227-0423-00L  Neural Network Theory

SemesterAutumn Semester 2020
LecturersH. Bölcskei
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
227-0423-00 VNeural Network Theory
«Hybrid».
Up to 150 students can attend the course on-site. Further information will be announced to enrolled students by e-mail in the week before the semester starts.

The first lecture is on 21.9.
2 hrs
Mon10-12ETF C 1 »
H. Bölcskei
227-0423-00 UNeural Network Theory
«Hybrid».
Up to 150 students can attend the course on-site. Further information will be announced to enrolled students by e-mail in the week before the semester starts.

The first lecture is on 21.9.
1 hrs
Mon12-13ETF C 1 »
H. Bölcskei

Catalogue data

AbstractThe class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, basics of approximation theory, fundamental limits of deep neural network learning, geometry of decision surfaces, capacity of separating surfaces, dimension measures relevant for generalization, VC dimension of neural networks.
ObjectiveAfter attending this lecture, participating in the exercise sessions, and working on the homework problem sets, students will have acquired a working knowledge of the mathematical foundations of (deep) neural networks.
Content1. Universal approximation with single- and multi-layer networks

2. Introduction to approximation theory: Fundamental limits on compressibility of signal classes, Kolmogorov epsilon-entropy of signal classes, non-linear approximation theory

3. Fundamental limits of deep neural network learning

4. Geometry of decision surfaces

5. Separating capacity of nonlinear decision surfaces

6. Dimension measures: Pseudo-dimension, fat-shattering dimension, Vapnik-Chervonenkis (VC) dimension

7. Dimensions of neural networks

8. Generalization error in neural network learning
Lecture notesDetailed lecture notes will be provided.
Prerequisites / NoticeThis course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersH. Bölcskei
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 180 minutes
Written aidsNone
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkCourse website
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Groups

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Restrictions

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Offered in

ProgrammeSectionType
Data Science MasterInformation and LearningWInformation
Electrical Engineering and Information Technology MasterCore SubjectsWInformation
Electrical Engineering and Information Technology MasterRecommended SubjectsWInformation
Electrical Engineering and Information Technology MasterAdvanced Core CoursesWInformation
Electrical Engineering and Information Technology MasterSpecialisation CoursesWInformation
Computer Science MasterComputer Science Elective CoursesWInformation
Computer Science MasterElective Courses (only for Programme Regulations 2020)WInformation
Mathematics MasterSelection: Further RealmsWInformation
Physics MasterGeneral ElectivesWInformation
Computational Science and Engineering MasterElectivesWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation
Statistics MasterSubject Specific ElectivesWInformation