Deep learning has been widely applied to various computer vision tasks with excellent performance. Prior to the realization of the adversarial example phenomenon by Biggio et al., Szegedy et.al, model performance on clean examples was the main evaluation criteria. However, in security-critical applications, robustness to adversarial atttacks has emerged as a critical factor.
In this part, we would engage into experiments about the robustness of neural networks.
We would introduce one basic attack method which adds perturbation to clean images and one newest defense method calling fast adversarial training.
Our experiments are based on MNIST and the model we would use here is LeNet. Since the dataset is small and the network is simple, you can either run the code on the GPU or your personal PC.
Edited by Felix Xue.
An adversarial example is a sample of input data which has been modified very slightly in a way that is intended to cause a machine learn classifier to misclassify it.
Scenarious of possible adversarial attacks can be categorized along different dimensions.
First of all, attacks can be classified by the type of outcome the adversary desires:
Second, attack scenarious can be classified by the amout of knowledge the adversary has about the model:
Third, attacks can be classified by the way adversary can feed data into the model:
One of the fist and most popular adversarial attacks to date is referred to as the Fast Gradient Sign Attack(FGSM) and is described by Goodfellow et.al. in Explaining and Harnessing Adversarial Examples. The attack is remarkably powerful, and yet intuitive. It is designed to attack neural networks by leveraging the way they learn, gradients. The idea is simple, rather than working to minimize the loss by adjusting the weights based on the backpropagated gradients, the attack adjusts the input data to maximize the loss based on the same backpropagated gradients. In other words, the attack uses the gradient of the loss w.r.t the input data, then adjusts the input data to maximize the loss.
Before we jump into the code, let's look at the famous FGSM panda example and extract some notation.
From the figure, $\mathbf{x}$ is the original input image correctly classified as a “panda”, $y$ is the ground truth label for $\mathbf{x}$, $\mathbf{\theta}$ represents the model parameters, and $J(\mathbf{\theta}, \mathbf{x}, y)$ is the loss that is used to train the network. The attack backpropagates the gradient back to the input data to calculate $\nabla_{x} J(\mathbf{\theta}, \mathbf{x}, y)$. Then, it adjusts the input data by a small step ($\epsilon$ or $0.007$ in the picture) in the direction (i.e. $sign(\nabla_{x} J(\mathbf{\theta}, \mathbf{x}, y))$) that will maximize the loss. The resulting perturbed image, $x'$, is then misclassified by the target network as a “gibbon” when it is still clearly a “panda”.
In [1]:
%matplotlib inline
%load_ext autoreload
%autoreload 2
In [2]:
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torchvision import datasets, transforms
import resnet
import numpy as np
import matplotlib.pyplot as plt
In [3]:
# start
Int this section, we will discuss the input parameters for the tutorial, define the model under attack, then code the attack and run some tests.
There are only three inputs for this tutorial, and are defined as follows:
Please try to detect available gpu device with torch.cuda
In [5]:
epsilons = [0, .05, .15, .25]
# epsilons = [0, .05, .1, .15, .2, .25, .3]
# Use pretrained model or not
# pretrained_model = "data/mnist_cnn.pt"
# Both of the network and dataset are simple, so we can use small number of epochs.
epochs = 3
use_cuda = True
# Define what device we are using
# Code here
print("CUDA Available: ", torch.cuda.is_available())
# hint: torch.cuda.is_available()
device = torch.device("cuda" if (use_cuda and torch.cuda.is_available()) else "cpu")
# device = torch.device("cuda" if (use_cuda and 'code' here) else "cpu")
In [18]:
# MNIST dataloader
def dataset_mnist(train_batch=32, test_batch=1):
# MNIST Train dataset
# train_loader = torch.utils.data.DataLoader(
# datasets.MNIST('./data/mnist', train=True, download=False,
# transform=transforms.Compose([transforms.ToTensor()])),
# batch_size=train_batch, shuffle=True)
train_loader = torch.utils.data.DataLoader(
datasets.MNIST('./data/mnist', train=False, download=True,
transform=transforms.Compose([transforms.ToTensor()])),
batch_size=train_batch, shuffle=True)
# MNIST Test dataset and dataloader declaration
test_loader = torch.utils.data.DataLoader(
datasets.MNIST('./data/mnist', train=False, download=True,
transform=transforms.Compose([transforms.ToTensor()])),
batch_size=test_batch, shuffle=False)
return train_loader, test_loader
As mentioned, the model under attack is the same MNIST model from resnet.py. You may
train and save your own MINST model or you can use the provided model.
The Net definition and test dataloader here have benn copied from
the MNIST example. The purpose of this section is to define the
model and dataloader, then initialize the model and load the pretrained
weights.
