This repository is the official implementation of EEV, a system for efficient and exact (complete and sound) verification of binarized neural networks.

Verifiers that claim to be exact for real-valued neural networks face two fundamental challenges due to the complexity of floating point arithmetic:

1. They are slow.
2. They provide no correctness guarantee due to floating point errors, which can be exploited to construct adversarial examples for networks that are claimed to be robust by an exact verifier.

We present the first exact verification results with guaranteed correctness for adversarial robustness of neural networks on MNIST and CIFAR10, which is also several orders of magnitude faster compared to previous verification results.

Our main contributions:

1. We incorporate native support for reified cardinality constraints into a SAT solver, which improves the performance of BNN verification by more than a factor of one hundred compared to an unmodified SAT solver.
2. We propose to train solver-friendly BNNs by inducing balanced layerwise sparsity and low cardinality bounds.
3. We propose adaptive gradient cancelling to train verifiably robust BNNs with the PGD adversary.
4. We present the first exact verification of robustness against Linf-norm bounded input perturbations of convolutional BNNs on MNIST and CIFAR10.

Comparing with a state-of-the-art real-valued verifier on CIFAR10:

The code needs python >= 3.7, and a recent C++ compiler that supports C++17. It is supposed to be cross-platform, but has only been tested on Arch Linux. The code is known to work with pytorch 1.4.0 and 1.6.0. Assuming you are starting in a fresh virtualenv, run the following command to install the dependencies:

pip install --upgrade pip
pip install tqdm torch torchvision cython opencv-python 'python-sat[pblib,aiger]'

If the newest libraries do not work with the code, you can try installing the versions that we have tested with:

pip install --upgrade pip
pip install -r requirements.txt

MiniSatCS is the SAT solver proposed in this work. It is hosted in another github repository. Please first initialize all the submodules:

git submodule update --init --recursive

Then build MiniSatCS:

pushd eevbnn/minisatcs
mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=RelWithDebInfo
make -j$(nproc)
popd

Dependencies needed to run the benchmarks of baseline methods for comparison:

1. To run the Z3 benchmarks, install Z3 by pip install z3-solver.
2. To run the RoundingSat benchmarks, download soplex-5.0.1.tgz and place it at eevbnn/roundingsat_repo, and then execute ./eevbnn/roundingsat_build.sh.

The implementation is in the eevbnn python package. A few modules have main functions and can be executed from command line, such as python -m eevbnn train_bin for training or python -m eevbnn eval_bin for verification. If you need to verify your own BNN models using EEV, please have a look at class ModelVerifier in eevbnn/eval_bin.py. The pretrained models can be downloaded here. To run the verifier:

# Download and extract the pretrained models

# verifying with MiniSatCS and eps=0.08
python -m eevbnn eval_bin -e 0.08 output-0527/mnist-mlp/last.pth

# verifying with RoundingSat
python -m eevbnn eval_bin -e 0.08 output-0527/mnist-mlp/last.pth  --sat roundingsat

To reproduce the results in the paper:

1. Run ./train_all_parallel.sh workdir to train all the models. The script assumes the workstation configuration reported in the paper, which uses two GPUs and six parallel processes for training. You may want to modify the GPU_LIST and JOBS variables. The training tasks are described in train_all_task.txt.
2. Run ./eval_all_parallel.sh workdir to verify all the models. This script also assumes the workstation configuration reported in the paper, and you may need to modify the variables. The verification tasks are described in eval_all_task.txt.
3. Run ./attack_all_parallel.sh workdir run the PGD attack.
4. Run ./gen_paper_fig.py workdir workdir/fig to generate the figures, tables, and numbers reported in the paper.

Note that the train_all_parallel.sh and eval_all_parallel.sh scripts are designed to be interruptible. Running the scripts again with the same workdir would continue from previous checkpoints.

@inproceedings{jia2020efficient,
 author = {Jia, Kai and Rinard, Martin},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {H. Larochelle and M. Ranzato and R. Hadsell and M. F. Balcan and H. Lin},
 pages = {1782--1795},
 publisher = {Curran Associates, Inc.},
 title = {Efficient Exact Verification of Binarized Neural Networks},
 url = {https://proceedings.neurips.cc/paper/2020/file/1385974ed5904a438616ff7bdb3f7439-Paper.pdf},
 volume = {33},
 year = {2020}
}