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This tutorial creates an adversarial example using the Fast Gradient Signed Method (FGSM) attack as described in Explaining and Harnessing Adversarial Examples by Goodfellow et al. This was one of the first and most popular attacks to fool a neural network.
What is an adversarial example?
Adversarial examples are specialised inputs created with the purpose of confusing a neural network, resulting in the misclassification of a given input. These notorious inputs are indistinguishable to the human eye, but cause the network to fail to identify the contents of the image. There are several types of such attacks, however, here the focus is on the fast gradient sign method attack, which is a white box attack whose goal is to ensure misclassification. A white box attack is where the attacker has complete access to the model being attacked. One of the most famous examples of an adversarial image shown below is taken from the aforementioned paper.
Here, starting with the image of a panda, the attacker adds small perturbations (distortions) to the original image, which results in the model labelling this image as a gibbon, with high confidence. The process of adding these perturbations is explained below.
Fast gradient sign method
The fast gradient sign method works by using the gradients of the neural network to create an adversarial example. For an input image, the method uses the gradients of the loss with respect to the input image to create a new image that maximises the loss. This new image is called the adversarial image. This can be summarised using the following expression:
\[adv\_x = x + \epsilon*\text{sign}(\nabla_xJ(\theta, x, y))\]
where
- adv_x : Adversarial image.
- x : Original input image.
- y : Original input label.
- \(\epsilon\) : Multiplier to ensure the perturbations are small.
- \(\theta\) : Model parameters.
- \(J\) : Loss.
An intriguing property here, is the fact that the gradients are taken with respect to the input image. This is done because the objective is to create an image that maximises the loss. A method to accomplish this is to find how much each pixel in the image contributes to the loss value, and add a perturbation accordingly. This works pretty fast because it is easy to find how each input pixel contributes to the loss by using the chain rule and finding the required gradients. Hence, the gradients are taken with respect to the image. In addition, since the model is no longer being trained (thus the gradient is not taken with respect to the trainable variables, i.e., the model parameters), and so the model parameters remain constant. The only goal is to fool an already trained model.
So let's try and fool a pretrained model. In this tutorial, the model is MobileNetV2 model, pretrained on ImageNet.
import tensorflow as tf
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rcParams['figure.figsize'] = (8, 8)
mpl.rcParams['axes.grid'] = False
2024-08-16 03:28:26.383666: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered 2024-08-16 03:28:26.404965: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered 2024-08-16 03:28:26.411404: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
Let's load the pretrained MobileNetV2 model and the ImageNet class names.
pretrained_model = tf.keras.applications.MobileNetV2(include_top=True,
weights='imagenet')
pretrained_model.trainable = False
# ImageNet labels
decode_predictions = tf.keras.applications.mobilenet_v2.decode_predictions
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1723778909.276621 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.280463 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.283688 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.286883 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.298919 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.302499 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.305486 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.308404 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.311810 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.317284 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.320250 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778909.323296 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.546772 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.548872 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.550961 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.552980 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.554996 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.556955 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.558926 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.560858 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.562763 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.564710 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.566667 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.568585 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.607376 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.609421 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.611436 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.613411 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.615364 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.617323 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.619300 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.621249 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.623195 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.625633 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.628011 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1723778910.630359 146462 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 Downloading data from https://storage.googleapis.com/tensorflow/keras-applications/mobilenet_v2/mobilenet_v2_weights_tf_dim_ordering_tf_kernels_1.0_224.h5 14536120/14536120 ━━━━━━━━━━━━━━━━━━━━ 0s 0us/step
# Helper function to preprocess the image so that it can be inputted in MobileNetV2
def preprocess(image):
image = tf.cast(image, tf.float32)
image = tf.image.resize(image, (224, 224))
image = tf.keras.applications.mobilenet_v2.preprocess_input(image)
image = image[None, ...]
return image
# Helper function to extract labels from probability vector
def get_imagenet_label(probs):
return decode_predictions(probs, top=1)[0][0]
Original image
Let's use a sample image of a Labrador Retriever by Mirko CC-BY-SA 3.0 from Wikimedia Common and create adversarial examples from it. The first step is to preprocess it so that it can be fed as an input to the MobileNetV2 model.
