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

SemesterHerbstsemester 2019
DozierendeC. Schwab
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarNumber of participants limited to 6. Consent of Instructor needed.



Lehrveranstaltungen

NummerTitelUmfangDozierende
401-3650-00 SNumerical Analysis Seminar: Mathematics of Deep Neural Network Approximation
Bewilligung der Dozierenden für alle Studierenden notwendig.
Preliminary discussions and assignment of seminar topic to participants: Monday, 16 September 2019 at 13:15 in HG E 33.1.
Student talks are planned to take place on .... The room reservations will be announced in due course.
2 Std.
16.09.13:15-15:00HG E 33.1 »
23.09.13:15-15:00HG F 26.3 »
14.10.13:15-15:00HG F 26.3 »
28.10.13:15-15:00HG F 26.3 »
11.11.13:15-15:00HG E 23 »
25.11.13:15-15:00HG F 26.3 »
02.12.12:15-14:00HG F 26.3 »
09.12.13:15-16:00ML H 43 »
16.12.13:15-15:00HG F 26.3 »
C. Schwab

Katalogdaten

KurzbeschreibungThe 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.
Lernziel
InhaltPresentation 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
https://arxiv.org/abs/1901.05639
and, more mathematical and closer to the seminar theme,
https://arxiv.org/abs/1901.02220

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.

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte4 KP
PrüfendeC. Schwab
Formunbenotete Semesterleistung
PrüfungsspracheEnglisch
RepetitionRepetition nur nach erneuter Belegung der Lerneinheit möglich.
ZulassungsbedingungCompleted BSc MATH ETH and Consent of Instructor
Zusatzinformation zum PrüfungsmodusPassing 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.

Lernmaterialien

Keine öffentlichen Lernmaterialien verfügbar.
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

Keine Informationen zu Gruppen vorhanden.

Einschränkungen

AllgemeinBewilligung der Dozierenden für alle Studierenden notwendig
PlätzeMaximal 6
VorrangDie Belegung der Lerneinheit ist nur durch die primäre Zielgruppe möglich
Primäre ZielgruppeMathematik MSc (437000)
Angewandte Mathematik MSc (437100)
Rechnergestützte Wissenschaften MSc (438000)
WartelisteBis 19.09.2019

Angeboten in

StudiengangBereichTyp
Mathematik MasterSeminareWInformation