Name | Prof. Dr. Helmut Bölcskei |

Field | Mathematical Information Science |

Address | Professur Math. Informationswiss. ETH Zürich, ETF E 122 Sternwartstrasse 7 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 33 |

hboelcskei@ethz.ch | |

URL | https://www.mins.ee.ethz.ch/people/show/boelcskei |

Department | Information Technology and Electrical Engineering |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

227-0045-00L | Signals and Systems I | 4 credits | 2V + 2U | H. Bölcskei | |

Abstract | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | ||||

Objective | Introduction to mathematical signal processing and system theory. | ||||

Content | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | ||||

Lecture notes | Lecture notes, problem set with solutions. | ||||

227-0423-00L | Neural Network Theory | 4 credits | 2V + 1U | H. Bölcskei, E. Riegler | |

Abstract | 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 | ||||

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 neural networks. | ||||

Content | 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 | ||||

Lecture notes | Detailed lecture notes will be provided as we go along. | ||||

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. | ||||

401-5680-00L | Foundations of Data Science Seminar | 0 credits | P. L. Bühlmann, A. Bandeira, H. Bölcskei, J. M. Buhmann, T. Hofmann, A. Krause, A. Lapidoth, H.‑A. Loeliger, M. H. Maathuis, G. Rätsch, C. Uhler, S. van de Geer | ||

Abstract | Research colloquium | ||||

Objective |