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As requested by IBM, this repository is moved to, but we aim to keep both repositories synced up. The code is released under Apache License v2.

CLEVER: A Robustness Metric For Deep Neural Networks

CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is a metric for measuring the robustness of deep neural networks. It estimates the robustness lower bound by sampling the norm of gradients and fitting a limit distribution using extreme value theory. CLEVER score is attack-agnostic; a higher score number indicates that the network is likely to be less venerable to adversarial examples. CLEVER can be efficiently computed even for large state-of-the-art ImageNet models like ResNet-50 and Inception-v3.

For more details, please see our paper:

  1. Tsui-Wei Weng*, Huan Zhang*, Pin-Yu Chen, Jinfeng Yi, Dong Su, Yupeng Gao, Cho-Jui Hsieh and Luca Daniel,"Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach", ICLR 2018

  2. Tsui-Wei Weng*, Huan Zhang*, Pin-Yu Chen, Aurelie Lozano, Cho-Jui Hsieh and Luca Daniel, "On Extensions of CLEVER: A Neural Network Robustness Evaluation Algorithm", IEEE GlobalSIP 2018

* Equal contribution

Cite our works

  author = "Tsui-Wei Weng AND Huan Zhang AND Pin-Yu Chen AND Jinfeng Yi AND Dong Su AND Yupeng Gao AND Cho-Jui Hsieh AND Luca Daniel",
  title = "Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach",
  booktitle = "International Conference on Learning Representations (ICLR)",
  year = "2018",
  month = "may"
  author = "Tsui-Wei Weng AND Huan Zhang AND Pin-Yu Chen AND Aurelie Lozano AND Cho-Jui Hsieh AND Luca Daniel",
  title = "On Extensions of CLEVER: A Neural Network Robustness Evaluation Algorithm",
  booktitle = "IEEE Global Conference on Signal and Information Processing (GlobalSIP)",
  year = "2018",
  month = "nov"


  • Aug 6, 2018: CLEVER evaluation with input transformations (e.g., staircase function or JPEG compression) is implemented via BPDA (Backward Pass Differentiable Approximation)
  • Aug 16, 2018: added 2nd order CLEVER evaluation implementation, which can be used to evaluate robustness on classifiers that are twice-differentiable.
  • Oct 23, 2018: Our work on extension of CLEVER is accepted by GlobalSIP 2018: On Extensions of CLEVER: A Neural Network Robustness Evaluation Algorithm

Discussion with Ian Goodfellow and Our Clarifications

We received some inquires on Ian Goodfellow's commentGradient Masking Causes CLEVER to Overestimate Adversarial Perturbation Size” on our paper. We thank Ian for the discussion but the comments are inappropriate and not applicable to our paper. CLEVER is intended to be a tool for network designer and to evaluate network robustness in the “white-box” setting. Especially, the argument that on digital computers all functions are not Lipschitz continuous and behave like a staircase function (where the gradient is zero almost everywhere) is incorrect. Under the white-box setting, gradients can be computed via automatic differentiation, which is well supported by mature packages like TensorFlow. See our reply and discussions with Ian Goodfellow on gradient masking and implmentation on digital computers.

Setup and train models

The code is tested with python3 and TensorFlow v1.3, v1.4 and v1.5. The following packages are required:

sudo apt-get install python3-pip python3-dev
sudo pip3 install --upgrade pip
sudo pip3 install six pillow scipy numpy pandas matplotlib h5py posix_ipc tensorflow-gpu

Then clone this repository:

git clone

Prepare the MNIST and CIFAR-10 data and models with different activation functions:

python3 --model mnist --modeltype cnn --activation tanh 32 32 64 64 200 200 
python3 --model cifar --modeltype cnn --activation tanh 64 64 128 128 256 256 

To download the ImageNet models:


To prepare the ImageNet dataset, download and unzip the following archive:

and put the imgs folder in ../imagenetdata, relative to the CLEVER repository. This path can be changed in

cd ..
mkdir imagenetdata && cd imagenetdata
tar zxf img.tar.gz
cd ../CLEVER

How to run

Step 1: Collect gradients

The first step for computing CLEVER score is to collect gradient samples. The following command collects gradient samples for 10 images in MNIST dataset; for each image, 3 target attack classes are chosen (random, top-2 and least likely). Images that are classified incorrectly will be skipped, so you might get less than 10 images. The default network used has a 7-layer AlexNet-like CNN structure.

python3 --dataset mnist --numimg 10

Results will be saved into folder lipschitz_mat/mnist_normal by default (which can be changed by specifying the --saved <folder name> parameter), as a few .mat files.

Run python3 -h for additional help information.

Updated: For model with input transformation, use an additional parameter --transform. Currently three input transformations are supported (bit-depth reduction, JPEG compression and PNG compression, corresponding to defend_reduce, defend_jpeg, defend_png options). For example:

python3 --dataset cifar --numimg 10 --transform defend_jpeg

You should expect roughly the same CLEVER score with input transformations, as input transformations do not increase model's intrinsic robustness and can be broken by BPDA. See for the implementations of input transformations.

Updated: To run 2nd order clever score, can be used and set order = 2:

./ model modeltype nsamp niters activation order target gpuNum

For example, to get 1000 samples of 2nd order clever with 100 iterations on a mnist 7-layer cnn model with tanh activation and random target:

./ mnist normal 1000 100 tanh 2 rand 

To get samples for the original clever score (1st order approximation), set order = 1.

Step 2: Compute the CLEVER score

To compute CLEVER score using the collected gradients, run with data saving folder as a parameter:

python3 lipschitz_mat/mnist_normal

Run python3 -h for additional help information.

Step 3: How to interpret the score?

