Assess students' ability to analyze convergence behavior and generalization trade-offs in non‑convex stochastic optimization for overparameterized deep networks, including deriving or critiquing convergence rates of SGD/variants, explaining implicit regularization mechanisms (e.g., noise, early stopping, momentum, geometry), connecting NTK/mean‑field or SDE approximations to generalization phenomena (double descent, sharpness vs flatness), and designing/interpreting experiments or proof sketches that illustrate optimization–generalization trade-offs.