针对卷积层为nn.Conv2d(1, 10, kernel_size=5) 的神经网络，用pytorch针对MNIST数据集写DeepFool算法的代码，并写出测试代码验证用Deepfool算法生成的对抗性示例攻击神经网络得到的正确率。要求在cpu上运行

以下是针对MNIST数据集的DeepFool攻击代码和测试代码：

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.datasets as datasets
import torchvision.transforms as transforms
import numpy as np


class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

    def forward(self, x):
        x = nn.functional.relu(nn.functional.max_pool2d(self.conv1(x), 2))
        x = nn.functional.relu(nn.functional.max_pool2d(self.conv2(x), 2))
        x = x.view(-1, 320)
        x = nn.functional.relu(self.fc1(x))
        x = self.fc2(x)
        return x


def deepfool(net, image, num_classes=10, overshoot=0.02, max_iter=50):
    """
    DeepFool算法的实现
    """
    image = image.unsqueeze(0).clone().detach().requires_grad_(True)
    f_image = net(image)
    I = f_image.argmax().item()
    w = torch.zeros_like(image)
    r = torch.zeros_like(image)

    for k in range(max_iter):
        pert = np.inf
        f_image = net(image)
        for i in range(num_classes):
            if i == I:
                continue

            # compute w^k_i and f^k_i
            net.zero_grad()
            f_i = f_image[0, i]
            f_i.backward(retain_graph=True)
            grad_i = image.grad.clone().detach()
            net.zero_grad()
            f_I = f_image[0, I]
            f_I.backward(retain_graph=True)
            grad_I = image.grad.clone().detach()
            w_i = grad_i - grad_I
            f_i = f_i - f_I

            # compute perturbation
            pert_i = abs(f_i) / w_i.norm()
            if pert_i < pert:
                pert = pert_i
                w = w_i

        # compute r^k+1
        r = r + pert * w / w.norm()
        image = image + pert * w / w.norm()
        image = torch.clamp(image, 0, 1)

    return image.squeeze()


if __name__ == '__main__':
    # 加载MNIST数据集
    transform = transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
    ])
    testset = datasets.MNIST(root='./data', train=False, download=True, transform=transform)
    testloader = torch.utils.data.DataLoader(testset, batch_size=1, shuffle=True)

    # 加载神经网络
    net = Net()
    net.load_state_dict(torch.load('mnist_cnn.pt', map_location=torch.device('cpu')))
    net.eval()

    # 对抗性攻击
    num_samples = 100
    num_classes = 10
    num_success = 0
    for i, (image, label) in enumerate(testloader):
        if i == num_samples:
            break

        image = image.squeeze()
        label = label.item()
        adv_image = deepfool(net, image)

        # 测试攻击成功率
        f_image = net(image.unsqueeze(0)).squeeze()
        f_adv_image = net(adv_image.unsqueeze(0)).squeeze()
        I = f_image.argmax().item()
        J = (f_adv_image - f_image).argmax().item()
        if I != J:
            num_success += 1

        print('Sample %d, true label: %d, predicted label: %d, adversarial label: %d' % (i+1, label, I, J))

    print('Success rate: %.2f%%' % (num_success / num_samples * 100))

在上面的代码中，我们首先加载了MNIST数据集和训练好的神经网络，然后定义了DeepFool算法的实现。对于每个测试样本，我们使用DeepFool算法生成对抗性样本，并计算攻击成功率。最终输出测试结果，其中包括每个样本的真实标签、神经网络的预测标签和攻击后的标签，以及整个测试集的攻击成功率。

需要注意的是，由于DeepFool算法需要对每个类别都进行一次梯度计算，因此攻击的时间会比较长。为了加速测试过程，可以将测试样本数量设置为较小的值。