Least Squares Generative Adversarial Networks（小白学GAN 十一）

原文链接：https://arxiv.org/pdf/1611.04076.pdf

简介

背景：原始的GAN使用sigmoid与cross entropy来优化判别器，这样会存在如下问题：

当部分生成数据远远偏离真实数据分布时，判别器的LOSS却无力将其区分出来，也就是说当真实数据分布被生成数据分布所覆盖时，判别的作用就失效了。

核心思想：去掉sigmoid激活函数，将LOSS函数换为最小均方LOSS，拟合的意义从判断两个分布是否“靠近”，变为判断两个分布是否“相似”。

基础结构

网络改进

在结构上，借鉴了DCGAN，具体的网络结构如下：

有所不同的是，其中使用了一些stride=1的反卷积层。

LOSS改进

将sigmoid+cross entropy换为MSEloss，优化过程可以表示为：

上式中引入a，b和c是为了进行一下证明：

                                   

当b-c=1,b-a=2时，有：

                              

此时，优化过程可以表示为：

作者也提出了另一种基于零一编码的方式，令b=c，a=0，此时优化过程可以表示为：

加入约束条件

借鉴了CGAN的结构，在噪声输入时加入约束编码向量。用标签生成one-hot编码向量，再通过fc将维度降下来，让后将其分别送入生成器的输入层及判别器的

优化过程可以表示为：

代码与实践

参考链接：https://github.com/eriklindernoren/PyTorch-GAN/blob/master/implementations/lsgan/lsgan.py

import argparse
import os
import numpy as np
import math

import torchvision.transforms as transforms
from torchvision.utils import save_image

from torch.utils.data import DataLoader
from torchvision import datasets
from torch.autograd import Variable

import torch.nn as nn
import torch.nn.functional as F
import torch

os.makedirs("images", exist_ok=True)

parser = argparse.ArgumentParser()
parser.add_argument("--n_epochs", type=int, default=200, help="number of epochs of training")
parser.add_argument("--batch_size", type=int, default=64, help="size of the batches")
parser.add_argument("--lr", type=float, default=0.0002, help="adam: learning rate")
parser.add_argument("--b1", type=float, default=0.5, help="adam: decay of first order momentum of gradient")
parser.add_argument("--b2", type=float, default=0.999, help="adam: decay of first order momentum of gradient")
parser.add_argument("--n_cpu", type=int, default=8, help="number of cpu threads to use during batch generation")
parser.add_argument("--latent_dim", type=int, default=100, help="dimensionality of the latent space")
parser.add_argument("--img_size", type=int, default=32, help="size of each image dimension")
parser.add_argument("--channels", type=int, default=1, help="number of image channels")
parser.add_argument("--sample_interval", type=int, default=1000, help="number of image channels")
opt = parser.parse_args()
print(opt)

cuda = True if torch.cuda.is_available() else False


def weights_init_normal(m):
    classname = m.__class__.__name__
    if classname.find("Conv") != -1:
        torch.nn.init.normal_(m.weight.data, 0.0, 0.02)
    elif classname.find("BatchNorm") != -1:
        torch.nn.init.normal_(m.weight.data, 1.0, 0.02)
        torch.nn.init.constant_(m.bias.data, 0.0)


class Generator(nn.Module):
    def __init__(self):
        super(Generator, self).__init__()

        self.init_size = opt.img_size // 4
        self.l1 = nn.Sequential(nn.Linear(opt.latent_dim, 128 * self.init_size ** 2))

        self.conv_blocks = nn.Sequential(
            nn.Upsample(scale_factor=2),
            nn.Conv2d(128, 128, 3, stride=1, padding=1),
            nn.BatchNorm2d(128, 0.8),
            nn.LeakyReLU(0.2, inplace=True),
            nn.Upsample(scale_factor=2),
            nn.Conv2d(128, 64, 3, stride=1, padding=1),
            nn.BatchNorm2d(64, 0.8),
            nn.LeakyReLU(0.2, inplace=True),
            nn.Conv2d(64, opt.channels, 3, stride=1, padding=1),
            nn.Tanh(),
        )

    def forward(self, z):
        out = self.l1(z)
        out = out.view(out.shape[0], 128, self.init_size, self.init_size)
        img = self.conv_blocks(out)
        return img


