6. Generative Adversarial Networks

Generative Networks

What is a GAN?

Introduced by Ian Goodfellow in 2014, GANs consist of two neural networks competing in a minimax game:

• Generator (G) — Takes random noise z and generates fake data G(z)
• Discriminator (D) — Attempts to distinguish real data from fake data

The generator tries to fool the discriminator, while the discriminator tries to avoid being fooled. Both improve through this adversarial process.

Figure: The GAN training loop — generator creates fakes, discriminator evaluates them.

Training Objective

The minimax objective: min_G max_D V(D,G) = E[log D(x)] + E[log(1 - D(G(z)))]

# Simplified GAN training loop
for epoch in range(epochs):
    # Train discriminator
    real = sample_real_data(batch_size)
    fake = generator(noise(batch_size))
    d_loss = -mean(log(D(real)) + log(1 - D(fake)))
    d_optimizer.step(d_loss)

    # Train generator
    fake = generator(noise(batch_size))
    g_loss = -mean(log(D(fake)))  # -log(D) trick
    g_optimizer.step(g_loss)

Important GAN Variants

• DCGAN — Convolutional GAN with architectural guidelines for stable training
• Conditional GAN (cGAN) — Both G and D receive class labels, enabling controlled generation
• StyleGAN — Style-based generator that separates high-level attributes from stochastic details
• CycleGAN — Unpaired image-to-image translation (e.g., horse → zebra)
• Progressive GAN — Training starts at low resolution, progressively adds layers
• BigGAN — Large-scale GAN for high-fidelity class-conditional image generation

Challenges in Training GANs

• Mode Collapse — Generator produces limited varieties of outputs
• Non-Convergence — Oscillations instead of stable equilibrium
• Vanishing Gradients — Discriminator becomes too good, generator learns nothing
• Hyperparameter Sensitivity — Architecture, learning rates, and initialization are delicate