In [7]:
# Train a traditional classifier with resnet or use the pretrained one.
raw_resnet_path = './data/mnist_resnet.pt'
In [8]:
# Train model
def train(model, device, train_loader, optimizer, criterion, epoch):
model.train() # set model state to `train`
for batch_idx, (data, target) in enumerate(train_loader):
data, target = data.to(device), target.to(device)
optimizer.zero_grad()
output = model(data)
loss = criterion(output, target)
loss.backward()
optimizer.step()
if batch_idx % 100 == 0:
print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
epoch, batch_idx * len(data), len(train_loader.dataset),
100. * batch_idx / len(train_loader), loss.item()))
# Test model
def test(model, device, criterion, test_loader):
model.eval()
test_loss = 0
correct = 0
with torch.no_grad():
for data, target in test_loader:
data, target = data.to(device), target.to(device)
output = model(data)
test_loss += criterion(output, target)
pred = output.argmax(dim=1, keepdim=True) # get the index of the max log-probability
correct += pred.eq(target.view_as(pred)).sum().item()
test_loss /= len(test_loader.dataset)
print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
test_loss, correct, len(test_loader.dataset),
100. * correct / len(test_loader.dataset)))
def raw_train(save_name=raw_resnet_path):
'''
Main function to train and save the model under atttack.
params:
save_name: The model to be saved.
'''
train_loader, test_loader = dataset_mnist()
# Initialize the network
model = resnet.ResNet18().to(device)
# Define the optimizer
optimizer = optim.SGD(model.parameters(), lr=0.1, momentum=0.9, weight_decay=5e-4)
# Define the criterion
criterion = nn.CrossEntropyLoss()
for epoch in range(1, epochs+1):
train(model, device, train_loader, optimizer, criterion, epoch)
test(model, device, criterion, test_loader)
# Save model
torch.save(model.state_dict(), save_name)
print('Model saved at ', save_name)
Call this function, you can get a well trained classifier with accuracy up to 95+%.
In [7]:
# raw_train()
# Call this function, you can get a well trained classifier with accuracy up to 95+%.
Now, we can define the function that creates the adversarial examples by
perturbing the original inputs. The fgsm_attack function takes three
inputs, image is the original clean image ($x$), epsilon is
the pixel-wise perturbation amount ($\epsilon$), and data_grad
is gradient of the loss w.r.t the input image
($\nabla_{x} J(\mathbf{\theta}, \mathbf{x}, y)$). The function
then creates perturbed image as
Finally, in order to maintain the original range of the data, the perturbed image is clipped to range $[0,1]$.
Please try to finish the attack code with the information above.
In [9]:
# FGSM attack code
def fgsm_attack(image, epsilon, data_grad):
# Collect the element-wise sign of the data gradient
sign_data_grad = data_grad.sign()
# Create the perturbed image by adjusting each pixel of the input image
# code here
perturbed_image = image + epsilon * sign_data_grad
# Note: Adding clipping to maintain [0,1] range
perturbed_image = torch.clamp(perturbed_image, 0, 1)
# Return the perturbed image
return perturbed_image
Finally, the central result of this tutorial comes from the test
function. Each call to this test function performs a full test step on
the MNIST test set and reports a final accuracy. However, notice that
this function also takes an epsilon input. This is because the
test function reports the accuracy of a model that is under attack
from an adversary with strength $\epsilon$. More specifically, for
each sample in the test set, the function computes the gradient of the
loss w.r.t the input data ($data\_grad$), creates a perturbed
image with fgsm_attack ($perturbed\_data$), then checks to see
if the perturbed example is adversarial. In addition to testing the
accuracy of the model, the function also saves and returns some
successful adversarial examples to be visualized later.
Please try to finish the test code with `fgsm_attack` function.
