Explore the foundations of deep learning in this lecture focusing on stochastic gradient descent, overparametrization, and generalization. Delve into fundamental questions and challenges in the field, examining the landscape of optimization and how gradient descent finds global minima. Investigate the dynamics of prediction, local geometry, and the interplay between local and global geometry. Analyze generalization error and the impact of overparametrization on model performance. Gain insights into margin theory, max margin via logistic loss, and how overparametrization improves the margin. Compare optimization with regularizers to Neural Tangent Kernel (NTK) approaches. Examine the unique properties of gradient descent and explore steepest descent methods with examples. Investigate deep networks beyond linear models, discussing implicit regularization and the importance of architecture. Consider the effects of changing depth in linear and convolutional networks, concluding with thought-provoking ideas on the future of deep learning. Read more