image_path = tf.keras.utils.get_file('YellowLabradorLooking_new.jpg', 'https://storage.googleapis.com/download.tensorflow.org/example_images/YellowLabradorLooking_new.jpg')
image_raw = tf.io.read_file(image_path)
image = tf.image.decode_image(image_raw)
image = preprocess(image)
image_probs = pretrained_model.predict(image)
Downloading data from https://storage.googleapis.com/download.tensorflow.org/example_images/YellowLabradorLooking_new.jpg 83281/83281 ━━━━━━━━━━━━━━━━━━━━ 0s 0us/step WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1723778914.121474 146628 service.cc:146] XLA service 0x7f7f68002620 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices: I0000 00:00:1723778914.121511 146628 service.cc:154] StreamExecutor device (0): Tesla T4, Compute Capability 7.5 I0000 00:00:1723778914.121515 146628 service.cc:154] StreamExecutor device (1): Tesla T4, Compute Capability 7.5 I0000 00:00:1723778914.121518 146628 service.cc:154] StreamExecutor device (2): Tesla T4, Compute Capability 7.5 I0000 00:00:1723778914.121520 146628 service.cc:154] StreamExecutor device (3): Tesla T4, Compute Capability 7.5 1/1 ━━━━━━━━━━━━━━━━━━━━ 4s 4s/step I0000 00:00:1723778916.622230 146628 device_compiler.h:188] Compiled cluster using XLA! This line is logged at most once for the lifetime of the process.
Let's have a look at the image.
plt.figure()
plt.imshow(image[0] * 0.5 + 0.5) # To change [-1, 1] to [0,1]
_, image_class, class_confidence = get_imagenet_label(image_probs)
plt.title('{} : {:.2f}% Confidence'.format(image_class, class_confidence*100))
plt.show()
Downloading data from https://storage.googleapis.com/download.tensorflow.org/data/imagenet_class_index.json 35363/35363 ━━━━━━━━━━━━━━━━━━━━ 0s 0us/step
Create the adversarial image
Implementing fast gradient sign method
The first step is to create perturbations which will be used to distort the original image resulting in an adversarial image. As mentioned, for this task, the gradients are taken with respect to the image.
loss_object = tf.keras.losses.CategoricalCrossentropy()
def create_adversarial_pattern(input_image, input_label):
with tf.GradientTape() as tape:
tape.watch(input_image)
prediction = pretrained_model(input_image)
loss = loss_object(input_label, prediction)
# Get the gradients of the loss w.r.t to the input image.
gradient = tape.gradient(loss, input_image)
# Get the sign of the gradients to create the perturbation
signed_grad = tf.sign(gradient)
return signed_grad
The resulting perturbations can also be visualised.
# Get the input label of the image.
labrador_retriever_index = 208
label = tf.one_hot(labrador_retriever_index, image_probs.shape[-1])
label = tf.reshape(label, (1, image_probs.shape[-1]))
perturbations = create_adversarial_pattern(image, label)
plt.imshow(perturbations[0] * 0.5 + 0.5); # To change [-1, 1] to [0,1]
W0000 00:00:1723778917.231575 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.249303 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.249967 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.250637 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.251308 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.251974 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.252637 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.253295 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.253941 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.254597 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.255261 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.255927 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.256596 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.257261 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.257939 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.774586 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.783971 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.785212 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.786499 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.835739 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.838522 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.866113 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.875897 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.881828 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.884128 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.885405 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.889486 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.890814 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.892954 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.894383 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.897172 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced W0000 00:00:1723778917.900723 146462 gpu_timer.cc:114] Skipping the delay kernel, measurement accuracy will be reduced
Let's try this out for different values of epsilon and observe the resultant image. You'll notice that as the value of epsilon is increased, it becomes easier to fool the network. However, this comes as a trade-off which results in the perturbations becoming more identifiable.
def display_images(image, description):
_, label, confidence = get_imagenet_label(pretrained_model.predict(image))
plt.figure()
plt.imshow(image[0]*0.5+0.5)
plt.title('{} \n {} : {:.2f}% Confidence'.format(description,
label, confidence*100))
plt.show()
epsilons = [0, 0.01, 0.1, 0.15]
descriptions = [('Epsilon = {:0.3f}'.format(eps) if eps else 'Input')
for eps in epsilons]
for i, eps in enumerate(epsilons):
adv_x = image + eps*perturbations
adv_x = tf.clip_by_value(adv_x, -1, 1)
display_images(adv_x, descriptions[i])
1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step
1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 45ms/step
1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step
1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 46ms/step
Next steps
Now that you know about adversarial attacks, try this out on different datasets and different architectures. You may also create and train your own model, and then attempt to fool it using the same method. You can also try and see how the confidence in predictions vary as you change epsilon.
Though powerful, the attack shown in this tutorial was just the start of research into adversarial attacks, and there have been multiple papers creating more powerful attacks since then. In addition to adversarial attacks, research has also led to the creation of defenses, which aims at creating robust machine learning models. You may review this survey paper for a comprehensive list of adversarial attacks and defences.
For many more implementations of adversarial attacks and defenses, you may want to see the adversarial example library CleverHans.