227-0423-00L Neural Network Theory

Abstract	The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, basics of approximation theory, fundamental limits of deep neural network learning, geometry of decision surfaces, capacity of separating surfaces, dimension measures relevant for generalization, VC dimension of neural networks.
Learning objective	After attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the mathematical foundations of (deep) neural networks.
Content	1. Universal approximation with single- and multi-layer networks 2. Introduction to approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, non-linear approximation theory 3. Fundamental limits of deep neural network learning 4. Geometry of decision surfaces 5. Separating capacity of nonlinear decision surfaces 6. Dimension measures: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis (VC) dimension 7. Dimensions of neural networks 8. Generalization error in neural network learning
Lecture notes	Detailed lecture notes will be provided.
Prerequisites / Notice	This course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular.