第 04 课 · 六大核心方法

生成对抗网络（GAN）

伪造者对抗侦探：两个网络相互竞争，直到都变得很强。

GAN 有两个网络：生成器把噪声变成伪造数据，判别器努力区分真假。两者轮流训练，直到生成器产生的数据让判别器无法分辨。

示例训练 GAN 生成圆周上 8 个簇的点，并检查是否覆盖全部 8 个簇——用来检测模式坍塌。

D: max E[log D(x)] + E[log(1 − D(G(z)))] G: max E[log D(G(z))] WGAN-GP critic: E[C(fake)] − E[C(real)] + λ·E[(‖∇C(x̂)‖ − 1)²]

问题	表现	解决办法
Mode collapse	只生成少数几种结果	WGAN-GP, minibatch tricks
梯度消失	D 太强，G 学不到东西	Wasserstein 损失 + 梯度惩罚
想指定类别	采样结果混在一起	Conditional GAN (CGAN)

要点

GAN 不建模 p(x)，而是直接学习采样，所以图像很清晰
训练 GAN 的关键在于平衡 D 和 G

generative-ai-ep04-gan.py

import math, torch, torch.nn as nn

torch.manual_seed(0)
# Real data: 8 Gaussian blobs on a circle, a classic test for "mode collapse"
centers = torch.tensor([[math.cos(2 * math.pi * k / 8), math.sin(2 * math.pi * k / 8)] for k in range(8)]) * 2
def real_batch(n=256):
    return centers[torch.randint(0, 8, (n,))] + 0.05 * torch.randn(n, 2)

def mlp(out):
    return nn.Sequential(nn.Linear(2, 256), nn.LeakyReLU(0.2),
                         nn.Linear(256, 256), nn.LeakyReLU(0.2), nn.Linear(256, out))

G, D = mlp(2), mlp(1)                       # generator: noise -> point, discriminator: point -> real?
opt_g = torch.optim.Adam(G.parameters(), lr=1e-4, betas=(0.5, 0.9))
opt_d = torch.optim.Adam(D.parameters(), lr=1e-4, betas=(0.5, 0.9))
bce = nn.BCEWithLogitsLoss()

for step in range(4001):
    real, fake = real_batch(), G(torch.randn(256, 2))
    # 1) discriminator: real -> 1, fake -> 0
    d_loss = bce(D(real), torch.ones(256, 1)) + bce(D(fake.detach()), torch.zeros(256, 1))
    opt_d.zero_grad(); d_loss.backward(); opt_d.step()
    # 2) generator: fool D into saying 1
    g_loss = bce(D(fake), torch.ones(256, 1))
    opt_g.zero_grad(); g_loss.backward(); opt_g.step()
    if step % 1000 == 0:
        with torch.no_grad():
            dist, nearest = torch.cdist(G(torch.randn(4000, 2)), centers).min(1)
        hit = dist < 0.25                                  # sample landed on a real blob
        covered = (torch.bincount(nearest[hit], minlength=8) > 100).sum().item()
        print(f"step {step:4d}  D {d_loss.item():.2f}  G {g_loss.item():.2f}  "
              f"on target {hit.float().mean():.0%}  modes covered {covered}/8")

输出结果

step    0  D 1.41  G 0.75  on target 0%  modes covered 0/8
step 1000  D 1.26  G 0.79  on target 44%  modes covered 8/8
step 2000  D 1.16  G 0.92  on target 60%  modes covered 8/8
step 3000  D 1.19  G 0.92  on target 69%  modes covered 8/8
step 4000  D 1.21  G 1.00  on target 74%  modes covered 8/8

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生成对抗网络（GAN）

要点