NPAQ (Neural Property Approximate Quantifier) is a quantitative verification tool that can quantify robustness, fairness and trojan attack success for binarized neural networks (BNNs). This work is by Teodora Baluta, Shiqi Shen, Shweta Shinde, Kuldeep S. Meel and Prateek Saxena, as published in CCS 2019. NPAQ relies on approximate model counting and uses the latest version of ApproxMCv3.

To build on Linux you need the following:

• Python 2.7
• (currently z3 requirement but will this dependency will be eliminated when we cleanup more of the code)
• ApproxMC

First, compile the encoder:

cd mlp2cnf; make

Next, install the other requirements in a virtualenv (here, npaq):

mkvirtualenv npaq

pip install -r requirements.txt

./setup.sh

Unless you want NPAQ to only encode your problem to a CNF formula and not do any quantification (for whatever reason) you will not need approxmc. Otherwise, please follow the setup instructions for ApproxMC here and make sure approxmc is in your path.

It is always a good idea to check the options with python npaq --help from the project's root directory but we will go over the options below.

• Architecture: You can specify the number of blocks and neurons per block either as a JSON file (see [1]) or you can select from the predefined ones: {1blk_100, 2blk_100_50} See npaq/models/bnn.py for the definitions and project page for details on the BNN models in the benchmark.

• Dataset: By default, the dataset is MNIST (--dataset mnist), you can select UCI Adult dataset using the option --dataset uci_adult.

• Input size: The input size is a pair width,height where (--resize) and the dataset (--dataset).

• Encoding to CNF formulas: encode. This just encodes the BNN to a CNF formula. The encode option assumes there is a trained model in models/mnist/ in the format of a .pt file (PyTorch model). For example, for a BNN with architecture of 3 internal blocks with 200 neurons and an output block with 100 neuron-input trained over an input of 28x28 (the default MNIST input) the file name should be in the following format bnn_784_3blks_200_100.pt. Example query:

python npaq bnn --arch 1blk_100 --dataset uci_adult --resize 10,10 encode

• Quantify Fairness: quant-fair constraints_fname. To quantify fairness you need to specify the path to the constraints file. To reproduce the results in the paper, you need to select the right dataset --dataset uci_adult and the corresponding constraints file from the provided fairness constraints in the benchmarks. You can specify to just encode the property to a CNF formula without quantifying by adding the --just-encode flag. Example query:

python npaq bnn --arch 1blk_100 --dataset uci_adult --resize 1,66 quant-fair uci_adult-marital.txt

• Quantify Robustness: quant-robust perturb. To quantify robustness, specify the perturbation size as a L1-distance, i.e., the number of bits different in the adversarial example. You can specify to just encode the property to a CNF formula without quantifying by adding the --just-encode flag. Example query:

python npaq bnn --arch 1blk_100 --dataset mnist --resize 10,10 quant-robust 2

The query above is taking an image from mnist at random. You may specify a concrete input as following:

python npaq bnn --encoder card --arch 1blk_100 --dataset mnist --resize 10,10 quant-robust 2 --concrete_ip concrete_inputs --num_samples 1

• Trojan Attack Success: The trojan attack success property reduces to quantifying how many inputs with specific input constraints (the trigger constraints found under trojan_imgs folder) are labeled as the attack's target label. We encode the trojan sucess for all labels and all epochs for a specific architecture as follows:

python npaq bnn --encoder card --arch 1blk_100 --dataset mnist --resize 10,10 quant-label --w_trojan trojan-success --just-encode

We provide the trained models used in the paper as .pt files in at our project page. Just copy them in the models/mnist folder and specify the architecture with the --arch option

We used the PyTorch implementation of the binarized neural networks available at BinaryNet.pytorch, hence there might be differences in the API between current PyTorch versions and the older versions torch==1.0.1.post2 and torchvision==0.2.2.post3. To use GPU you should make sure you have the right version for cuda and cuDNN (these should ship with the pytorch installation). If there are any issues with running on GPU, you may use the --no-cuda flag to disable GPU.

You can train your own BNNs using NPAQ. For example, you may write the following command to train a BNN on the MNIST dataset:

python npaq bnn --dataset mnist train --no-cuda

See training help menu with python npaq bnn train --help.

If you use NPAQ, please cite our work.

The benchmarks used in our evaluation can be found here. More info on the project page, NPAQ.

Checkout our subsequent work on this in PROVERO.