Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
GANs & Adversarial Divergence Minimization
Adversarial min-max ideas appear in adversarial training and some alignment techniques
#8GANsGenerative Models
key equation
\min_G \max_D \; \mathbb E_{p_{\text{data}}}[\log D(x)] + \mathbb E_{p(z)}[\log(1 - D(G(z)))]Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 8 of 100GANsGenerative Models / Phase 4: Generative modeling families
Current question
Why JS divergence leads to vanishing gradients when supports don't overlap, and how Wasserstein distances fix this
\min_G \max_D \; \mathbb E_{p_{\text{data}}}[\log D(x)] + \mathbb E_{p(z)}[\log(1 - D(G(z)))]Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.
Why It Matters for Modern Models
- Adversarial min-max ideas appear in adversarial training and some alignment techniques
- GAN-like training still influential in high-fidelity image/video generation
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Why JS divergence leads to vanishing gradients when supports don't overlap, and how Wasserstein distances fix this
- Geometric visualizations of discriminator decision surfaces over latent manifolds
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Original GAN objective:
At optimum, with optimal discriminator , this minimizes the Jensen–Shannon divergence between model and data.
WGAN replaces JS with Earth-Mover (Wasserstein-1) distance, with Lipschitz constraints on .