401-3650-68L  Numerical Analysis Seminar: Mathematics of Deep Neural Network Approximation

SemesterAutumn Semester 2020
LecturersC. Schwab
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 6. Consent of Instructor needed.



Courses

NumberTitleHoursLecturers
401-3650-00 SNumerical Analysis Seminar: Mathematics of Deep Neural Network Approximation
Permission from lecturers required for all students.
Preliminary discussions and assignment of seminar topic to participants: 15 September 2020, 13-15 in HG G 19.2.
Student talks are planned to take place via zoom on a date that will be communicated later.
2 hrsby appt.C. Schwab

Catalogue data

AbstractThe 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.
Objective
ContentPresentation 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 big data analysis, DNNs achieved remarkable performance
in computer vision, speech recognition and natural language processing.
In many cases, these successes have been achieved by
heuristic implementations combined
with massive compute power and training data.

For a (bird's eye) view, see
Link
and, more mathematical and closer to the seminar theme,
Link

The 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.

Format of the Seminar:
The seminar format will be oral student presentations, combined with written report.
Student presentations will be
based on a recent research paper selected in two meetings
at the start of the semester.

Grading of the Seminar:
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.

Each seminar topic will allow expansion to a semester or a
master thesis in the MSc MATH or MSc Applied MATH.

Disclaimer:
The seminar will _not_ address recent developments in DNN software,
eg. TENSORFLOW, and algorithmic 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 credits4 credits
ExaminersC. Schwab
Typeungraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.
Admission requirementCompleted BSc MATH ETH and Consent of Instructor
Additional information on mode of examinationPassing 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

GeneralPermission from lecturers required for all students
PlacesLimited number of places. Special selection procedure.
Beginning of registration periodRegistration possible from 01.08.2020
PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupMathematics MSc (437000)
Applied Mathematics MSc (437100)
Computational Science and Engineering MSc (438000)
Waiting listuntil 21.09.2020
End of registration periodRegistration only possible until 15.09.2020

Offered in

ProgrammeSectionType
Mathematics MasterSeminarsWInformation