Lecture
This lecture delves into the concept of generalization in deep learning, exploring the trade-off between model complexity and expected risk. Topics covered include the classical trade-off, generalization bounds, implicit regularization, and the double descent phenomenon. The instructor discusses the challenges in understanding deep learning generalization, the mathematics behind model complexity, and the implicit bias of optimization algorithms. Various examples and experiments are presented to illustrate the double descent curve, the dangers of complex function classes, and the behavior of optimization algorithms. The lecture concludes with insights on benign overfitting and the probability of interpolation in high-dimensional datasets.