In [14]:
def adv_test( model, device, test_loader, epsilon ):
# Accuracy counter
correct = 0
adv_examples = []
# Loop over all examples in test set
for data, target in test_loader:
# Send the data and label to the device
data, target = data.to(device), target.to(device)
# Set requires_grad attribute of tensor. Important for Attack
data.requires_grad = True
# Forward pass the data through the model
output = model(data)
init_pred = output.max(1, keepdim=True)[1] # get the index of the max log-probability
# If the initial prediction is wrong, dont bother attacking, just move on
if init_pred.item() != target.item():
continue
# Calculate the loss
loss = F.nll_loss(output, target)
# Zero all existing gradients
model.zero_grad()
# Calculate gradients of model in backward pass
loss.backward()
# Collect datagrad
data_grad = data.grad.data
# Call FGSM Attack
# code here
perturbed_data = fgsm_attack(data, epsilon, torch.sign(data_grad))
# Re-classify the perturbed image
output = model(perturbed_data)
# Check for success
final_pred = output.max(1, keepdim=True)[1] # get the index of the max log-probability
if final_pred.item() == target.item():
correct += 1
# Special case for saving 0 epsilon examples
if (epsilon == 0) and (len(adv_examples) < 5):
adv_ex = perturbed_data.squeeze().detach().cpu().numpy()
adv_examples.append( (init_pred.item(), final_pred.item(), adv_ex) )
else:
# Save some adv examples for visualization later
if len(adv_examples) < 5:
adv_ex = perturbed_data.squeeze().detach().cpu().numpy()
adv_examples.append( (init_pred.item(), final_pred.item(), adv_ex) )
# Calculate final accuracy for this epsilon
final_acc = correct/float(len(test_loader))
print("Epsilon: {}\tAccuracy: {}/{} ({:.2f}%)".format(epsilon, correct, len(test_loader), 100.0 * final_acc))
# Return the accuracy and an adversarial example
return final_acc, adv_examples
The last part of the implementation is to actually run the attack. Here, we run a full test step for each epsilon value in the epsilons input. For each epsilon we also save the final accuracy and some successful adversarial examples to be plotted in the coming sections. Notice how the printed accuracies decrease as the epsilon value increases. Also, note the $\epsilon=0$ case represents the original test accuracy, with no attack.
In [12]:
def attack_test(model_path):
model = resnet.ResNet18().to(device)
# Load the pretrained model
print('Pretrained Model', model_path)
model.load_state_dict(torch.load(model_path, map_location='cpu'))
# Set the model in evaluation mode. In this case this is for the Dropout layers
model.eval()
_, test_loader = dataset_mnist()
accuracies = []
examples = []
# Run test for each epsilon
for eps in epsilons:
acc, ex = adv_test(model, device, test_loader, eps)
accuracies.append(acc)
examples.append(ex)
return accuracies, examples
Run the attack function here.
In [19]:
# Remember we have saved the model at 'raw_resnet_path'.
pretrained_model = raw_resnet_path
accuracies, examples = attack_test(pretrained_model)
# Hints: below are the accuracies under FGSM attack with different epsilons.
# Epsilon Accuracy
# 0 ~raw
# 0.05 < 60%
# 0.15 < 30%
# 0.25 < 10%
The first result is the accuracy versus epsilon plot. As alluded to earlier, as epsilon increases we expect the test accuracy to decrease. This is because larger epsilons mean we take a larger step in the direction that will maximize the loss. Notice the trend in the curve is not linear even though the epsilon values are linearly spaced. For example, the accuracy at $\epsilon=0.05$ is only about 4% lower than $\epsilon=0$, but the accuracy at $\epsilon=0.2$ is 25% lower than $\epsilon=0.15$. Also, notice the accuracy of the model hits random accuracy for a 10-class classifier between $\epsilon=0.25$ and $\epsilon=0.3$.
In [20]:
def plt_acc_vs_eps(epsilons, accuracies):
plt.figure(figsize=(5,5))
plt.plot(epsilons, accuracies, "*-")
plt.yticks(np.arange(0, 1.1, step=0.1))
plt.xticks(np.arange(0, .35, step=0.05))
plt.title("Accuracy vs Epsilon")
plt.xlabel("Epsilon")
plt.ylabel("Accuracy")
plt.show()
In [21]:
print('Blue: Raw ResNet under white-box attack.')
plt_acc_vs_eps(epsilons, accuracies)
Remember the idea of no free lunch? In this case, as epsilon increases the test accuracy decreases BUT the perturbations become more easily perceptible. In reality, there is a tradeoff between accuracy degredation and perceptibility that an attacker must consider. Here, we show some examples of successful adversarial examples at each epsilon value. Each row of the plot shows a different epsilon value. The first row is the $\epsilon=0$ examples which represent the original “clean” images with no perturbation. The title of each image shows the “original classification -> adversarial classification.” Notice, the perturbations start to become evident at $\epsilon=0.15$ and are quite evident at $\epsilon=0.3$. However, in all cases humans are still capable of identifying the correct class despite the added noise.
In [22]:
def plt_examples(epsilons, examples):
# Plot several examples of adversarial samples at each epsilon
cnt = 0
plt.figure(figsize=(8,10))
for i in range(len(epsilons)):
for j in range(len(examples[i])):
cnt += 1
plt.subplot(len(epsilons),len(examples[0]),cnt)
plt.xticks([], [])
plt.yticks([], [])
if j == 0:
plt.ylabel("Eps: {}".format(epsilons[i]), fontsize=14)
orig,adv,ex = examples[i][j]
plt.title("{} -> {}".format(orig, adv))
plt.imshow(ex, cmap="gray")
plt.tight_layout()
plt.show()
In [23]:
plt_examples(epsilons, examples)
The most popular defense in current research papers is probably adversarial training.
