CROWN: A Neural Network Verification Framework

We proposed a new framework, CROWN, to certify robustness of neural networks with general activation functions including but not limited to ReLU, tanh, sigmoid, arctan, etc. CROWN is efficient and can deliver lower bounds of minimum adversarial distortions with guarantees (the so-called certified lower bound or certified robustness).

We compare CROWN with various certified lower bounds methods including Global Lipschitz constant and Fast-Lin and show that CROWN can certify much large lower bound than the Global Lipschitz constant based approach while improve the quality (up to 28%) of robustness lower bound on ReLU networks of state-of-the-art robustness certification algorithms Fast-Lin. We also compare CROWN with robustness score estimate CLEVER and adversarial attack methods (CW,EAD). Please See Section 4 and Appendix E of our paper for more details.

Cite our work:

Huan Zhang*, Tsui-Wei Weng*, Pin-Yu Chen, Cho-Jui Hsieh and Luca Daniel, "Efficient Neural Network Robustness Certification with General Activation Functions", NuerIPS 2018. (* Equal Contribution)

@inproceedings{zhang2018crown,
  author = "Huan Zhang AND Tsui-Wei Weng AND Pin-Yu Chen AND Cho-Jui Hsieh AND Luca Daniel",
  title = "Efficient Neural Network Robustness Certification with General Activation Functions",
  booktitle = "Advances in Neural Information Processing Systems (NuerIPS)",
  year = "2018",
  month = "dec"
}

Prerequisites

The code is tested with python3 and TensorFlow v1.8 and v1.10. We suggest to use Conda to manage your Python environments. The following Conda packages are required:

conda install pillow numpy scipy pandas tensorflow-gpu h5py
conda install --channel numba llvmlite numba
grep 'AMD' /proc/cpuinfo >/dev/null && conda install nomkl

You will also need to install Gurobi and its python bindings if you want to try the LP based methods.

After installing prerequisites, clone our repository:

git clone https://github.com/huanzhang12/CROWN-Robustness-Certification.git
cd CROWN-Robustness-Certification

Our pretrained models can be download here:

wget http://jaina.cs.ucdavis.edu/datasets/adv/relu_verification/models_crown.tar
tar xvf models_crown.tar

This will create a models folder. We include all models reported in our paper.

How to Run

We have provided an interfacing script, run.sh to reproduce the experiments in our paper.

Usage: ./run.sh model modeltype layer neuron norm solver target --activation ACT

• model: mnist or cifar
• modeltype: vanilla (undefended), adv_retrain (adversarially trained)
• layer: number of layers (2,3,4 for MNIST and 5,6,7 for CIFAR)
• neuron: number of neurons for each layer (20 or 1024 for MNIST, 2048 for CIFAR)
• norm: p-norm, 1,2 or i (infinity norm)
• solver: adaptive (CROWN-adaptive for improved bounds for ReLU Networks), general (CROWN-general for networks with general activation functions)
• target: least, top2 (runner up), random, untargeted
• --activation: followed by a activation function of network (relu, tanh, sigmoid or arctan)

The main interfacing code is main.py, which provides additional options. Use python main.py -h to explore these options.

Examples

For example, to evaluate the Linf robustness of MNIST 3*[1024] adversarially trained model using CROWN-adaptive on least likely targets, run

./run.sh mnist adv_retrain 3 1024 i adaptive least

A log file will be created in the logs folder. The last line of the log (starting with [L0]) will report the average robustness lower bounds on 100 MNIST test images. Lines starting with [L1] reports per-image information.

 tail logs/mnist/3/mnist_adv_retrain_3_1024_Li_adaptive_least_none_*.log

[L0] model = models/mnist_3layer_relu_1024_adv_retrain, avg robustness_gx = 0.21916, numimage = 96, total_time = 85.4255

The adversarially trained model (with adversarial examples crafted by PGD with eps = 0.3) has a robustness lower bound of 0.21916.

Similarly, to evaluate the L1 robustness of MNIST 3*[20] model with tanh activation on random targets using CROWN-general, run the following command:

./run.sh mnist vanilla 3 20 1 general random --activation tanh

The following result in log file is obtained:

[L0] model = models/mnist_3layer_tanh_20, avg robustness_gx = 1.42974, numimage = 97, total_time = 14.1968

Training your own models and evaluating your own models with various methods

0. We provide our pre-trained MNIST and CIFAR models that are used in the paper here.

1. To train a new multilayer perceptron (MLP) model, we provide the training script train_nlayer.py to train a n-layer MLP with k hidden neurons per layer. For example, n = 4, k = 20, dataset = MNIST, activation = relu, save model name = mnist_4layer_relu_20:

python train_nlayer.py 20 20 20 --model mnist --activation relu --lr LEARNING_RATE --epochs EPOCHS --modelfile mnist_4layer_relu_20

2. Put your saved model mnist_4layer_relu_20 in the folder models:

mkdir models
mv mnist_4layer_relu_20 models/ 

3. Evaluate the saved model mnist_4layer_relu_20 and compare with the following methods reported in the paper: CROWN, Fast-Lin, Fast-Lip, Op-norm, LP-Full, LP

• If you want to run CROWN-Ada (the adaptive upper and lower bounds on ReLU activations, this improves Fast-Lin's result) with random target and L_inf norm on one image:

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method general 

• If you want to run Fast-Lin on the same model:

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method ours

• If you want to run Fast-Lip on the same model:

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method ours --lipsbnd fast

• If you want to run Op-norm (the global lipschitz constant based approach, see [3])

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method spectral 

• If you want to run LP-Full (the convex outer polytope approach, casted as Linear/Quadratic programming, see Formulation in [18]):

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method LPFULL

(please install gurobipy in advance)

• If you want to run LP (the convex outer polytope approach. The intermediate bounds are obtained by Fast-Lin and only solve one LP at the last layer.)

python main.py --model mnist --hidden 20 --numlayer 4 --targettype random --norm i --numimage 1 --activation relu --method LP

For more argument options, please use --help to check:

python train_nlayer.py --help
python main.py --help

Other notes

Note that in our experiments we set the number of threads to 1 for a fair comparison to other methods. To enable multithreaded computing, changing the number 1 in run.sh to the number of cores in your system.

NUMBA_NUM_THREADS=1 MKL_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1

The code in this repository is released under Apache-2.0 License and is intended to reproduce paper results only (see LICENSE for more details).