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原理

同时训练两个网络：辨别器Discriminator 和 生成器Generator
Generator是 造假者，用来生成假数据。
Discriminator 是警察，尽可能的分辨出来哪些是造假的，哪些是真实的数据。

目的：使得判别模型尽量犯错，无法判断数据是来自真实数据还是生成出来的数据。

GAN的梯度下降训练过程：

上图来源：https://arxiv.org/abs/1406.2661

Train 辨别器: $max$ $log(D(x))+log(1-D(G(z)))$

Train 生成器: $min$ $log(1-D(G(z)))$

我们可以使用BCEloss来计算上述两个损失函数

BCEloss的表达式：$min-[ylnx+(1-y)ln(1-x)]$
具体过程参加代码中注释

代码

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision
import torchvision.datasets as datasets
from torch.utils.data import DataLoader
import torchvision.transforms as transforms
from torch.utils.tensorboard import SummaryWriter  # to print to tensorboardclass Discriminator(nn.Module):def __init__(self, img_dim):super(Discriminator, self).__init__()self.disc = nn.Sequential(nn.Linear(img_dim, 128),nn.LeakyReLU(0.1),nn.Linear(128, 1),nn.Sigmoid(),)def forward(self, x):return self.disc(x)class Generator(nn.Module):def __init__(self, z_dim, img_dim): # z_dim 噪声的维度super(Generator, self).__init__()self.gen = nn.Sequential(nn.Linear(z_dim, 256),nn.LeakyReLU(0.1),nn.Linear(256, img_dim), # 28x28 -> 784nn.Tanh(),)def forward(self, x):return self.gen(x)# Hyperparameters
device = 'cuda' if torch.cuda.is_available() else 'cpu'
lr = 3e-4 # 3e-4是Adam最好的学习率
z_dim = 64 # 噪声维度
img_dim = 784 # 28x28x1
batch_size = 32
num_epochs = 50disc = Discriminator(img_dim).to(device)
gen = Generator(z_dim, img_dim).to(device)fixed_noise = torch.randn((batch_size, z_dim)).to(device)
transforms = transforms.Compose( # MNIST标准化系数：(0.1307,), (0.3081,)[transforms.ToTensor(), transforms.Normalize((0.1307, ), (0.3081,))] # 不同数据集就有不同的标准化系数
)dataset = datasets.MNIST(root='dataset/', transform=transforms, download=True)
loader = DataLoader(dataset, batch_size=batch_size, shuffle=True)opt_disc = optim.Adam(disc.parameters(), lr=lr)
opt_gen = optim.Adam(gen.parameters(), lr=lr)
# BCE 损失
criterion = nn.BCELoss()# 打开tensorboard：在该目录下，使用 tensorboard --logdir=runs
writer_fake = SummaryWriter(f"runs/GAN_MNIST/fake")
writer_real = SummaryWriter(f"runs/GAN_MNIST/real")
step = 0for epoch in range(num_epochs):for batch_idx, (real, _) in enumerate(loader):real = real.view(-1, 784).to(device) # view相当于reshapebatch_size = real.shape[0]### Train Discriminator: max log(D(real)) + log(1 - D(G(z)))noise = torch.randn(batch_size, z_dim).to(device)fake = gen(noise) # G(z)disc_real = disc(real).view(-1) # flatten# BCEloss的表达式：min -[ylnx + (1-y)ln(1-x)]# max log(D(real)) 相当于 min -log(D(real))# ones_like: 用1填充得到y=1, 即可忽略  min -[ylnx + (1-y)ln(1-x)]中的后一项# 得到 min -lnx,这里的x就是我们的real图片lossD_real = criterion(disc_real, torch.ones_like(disc_real))disc_fake = disc(fake).view(-1)# max log(1 - D(G(z))) 相当于 min -log(1 - D(G(z)))# zeros_like用0填充，得到y=0，即可忽略  min -[ylnx + (1-y)ln(1-x)]中的前一项# 得到 min -ln(1-x),这里的x就是我们的fake噪声lossD_fake = criterion(disc_fake, torch.zeros_like(disc_fake))lossD = (lossD_real + lossD_fake) / 2disc.zero_grad()lossD.backward(retain_graph=True)opt_disc.step()### Train Generator: min log(1-D(G(z))) <--> max log(D(G(z))) <--> min - log(D(G(z)))# 依然可使用BCEloss来做output = disc(fake).view(-1)lossG = criterion(output, torch.ones_like(output))gen.zero_grad()lossG.backward()opt_gen.step()if batch_idx == 0:print(f"Epoch [{epoch}/{num_epochs}] \ "f"Loss D: {lossD:.4f}, Loss G: {lossG:.4f}")with torch.no_grad():fake = gen(fixed_noise).reshape(-1, 1, 28, 28)data = real.reshape(-1, 1, 28, 28)img_grid_fake = torchvision.utils.make_grid(fake, normalize=True)img_grid_real = torchvision.utils.make_grid(data, normalize=True)writer_fake.add_image("Mnist Fake Images", img_grid_fake, global_step=step)writer_real.add_image("Mnist Real Images", img_grid_real, global_step=step)step += 1

结果

训练50轮的的损失

Epoch [0/50] \ Loss D: 0.7366, Loss G: 0.7051
Epoch [1/50] \ Loss D: 0.2483, Loss G: 1.6877
Epoch [2/50] \ Loss D: 0.1049, Loss G: 2.4980
Epoch [3/50] \ Loss D: 0.1159, Loss G: 3.4923
Epoch [4/50] \ Loss D: 0.0400, Loss G: 3.8776
Epoch [5/50] \ Loss D: 0.0450, Loss G: 4.1703
...
Epoch [43/50] \ Loss D: 0.0022, Loss G: 7.7446
Epoch [44/50] \ Loss D: 0.0007, Loss G: 9.1281
Epoch [45/50] \ Loss D: 0.0138, Loss G: 6.2177
Epoch [46/50] \ Loss D: 0.0008, Loss G: 9.1188
Epoch [47/50] \ Loss D: 0.0025, Loss G: 8.9419
Epoch [48/50] \ Loss D: 0.0010, Loss G: 8.3315
Epoch [49/50] \ Loss D: 0.0007, Loss G: 7.8302

使用

tensorboard --logdir=runs

打开tensorboard：

可以看到效果并不好，这是由于我们只是采用了简单的线性网络来做辨别器和生成器。后面的博文我们会使用更复杂的网络来训练GAN。

参考

[1] Building our first simple GAN
[2] https://arxiv.org/abs/1406.2661