The idea is to inject adversarial examples into training process and train the model either on adversarial examples or on mix of clean and adversarial examples.
Here, we use the training model to generate adversarial examples by FGSM attack and then
feed them into the model.
The perturbed image is get by this equation:
We already have the raw image, and we can get the grad by one forward and backward pass. What we need here is
epsilon. Since we need it to train a more robust model, we set epsilon equals to 0.3. You can try different epsilon and see what happens.
Please try to finish the `fgsm_train` function.
In [24]:
def fgsm_train(model, device, train_loader, optimizer, criterion, epoch, epsilon=0.3):
model.train()
for batch_idx, (data, target) in enumerate(train_loader):
data, target = data.to(device), target.to(device)
data.requires_grad = True
#****** To get the grad *********
# Forward pass
output = model(data)
loss = criterion(output, target)
optimizer.zero_grad()
# Backward pass
loss.backward()
# Collect datagrad
sign_data_grad = torch.sign(data.grad.data)
#****** Get perturbed_data *********
# Code here
perturbed_data = data + epsilon * sign_data_grad
# Note: Adding clipping to maintain [0,1] range
perturbed_data.clamp_(0.0, 1.0)
#****** Train model with perturbed_data *********
optimizer.zero_grad()
pert_output = model(perturbed_data)
pert_loss = criterion(pert_output, target)
pert_loss.backward()
optimizer.step()
if batch_idx % 100 == 0:
print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
epoch, batch_idx * len(data), len(train_loader.dataset),
100. * batch_idx / len(train_loader), pert_loss.item()))
In [25]:
def adv_main(save_name='./data/fgsm_adv_mnist_cnn.pt'):
train_loader, test_loader = dataset_mnist()
# Initialize the network
model = resnet.ResNet18().to(device)
# Define the optimizer
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
criterion = nn.CrossEntropyLoss()
for epoch in range(1, epochs+1):
fgsm_train(model, device, train_loader, optimizer,criterion, epoch)
test(model, device, criterion, test_loader)
# Save model
torch.save(model.state_dict(), save_name)
print('Model saved.')
Call the `adv_main` function to get a robust model.
In [26]:
adv_resnet = './data/fgsm_adv_mnist_cnn.pt'
adv_main(adv_resnet)
Repeat the test function and plot the figure of acc v.s. eps. and examples.
In [27]:
re_accuracies, re_examples = attack_test(adv_resnet)
# Epsilon Accuracy
# 0 ~raw
# 0.05 <= ~98%
# 0.15 <= ~98%
# 0.25 <= ~95%
In [28]:
plt_acc_vs_eps(epsilons, re_accuracies)
In [29]:
plt_examples(epsilons, re_examples)
In [30]:
def plt_comparion(epsilons, accs):
plt.figure(figsize=(5,5))
plt.plot(epsilons, accs[0], "*-")
plt.plot(epsilons, accs[1], "*-", c='red')
plt.yticks(np.arange(0, 1.1, step=0.1))
plt.xticks(np.arange(0, .35, step=0.05))
plt.title("Accuracy vs Epsilon")
plt.xlabel("Epsilon")
plt.ylabel("Accuracy")
plt.show()
In [31]:
print('Blue: Raw ResNet under white-box attack.')
print('Red : Robust ResNet under white-box attack.')
plt_comparion(epsilons, [accuracies, re_accuracies])
In [32]:
pretrained_lenet = 'data/mnist_lenet.pt' # the attack model
In [33]:
# LeNet Model definition
class LeNet(nn.Module):
def __init__(self):
super(LeNet, self).__init__()
self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
self.conv2_drop = nn.Dropout2d()
self.fc1 = nn.Linear(320, 50)
self.fc2 = nn.Linear(50, 10)
def forward(self, x):
x = F.relu(F.max_pool2d(self.conv1(x), 2))
x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
x = x.view(-1, 320)
x = F.relu(self.fc1(x))
x = F.dropout(x, training=self.training)
x = self.fc2(x)
return F.log_softmax(x, dim=1)
In [34]:
def raw_train_lenet(save_name='./data/mnist_lenet.pt'):
'''
Main function to train and save the model under atttack.
params:
save_name: The model to be saved.
