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401-3650-19L 4 Credits MSC D-MATH

Numerical Analysis Seminar: Deep Neural Network Approximation

Lecturers & Examiners: Prof. Dr. Christoph Schwab
Does not take place this semester.
VVZ CR n/a

Last Updated: 2026-02-05 15:54:07

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.

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.

General Information

Language
English
Levels
MSC
Frequency
Yearly recurring

Examination

Type
ungraded semester performance
Passing grade will requirea) 1hr oral presentation with Q/A from the seminar group andb) typed seminar report (``Ausarbeitung'') of several key aspects of the paper under review.

Registration & Places

Limited places (Special selection)
Signup Start
04.01.2021
Signup End
19.02.2021
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar 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.
  • By Appointment None-None
2 h weekly

Offered In

  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)