bounds are also supported for weight perturbations.

Contribute Additional Examples

If you have an example based on auto_LiRPA that can be potentially helpful for other users, you are encouraged to create a pull request so that we can include your example here. Any contributions from the community will be greatly appreciated.

BibTeX Entries

If you find our library useful, please kindly cite our papers:

@article{xu2020automatic,
  title={Automatic perturbation analysis for scalable certified robustness and beyond},
  author={Xu, Kaidi and Shi, Zhouxing and Zhang, Huan and Wang, Yihan and Chang, Kai-Wei and Huang, Minlie and Kailkhura, Bhavya and Lin, Xue and Hsieh, Cho-Jui},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  year={2020}
}

@inproceedings{xu2021fast,
    title={{Fast and Complete}: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers},
    author={Kaidi Xu and Huan Zhang and Shiqi Wang and Yihan Wang and Suman Jana and Xue Lin and Cho-Jui Hsieh},
    booktitle={International Conference on Learning Representations},
    year={2021},
    url={https://openreview.net/forum?id=nVZtXBI6LNn}
}

@article{wang2021beta,
  title={{Beta-CROWN}: Efficient bound propagation with per-neuron split constraints for complete and incomplete neural network verification},
  author={Wang, Shiqi and Zhang, Huan and Xu, Kaidi and Lin, Xue and Jana, Suman and Hsieh, Cho-Jui and Kolter, J Zico},
  journal={arXiv preprint arXiv:2103.06624},
  year={2021}
}