401-3650-19L Numerical Analysis Seminar: Deep Neural Network Approximation
| Semester | Spring Semester 2021 |
| Lecturers | C. Schwab |
| Periodicity | yearly recurring course |
| Course | Does not take place this semester. |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |
|---|---|---|---|---|
| 401-3650-00 S | Numerical Analysis Seminar: Deep Neural Network Approximation Does not take place this semester. Permission from lecturers required for all students. Planned to take place again in the spring semester 2022. | 2 hrs | by appt. | C. Schwab |
Catalogue data
| Abstract | This seminar will review recent _mathematical results_ on approximation power of deep neural networks (DNNs). The focus will be on mathematical proof techniques to obtain approximation rate estimates (in terms of neural network size and connectivity) on various classes of input data including, in particular, selected types of PDE solutions. |
| Learning objective | |
| Content | Presentation of the Seminar: Deep Neural Networks (DNNs) have recently attracted substantial interest and attention due to outperforming the best established techniques in a number of tasks (Chess, Go, Shogi, autonomous driving, language translation, image classification, etc.). In many cases, these successes have been achieved by heuristic implementations combined with massive compute power and training data. The seminar will address mathematical results on the approximation/ expressive power of DNNs. For a (bird's eye) overview, see https://arxiv.org/abs/1901.05639 and, more mathematical and closer to the seminar theme, https://arxiv.org/abs/1901.02220 Specifically, this seminar will review recent _mathematical results_ on approximation power of deep neural networks (DNNs). The focus will be on mathematical proof techniques to obtain approximation rate estimates (in terms of neural network size and connectivity) on various classes of input data including, in particular, selected types of PDE solutions. Mathematical results support that DNNs can equalize or outperform the best mathematical results known to date. Particular cases comprise: high-dimensional parametric maps, analytic and holomorphic maps, maps containing multi-scale features which arise as solution classes from PDEs, classes of maps which are invariant under group actions. |
| Prerequisites / Notice | Each seminar topic will allow expansion to a semester or a master thesis in the MSc MATH or MSc Applied MATH. The seminar format will be oral student presentations in the first half of May 2021, combined with a written report. Student presentations will be based on a recent research paper selected in two meetings at the start of the semester (end of February). Disclaimer: The seminar will _not_ address recent developments in DNN software, such as training heuristics, or programming techniques for DNN training in various specific applications. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 4 credits |
| Examiners | C. Schwab |
| Type | ungraded semester performance |
| Language of examination | English |
| Repetition | Repetition only possible after re-enrolling for the course unit. |
| Additional information on mode of examination | Passing grade will require a) 1hr oral presentation with Q/A from the seminar group and b) typed seminar report (``Ausarbeitung'') of several key aspects of the paper under review. |
Learning materials
| No public learning materials available. | |
| Only public learning materials are listed. |
Groups
| No information on groups available. |
Restrictions
| General | Permission from lecturers required for all students |
| Places | Limited number of places. Special selection procedure. |
| Beginning of registration period | Registration possible from 04.01.2021 |
| Priority | Registration for the course unit is only possible for the primary target group |
| Primary target group | Mathematics MSc (437000)
Applied Mathematics MSc (437100) Computational Science and Engineering MSc (438000) |
| Waiting list | until 01.03.2021 |
| End of registration period | Registration only possible until 19.02.2021 |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mathematics Master | Seminars | W |  |