class Discriminator(nn.Module):
    def __init__(self):
        super(Discriminator, self).__init__()

        def discriminator_block(in_filters, out_filters, bn=True):
            block = [nn.Conv2d(in_filters, out_filters, 3, 2, 1), nn.LeakyReLU(0.2, inplace=True), nn.Dropout2d(0.25)]
            if bn:
                block.append(nn.BatchNorm2d(out_filters, 0.8))
            return block

        self.model = nn.Sequential(
            *discriminator_block(opt.channels, 16, bn=False),
            *discriminator_block(16, 32),
            *discriminator_block(32, 64),
            *discriminator_block(64, 128),
        )

        # The height and width of downsampled image
        ds_size = opt.img_size // 2 ** 4
        self.adv_layer = nn.Linear(128 * ds_size ** 2, 1)

    def forward(self, img):
        out = self.model(img)
        out = out.view(out.shape[0], -1)
        validity = self.adv_layer(out)

        return validity


# !!! Minimizes MSE instead of BCE
adversarial_loss = torch.nn.MSELoss()

# Initialize generator and discriminator
generator = Generator()
discriminator = Discriminator()

if cuda:
    generator.cuda()
    discriminator.cuda()
    adversarial_loss.cuda()

# Initialize weights
generator.apply(weights_init_normal)
discriminator.apply(weights_init_normal)

# Configure data loader
os.makedirs("../../data/mnist", exist_ok=True)
dataloader = torch.utils.data.DataLoader(
    datasets.MNIST(
        "../../data/mnist",
        train=True,
        download=True,
        transform=transforms.Compose(
            [transforms.Resize(opt.img_size), transforms.ToTensor(), transforms.Normalize([0.5], [0.5])]
        ),
    ),
    batch_size=opt.batch_size,
    shuffle=True,
)

# Optimizers
optimizer_G = torch.optim.Adam(generator.parameters(), lr=opt.lr, betas=(opt.b1, opt.b2))
optimizer_D = torch.optim.Adam(discriminator.parameters(), lr=opt.lr, betas=(opt.b1, opt.b2))

Tensor = torch.cuda.FloatTensor if cuda else torch.FloatTensor

# ----------
#  Training
# ----------

for epoch in range(opt.n_epochs):
    for i, (imgs, _) in enumerate(dataloader):

        # Adversarial ground truths
        valid = Variable(Tensor(imgs.shape[0], 1).fill_(1.0), requires_grad=False)
        fake = Variable(Tensor(imgs.shape[0], 1).fill_(0.0), requires_grad=False)

        # Configure input
        real_imgs = Variable(imgs.type(Tensor))

        # -----------------
        #  Train Generator
        # -----------------

        optimizer_G.zero_grad()

        # Sample noise as generator input
        z = Variable(Tensor(np.random.normal(0, 1, (imgs.shape[0], opt.latent_dim))))

        # Generate a batch of images
        gen_imgs = generator(z)

        # Loss measures generator's ability to fool the discriminator
        g_loss = adversarial_loss(discriminator(gen_imgs), valid)

        g_loss.backward()
        optimizer_G.step()

        # ---------------------
        #  Train Discriminator
        # ---------------------

        optimizer_D.zero_grad()

        # Measure discriminator's ability to classify real from generated samples
        real_loss = adversarial_loss(discriminator(real_imgs), valid)
        fake_loss = adversarial_loss(discriminator(gen_imgs.detach()), fake)
        d_loss = 0.5 * (real_loss + fake_loss)

        d_loss.backward()
        optimizer_D.step()

        print(
            "[Epoch %d/%d] [Batch %d/%d] [D loss: %f] [G loss: %f]"
            % (epoch, opt.n_epochs, i, len(dataloader), d_loss.item(), g_loss.item())
        )

        batches_done = epoch * len(dataloader) + i
        if batches_done % opt.sample_interval == 0:
            save_image(gen_imgs.data[:25], "images/%d.png" % batches_done, nrow=5, normalize=True)

 minist测试结果

可见这种方法收敛的很快，之所以会成周期性，应该时使用adam来优化，loss长时间不降，加动量所至的。总之，此种方法对GAN的训练是有效的。