Learning in the Presence of Distribution Shifts: How does the Geometry of Perturbations Play a Role?

This lecture explores the challenges of learning in the presence of distribution shifts, focusing on the role of perturbation geometry. It covers topics such as deep learning in safety-critical applications, adversarial examples, sparse perturbations, norm-bounded perturbations, and natural variation. The instructor discusses the impact of perturbations on misclassification, the geometry of perturbations, and the development of robust classifiers. Additionally, the lecture delves into the concepts of L0 ball perturbations, model-based domain generalization, and the tradeoffs between standard and adversarial risks. The presentation concludes with insights on robust classification in the L0 setting and the importance of modeling natural variation for generalization.