227-0423-00L Neural Network Theory
Semester | Herbstsemester 2019 |
Dozierende | H. Bölcskei, E. Riegler |
Periodizität | jährlich wiederkehrende Veranstaltung |
Lehrsprache | Englisch |
Kurzbeschreibung | The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, capacity of separating surfaces, generalization, reproducing Kernel Hilbert spaces, support vector machines, fundamental limits of deep neural network learning, dimension measures, feature extraction with scattering networks |
Lernziel | 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 neural networks. |
Inhalt | 1. Universal approximation with single- and multi-layer networks 2. Geometry of decision surfaces 3. Separating capacity of nonlinear decision surfaces 4. Generalization 5. Reproducing Kernel Hilbert Spaces, support vector machines 6. Deep neural network approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, covering numbers, fundamental limits of deep neural network learning 7. Learning of real-valued functions: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis dimension 8. Scattering networks |
Skript | Detailed lecture notes will be provided as we go along. |
Voraussetzungen / Besonderes | This course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular. |