论文链接：https://arxiv.org/abs/1706.06083 源码出处：https://github.com/Harry24k/adversarial-attacks-pytorch/tree/master
PGDLinf源码
import torch
import torch.nn as nn
from ..attack import Attack
class PGD(Attack):
r"""
PGD in the paper 'Towards Deep Learning Models Resistant to Adversarial Attacks'
[https://arxiv.org/abs/1706.06083]
Distance Measure : Linf
Arguments:
model (nn.Module): model to attack.
eps (float): maximum perturbation. (Default: 8/255)
alpha (float): step size. (Default: 2/255)
steps (int): number of steps. (Default: 10)
random_start (bool): using random initialization of delta. (Default: True)
Shape:
- images: :math:`(N, C, H, W)` where `N = number of batches`, `C = number of channels`, `H = height` and `W = width`. It must have a range [0, 1].
- labels: :math:`(N)` where each value :math:`y_i` is :math:`0 \leq y_i \leq` `number of labels`.
- output: :math:`(N, C, H, W)`.
Examples::
>>> attack = torchattacks.PGD(model, eps=8/255, alpha=1/255, steps=10, random_start=True)
>>> adv_images = attack(images, labels)
"""
def __init__(self, model, eps=8/255,
alpha=2/255, steps=10, random_start=True):
super().__init__("PGD", model)
self.eps = eps
self.alpha = alpha
self.steps = steps
self.random_start = random_start
self.supported_mode = ['default', 'targeted']
def forward(self, images, labels):
r"""
Overridden.
"""
self._check_inputs(images)
images = images.clone().detach().to(self.device)
labels = labels.clone().detach().to(self.device)
if self.targeted:
target_labels = self.get_target_label(images, labels)
loss = nn.CrossEntropyLoss()
adv_images = images.clone().detach()
if self.random_start:
# Starting at a uniformly random point
adv_images = adv_images + torch.empty_like(adv_images).uniform_(-self.eps, self.eps)
adv_images = torch.clamp(adv_images, min=0, max=1).detach()
for _ in range(self.steps):
adv_images.requires_grad = True
outputs = self.get_logits(adv_images)
# Calculate loss
if self.targeted:
cost = -loss(outputs, target_labels)
else:
cost = loss(outputs, labels)
# Update adversarial images
grad = torch.autograd.grad(cost, adv_images,
retain_graph=False, create_graph=False)[0]
adv_images = adv_images.detach() + self.alpha*grad.sign()
delta = torch.clamp(adv_images - images, min=-self.eps, max=self.eps)
adv_images = torch.clamp(images + delta, min=0, max=1).detach()
return adv_images
解析
PGD算法（projected gradient descent）是在BIM算法的基础上的小改进，二者非常相近，BIM算法的源码解析在上一篇博客中，建议先看上一篇博客理解BIM算法的原理。
具体来说，在BIM算法开始迭代前，就先给图像加上扰动（在
ϵ
\epsilon
ϵ邻域内均匀分布）。换句话说，也就是图像开始迭代的起点随机，而不是像BIM算法一样从原始图像开始迭代。论文这么做的目的是为了研究从随机的起点开始迭代扰动，损失能够达到的不同的局部最大值的关系。
PGD算法的公式如下所示：
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X^{adv}_0=X+\eta,X^{adv}_{N+1}=Clip_{X,\epsilon}\{X^{adv}_N+\alpha sign(\triangledown_{x}J(X^{adv}_N,y_{true}))\}
X0adv=X+η,XN+1adv=ClipX,ϵ{XNadv+αsign(▽xJ(XNadv,ytrue))}其中，
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\eta
η是一个随机扰动，在
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\epsilon
ϵ邻域内均匀分布。
eps：即
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\epsilon
ϵ，表示最大扰动。 alpha：即
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\alpha
α，表示每次迭代中扰动的增加量（或减少量）。 steps：表示迭代次数。 random_start：迭代的起点是否随机，也就是是否要加随机扰动
η
\eta
η，若为False，则该算法就和BIM算法相同。 images = images.clone().detach().to(self.device)：clone()将图像克隆到一块新的内存区（pytorch默认同样的tensor共享一块内存区）；detach()是将克隆的新的tensor从当前计算图中分离下来，作为叶节点，从而可以计算其梯度；to()作用就是将其载入设备。 target_labels = self.get_target_label(images, labels)：若是有目标攻击的情况，获取目标标签。目标标签的选取有多种方式，例如可以选择与真实标签相差最大的标签，也可以随机选择除真实标签外的标签。 loss = nn.CrossEntropyLoss()：设置损失函数为交叉熵损失。
adv_images = adv_images + torch.empty_like(adv_images).uniform_(-self.eps, self.eps)
adv_images = torch.clamp(adv_images, min=0, max=1).detach()
以上两行代码作用即为添加随机扰动，torch.empty_like(adv_images)会返回一个形状同adv_images的空的Tensor，uniform_(-self.eps, self.eps)将Tensor中的值在
[
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ϵ
]
[-\epsilon,\epsilon]
[−ϵ,ϵ]范围内的均匀分布中随机取值。torch.clamp(adv_images, min=0, max=1)会将图像中大于1的值设为1、小于0的值设为0，防止超出范围。 adv_images.requires_grad = True：将requires_grad 参数设置为True，torch就会在图像的计算过程中自动计算计算图，用于反向梯度计算。 outputs = self.get_logits(images)：获得图像的在模型中的输出值。 cost = -loss(outputs, target_labels)：有目标情况下计算损失。 cost = loss(outputs, labels)：无目标情况下计算损失。 grad = torch.autograd.grad(cost, images, retain_graph=False, create_graph=False)[0]：cost对images求导，得到梯度grad。 adv_images = images + self.alpha*grad.sign()：根据公式在图像上沿着梯度上升方向以步长为
α
\alpha
α增加扰动。
delta = torch.clamp(adv_images - images, min=-self.eps, max=self.eps) # 得到改变量
adv_images = torch.clamp(images + delta, min=0, max=1).detach() # 防止图像超出有效范围
以上两行代码就是裁剪的过程，同BIM算法中的
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Clip
Clip过程，防止图像超出
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[0,1]范围。
PGDL2源码
import torch
import torch.nn as nn
from ..attack import Attack
class PGDL2(Attack):
r"""
PGD in the paper 'Towards Deep Learning Models Resistant to Adversarial Attacks'
[https://arxiv.org/abs/1706.06083]
Distance Measure : L2
Arguments:
model (nn.Module): model to attack.