'''
train_loader, test_loader = dataset_mnist()
# Initialize the network
model = LeNet().to(device)
# Define the optimizer
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9, weight_decay=5e-4)
# Define the criterion
criterion = nn.CrossEntropyLoss()
for epoch in range(1, epochs+1):
train(model, device, train_loader, optimizer, criterion, epoch)
test(model, device, criterion, test_loader)
# Save model
torch.save(model.state_dict(), save_name)
print('Model saved.')
# Uncomment the next line to train a new LeNet on yourself. The accuracy is about 97%.
# raw_train_lenet()
# Pay attentation to the learning rate compared with that in resnet.
Please finish the `black_box_attack` method.
Hints:
You need to generate adversarial examples by the attacking model(pretrained lenet), and then use the adversarial examples to test the robustness of the defending model (raw resnet or adversarially trained resnet).
In [36]:
def black_box_attack(attacker, defender, device, test_loader, epsilon):
'''
Use attacker model to generate adversarial examples.
And try to test the robustness of the defender.
'''
# Accuracy counter
correct = 0
adv_examples = []
# Loop over all examples in test set
for data, target in test_loader:
# Send the data and label to the device
data, target = data.to(device), target.to(device)
# Set requires_grad attribute of tensor. Important for Attack
data.requires_grad = True
# Forward pass the data through the **attacker**
# ********* Code here ****************
output = attacker(data) # attacker or defender
init_pred = output.max(1, keepdim=True)[1] # get the index of the max log-probability
# If the initial prediction is wrong, dont bother attacking, just move on
if init_pred.item() != target.item():
continue
# Calculate the loss
loss = F.nll_loss(output, target)
# Zero all existing gradients of the attacker model
attacker.zero_grad()
# Calculate gradients of model in backward pass
loss.backward()
# Collect datagrad
data_grad = data.grad.data
# ********* Code here ****************
# Call FGSM Attack
perturbed_data = fgsm_attack(data, epsilon, torch.sign(data_grad)) # we already have data, epsilon and data_grad now.
# Use the defender to classify the perturbed image
output = defender(perturbed_data) # attacker or defender ?
# Check for success
final_pred = output.max(1, keepdim=True)[1] # get the index of the max log-probability
if final_pred.item() == target.item():
correct += 1
# Special case for saving 0 epsilon examples
if (epsilon == 0) and (len(adv_examples) < 5):
adv_ex = perturbed_data.squeeze().detach().cpu().numpy()
adv_examples.append( (init_pred.item(), final_pred.item(), adv_ex) )
else:
# Save some adv examples for visualization later
if len(adv_examples) < 5:
adv_ex = perturbed_data.squeeze().detach().cpu().numpy()
adv_examples.append( (init_pred.item(), final_pred.item(), adv_ex) )
# Calculate final accuracy for this epsilon
final_acc = correct/float(len(test_loader))
print("Epsilon: {}\tAccuracy: {}/{} ({:.2f}%)".format(epsilon, correct, len(test_loader), 100.0 * final_acc))
# Return the accuracy and an adversarial example
return final_acc, adv_examples
In [37]:
def black_box_attack_test(attacker_path, defender_path):
'''
'''
attacker = LeNet().to(device)
defender = resnet.ResNet18().to(device)
# Load the pretrained model
print('Pretrained Attack Model', attacker_path)
attacker.load_state_dict(torch.load(attacker_path, map_location='cpu'))
print('Pretrained Defend Model', defender_path)
defender.load_state_dict(torch.load(defender_path, map_location='cpu'))
# Set the model in evaluation mode. In this case this is for the Dropout layers
attacker.eval()
defender.eval()
_, test_loader = dataset_mnist()
accuracies = []
examples = []
# Run test for each epsilon
for eps in epsilons:
acc, ex = black_box_attack(attacker, defender, device, test_loader, eps)
accuracies.append(acc)
examples.append(ex)
return accuracies, examples
In [38]:
pretrained_lenet = 'data/mnist_lenet.pt' # the attack model
raw_resnet = 'data/mnist_resnet.pt' # raw resnet
adv_resnet = 'data/fgsm_adv_mnist_cnn.pt' # adversarially trained resnet
Please use the `black_box_attack_test` method to test the raw resnet model.
In [39]:
raw_accs, raw_exs = black_box_attack_test(pretrained_lenet, raw_resnet)
Please use the `black_box_attack_test` method to test the adversarially trained resnet.
In [40]:
adv_accs, adv_exs = black_box_attack_test(pretrained_lenet, adv_resnet)
In [41]:
print('Blue: Raw ResNet attacked by LeNet.')
print('Red: Robust ResNet attacked by LeNet.')
plt_comparion(epsilons, [raw_accs, adv_accs])