I am working through Mathematical Foundations of Generative AI , Prof. Prathosh AP's public lectures. The playlist is the spine. These notes are my deep dive on each section: a visual when the picture is the point, a detour when a prerequisite is doing real work, and every formula read aloud with a plain-words line right after it.

Previously: Section 3b: The convex conjugate and the variational bound .

Week 2 roadmap

Week 2 picks up right where Week 1 stopped. Here is how the four sections of Week 2 fit together:

Section Topic

4a (this note) From the Week 1 lower bound to a trainable min–max game (generator vs critic)

4b The critic's output activation $\sigma_f$ and $\operatorname{dom} f^*$

4c GAN as a special case: picking one particular $f$ gives the familiar GAN loss

4d Training a GAN in practice: mini-batches and alternating updates

Prerequisites for this note (detours below): Week 1's lower bound on $D_f$, "an average is approximately an expectation", and what a saddle point is.

Symbol…