eps (float): maximum perturbation. (Default: 1.0)
alpha (float): step size. (Default: 0.2)
steps (int): number of steps. (Default: 10)
random_start (bool): using random initialization of delta. (Default: True)
Shape:
- images: :math:`(N, C, H, W)` where `N = number of batches`, `C = number of channels`, `H = height` and `W = width`. It must have a range [0, 1].
- labels: :math:`(N)` where each value :math:`y_i` is :math:`0 \leq y_i \leq` `number of labels`.
- output: :math:`(N, C, H, W)`.
Examples::
>>> attack = torchattacks.PGDL2(model, eps=1.0, alpha=0.2, steps=10, random_start=True)
>>> adv_images = attack(images, labels)
"""
def __init__(self, model, eps=1.0, alpha=0.2, steps=10,
random_start=True, eps_for_division=1e-10):
super().__init__("PGDL2", model)
self.eps = eps
self.alpha = alpha
self.steps = steps
self.random_start = random_start
self.eps_for_division = eps_for_division
self.supported_mode = ['default', 'targeted']
def forward(self, images, labels):
r"""
Overridden.
"""
self._check_inputs(images)
images = images.clone().detach().to(self.device)
labels = labels.clone().detach().to(self.device)
if self.targeted:
target_labels = self.get_target_label(images, labels)
loss = nn.CrossEntropyLoss()
adv_images = images.clone().detach()
batch_size = len(images)
if self.random_start:
# Starting at a uniformly random point
delta = torch.empty_like(adv_images).normal_()
d_flat = delta.view(adv_images.size(0), -1) # 将图片矩阵展平，方便计算范数
n = d_flat.norm(p=2, dim=1).view(adv_images.size(0), 1, 1, 1) # 计算每个向量的模长
r = torch.zeros_like(n).uniform_(0, 1) # 随机[0,1]之间均匀分布
delta *= r/n*self.eps # 即将delta向量变为模长为[0,eps]之间的向量
adv_images = torch.clamp(adv_images + delta, min=0, max=1).detach()
for _ in range(self.steps):
adv_images.requires_grad = True
outputs = self.get_logits(adv_images)
# Calculate loss
if self.targeted:
cost = -loss(outputs, target_labels)
else:
cost = loss(outputs, labels)
# Update adversarial images
grad = torch.autograd.grad(cost, adv_images,
retain_graph=False, create_graph=False)[0]
grad_norms = torch.norm(grad.view(batch_size, -1), p=2, dim=1) + self.eps_for_division # 这边加上了self.eps_for_division是为了防止下面除0
grad = grad / grad_norms.view(batch_size, 1, 1, 1) # 使梯度变为单位向量
adv_images = adv_images.detach() + self.alpha * grad
# 下面是为了改变后的图像与原图像的L2距离不超过eps
delta = adv_images - images
delta_norms = torch.norm(delta.view(batch_size, -1), p=2, dim=1) # 计算改变量的模长
factor = self.eps / delta_norms
# 如果eps/delta_norms小于1，则说明改变量的L2距离超过了eps
# 那么就会在factor与delta相乘的过程中被替换为eps
factor = torch.min(factor, torch.ones_like(delta_norms))
delta = delta * factor.view(-1, 1, 1, 1)
adv_images = torch.clamp(images + delta, min=0, max=1).detach()
return adv_images
解析
PGDL2和PGDLinf的区别就在于度量样本之间的距离的范式不同，假设样本
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X=(x_1,x_2,x_3,...,x_n)
X=(x1,x2,x3,...,xn)，L2范数
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||X||_2=\sqrt{x^2_1+x^2_2+x^2_3+...+x^2_n}
∣∣X∣∣2=x12+x22+x32+...+xn2
，Linf范数
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||X||_\infty=\sqrt[n]{x^n_1+x^n_2+x^n_3+...+x^n_n}
∣∣X∣∣∞=nx1n+x2n+x3n+...+xnn
，简单来说，L2范数可以理解为向量的模长，Linf范数可以理解为向量中最大元素的值。
二者在源码中的区别可以看我写在代码中的注释。