🧠 Deep LearningID: gan

GAN Adversarial Training

Q: Write GAN's min-max objective and derive the optimal discriminator $D^*(x)$?

【GAN Adversarial Training 核心考点 1】Write GAN's min-max objective and derive the optimal discriminator $D^*(x)$?。技术解析：Definition: GANs pit a generator G against a discriminator D in a zero-sum min-max game: \min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]. For fixed G, differentiating w.r.t. D yields the optimal discriminator as a likelih... 完整推导与工程落地见：https://talentme.airsota.com/resources/tech/roadmap/mindmap/DL/card/gan

Q: Why does substituting $D^*$ reduce GAN to minimizing $JSD(p_{data} \Vert p_g)$?

【GAN Adversarial Training 核心考点 2】Why does substituting $D^*$ reduce GAN to minimizing $JSD(p_{data} \Vert p_g)$?。技术解析：Definition: GANs pit a generator G against a discriminator D in a zero-sum min-max game: \min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]. For fixed G, differentiating w.r.t. D yields the optimal discriminator as a likelih... 完整推导与工程落地见：https://talentme.airsota.com/resources/tech/roadmap/mindmap/DL/card/gan

Q: Why is GAN training unstable? Mechanisms behind vanishing gradients and mode collapse?

【GAN Adversarial Training 核心考点 3】Why is GAN training unstable? Mechanisms behind vanishing gradients and mode collapse?。技术解析：Definition: GANs pit a generator G against a discriminator D in a zero-sum min-max game: \min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]. For fixed G, differentiating w.r.t. D yields the optimal discriminator as a likelih... 完整推导与工程落地见：https://talentme.airsota.com/resources/tech/roadmap/mindmap/DL/card/gan

Q: Why do GANs suffer mode collapse while VAEs do not? How do their sample qualities differ?

【GAN Adversarial Training 核心考点 4】Why do GANs suffer mode collapse while VAEs do not? How do their sample qualities differ?。技术解析：Definition: GANs pit a generator G against a discriminator D in a zero-sum min-max game: \min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]. For fixed G, differentiating w.r.t. D yields the optimal discriminator as a likelih... 完整推导与工程落地见：https://talentme.airsota.com/resources/tech/roadmap/mindmap/DL/card/gan

Q: Common techniques to stabilize GAN training (label smoothing / TTUR / spectral norm)?

【GAN Adversarial Training 核心考点 5】Common techniques to stabilize GAN training (label smoothing / TTUR / spectral norm)?。技术解析：Definition: GANs pit a generator G against a discriminator D in a zero-sum min-max game: \min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]. For fixed G, differentiating w.r.t. D yields the optimal discriminator as a likelih... 完整推导与工程落地见：https://talentme.airsota.com/resources/tech/roadmap/mindmap/DL/card/gan

GAN 对抗训练

🎯Core Definition

GANs pit a generator

G

against a discriminator

D

in a zero-sum min-max game:

\min_G\max_D V(D,G) = \mathbb{E}_{x \sim p_{data}}[\log D(x)] + \mathbb{E}_{z \sim p_z}[\log(1 - D(G(z)))]

. For fixed

G

, differentiating w.r.t.

D

yields the optimal discriminator as a likelihood ratio

D^*(x) = \frac{p_{data}(x)}{p_{data}(x) + p_g(x)}

; plugging it back gives

V(D^*, G) = -\log 4 + 2 \cdot JSD(p_{data} \Vert p_g)

, i.e. GAN minimizes the Jensen-Shannon divergence between the data and generated distributions, reaching the global optimum

-\log 4

iff

p_{data} = p_g

💡Use Cases

image generation (DCGAN/ProGAN/StyleGAN), super-resolution, image-to-image translation; interviews drill the min-max objective, the

D^*

derivation, and instability/mode-collapse mechanisms.

⚡Key Problems Solved

unlike VAEs with explicit density approximation and pixel-wise reconstruction losses, GANs make no distributional assumption and produce sharper samples; the cost is that alternating D/G training approximates a Nash equilibrium rather than minimizing a loss — with a too-strong