At the end of the output of, you will see three [STATS][L0] lines similar to the following:

[STATS][L0] info = least, least_clever_L1 = 2.7518, least_clever_L2 = 1.1374, least_clever_Li = 0.080179
[STATS][L0] info = random, random_clever_L1 = 2.9561, random_clever_L2 = 1.1213, random_clever_Li = 0.075569
[STATS][L0] info = top2, top2_clever_L1 = 1.6683, top2_clever_L2 = 0.70122, top2_clever_Li = 0.050181

The scores shown are the average scores for all (in the example above, 10) images, with three different target attack classes: least likely, random and top-2 (the class with second largest probability). Three scores are provided: CLEVER_L2, CLEVER_Linf and CLEVER_L1, representing the robustness for L2, L_infinity and L1 perturbations. CLEVER score for Lp norm roughly reflects the minimum Lp norm of adversarial perturbations. A higher CLEVER score indicates better network robustness, as the minimum adversarial perturbation is likely to have a larger Lp norm. As CLEVER uses a sampling based method, the scores may vary slightly for different runs.

More Examples

For example, the following command will evaluate the CLEVER scores on 1 ImageNet image, for a 50-layer ResNet model. We set the number of gradient samples per iterations to 512, and run 100 iterations:

python3 --dataset imagenet --model_name resnet_v2_50 -N 512 -i 100
python3 lipschitz_mat/imagenet_resnet_v2_50/


For this image (139.00029510.jpg, which is the first image given the default random seed) in dataset, the original class is 139 (bustard), least likely class is 20 (chickadee), top-2 class is 82 (ptarmigan), random class target is 708 (pay-phone). (These can be observed in [DATAGEN][L1] lines of the output of We get the following CLEVER scores:

[STATS][L0] info = least, least_clever_L1 = 8.1393, least_clever_L2 = 0.64424, least_clever_Li = 0.0029474 
[STATS][L0] info = random, random_clever_L1 = 4.6543, random_clever_L2 = 0.61181, random_clever_Li = 0.0023765 
[STATS][L0] info = top2, top2_clever_L1 = 0.99283, top2_clever_L2 = 0.13185, top2_clever_Li = 0.00062238

The L2 CLEVER score for the top-2, random and least-likely classes are 0.13185, 0.61181 and 0.64424, respectively. It indicates that it is very easy to attack this image from class 139 to 82. We then run the CW attack, which is the strongest L2 attack to date, on this image with the same three target classes. The distortion of adversarial images are 0.1598, 0.82025, 0.85298 for the three targets. Indeed, to misclassify the image to class 82, only a very small distortion (0.1598) is needed. Also, the CLEVER scores are (usually) less than the L2 distortions observed on adversarial examples, but are not too small to be useless, reflecting the nature that CLEVER is an estimated robustness lower bound.

CLEVER also has an untargeted version, which is essentially the smallest CLEVER score over all possible target classes. The following examples shows how to compute untargeted CLEVER score for 10 images from MNIST dataset, on the 2-layer MLP model:

python3 --data mnist --model_name 2-layer --target_type 16 --numimg 10
python3 --untargeted ./lipschitz_mat/mnist_2-layer/

Target type 16 (bit 4 set to 1) indicates that we are collecting gradients for untargeted CLEVER score (see python3 -h for more details). The results will look like the following:

[STATS][L0] info = untargeted, untargeted_clever_L1 = 3.4482, untargeted_clever_L2 = 0.69393, untargeted_clever_Li = 0.035387

For datasets which have many classes, it is very expensive to evaluate the untargeted CLEVER scores. However, usually the robustness of the top-2 targeted class can roughly reflect the untargeted robustness, as it is usually one of the easiest classes to change to.

Built-in Models

In the examples shown above we have used several different models. The code on this repository has a large number of built-in models for robustness evaluation. Model can be selected by changing the --model_name parameter to For MNIST and CIFAR dataset, the following models are available: "2-layer" (MLP), "normal" (7-layer CNN), "distilled" (7-layer CNN with defensive distillation), "brelu" (7-layer CNN with Bounded ReLU). For ImageNet, available options are: "resnet_v2_50", "resnet_v2_101", "resnet_v2_152", "inception_v1", "inception_v2", "inception_v3", "inception_v4", "inception_resnet_v2", "vgg_16", "vgg_19", "mobilenet_v1_025", "mobilenet_v1_050", "mobilenet_v1_100", "alexnet", "densenet121_k32", "densenet169_k32", "densenet161_k48" and "nasnet_larget". A total of 18 ImageNet models have been built in so far.

How to evaluate my own model?

Models for MNIST, CIFAR and ImageNet datasets are defined in, and For MNIST and CIFAR, you can modify the model definition in and directly. For ImageNet, a protobuf (.pb) model with frozen network parameters is expected, and new ImageNet models can be added into by adding a new AddModel() entry, similar to other ImageNet models. Please read the comments on AddModel() in for more details.

The following two links provide examples on how to prepare a frozen protobuf for ImageNet models:

Prepare DenseNet models

Prepare AlexNet model

Known Issues

If you encounter the following error:

posix_ipc.ExistentialError: Shared memory with the specified name already exists

Please delete those residual files in /dev/shm

rm -f /dev/shm/*all_inputs
rm -f /dev/shm/*input_example
rm -f /dev/shm/*randsphere
rm -f /dev/shm/*scale

For systemd based Linux distributions (for example, Ubuntu 16.04+), it is necessary to set RemoveIPC=no in /etc/systemd/logind.conf and restart systemd-logind (sudo systemctl restart systemd-logind.service) to avoid systemd from removing shared memory objects after user logout (which prevents CLEVER running in background).


CLEVER (Cross-Lipschitz Extreme Value for nEtwork Robustness) is a robustness metric for deep neural networks



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