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227-0423-00L 4 Credits DR , MSC D-ITET , D-INFK , D-MATH , D-PHYS
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Neural Network Theory

Lecturers & Examiners: Prof. Dr. Helmut Bölcskei
VVZ CR 4.0

Last Updated: 2026-06-01 11:30:51

Abstract

The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks: Universal approximation theorems, capacity of separating surfaces, generalization, fundamental limits of deep neural network learning, VC dimension.

Objective

After 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 neural networks.

Content

1. 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. Vapnik-Chervonenkis (VC) dimension 7. VC dimension of neural networks 8. Generalization error in neural network learning

Resources

Lecture Notes

Detailed lecture notes are available on the course web pagehttps://www.mins.ee.ethz.ch/teaching/nnt/

Learning Materials (Links)

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
None

Course Components

Type Title Time & Place Hours
lecture Neural Network Theory
  • Tue 10:15-12:00 (HG F 5)
2 h weekly
exercise Neural Network Theory
  • Tue 12:15-13:00 (HG F 5)
1 h weekly

Offered In