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401-3650-19L 4 Credits MSC D-MATH
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Numerical Analysis Seminar: Mathematics of Deep Neural Network Approximation

Lecturers & Examiners: Prof. Dr. Christoph Schwab
Number of participants limited to 6. Priority will be given to MSc students who did not complete a seminar.
VVZ CR n/a

Last Updated: 2026-02-05 15:41:17

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. 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 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

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
06.01.2020
Signup End
24.02.2020
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: Mathematics of Deep Neural Network Approximation
Permission from lecturers required for all students. Preliminary discussions and assignment of seminar topic to participants during the first two weeks of spring 2020 teaching term. Student talks are planned to take place several Fridays in May 2020.
  • 18.02 Date 12:15-14:00 (HG F 26.3)
  • 25.02 Date 12:15-14:00 (HG F 26.3)
  • 17.03 Date 12:15-14:00 (ML J 37.1)
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 afterwards choose an alternative seminar.)