Neural Network Theory

Prof. Dr. Helmut Bölcskei

Offered in:

Basic information:

Lecture:Tuesday, 10:15-12:00, HG F 5, live broadcast on the ETH video portal (live). The projected screen and audio will be broadcast and recorded. The recordings will be available the next day in the morning on the ETH video portal (lectures).
Discussion session:   Tuesday, 12:15-13:00, via Zoom. The Zoom meeting link and the recordings can be found on this page (access credentials are the same as for the lecture/exercise notes).
Instructors: Prof. Dr. Helmut Bölcskei
Teaching assistants: Weigutian Ou, Dennis Elbrächter
Office hours:Tuesday, 16:00-17:00, via Zoom. Please contact the TAs for their Zoom ID.
Lecture notes:The download link is provided below.
Credits: 4 ECTS credits
Course structure: The class will be taught in English. There will be a written exam in English of duration 180 minutes.


We will post important announcements, links, and other information here in the course of the semester.

Course Information

The class focuses on fundamental mathematical aspects of neural networks with an emphasis on deep networks.


The course is aimed at students with a strong mathematical background in general, and in linear algebra, analysis, and probability theory in particular.

Lecture notes

Lecture notes

Handwritten notes on second part of class

Handwritten notes

Here we will post notes written on the iPad during the lectures.
iPad notes of lecture of 21.09.2021
iPad notes of lecture of 28.09.2021
iPad notes of lecture of 05.10.2021
iPad notes of lecture of 12.10.2021
iPad notes of lecture of 19.10.2021
iPad notes of lecture of 26.10.2021
iPad notes of lecture of 02.11.2021
iPad notes of lecture of 09.11.2021
iPad notes of lecture of 16.11.2021
iPad notes of lecture of 23.11.2021
iPad notes of lecture of 30.11.2021
iPad notes of lecture of 07.12.2021
iPad notes of lecture of 14.12.2021
iPad notes of lecture of 21.12.2021

Problem sets and solutions

There will be several problem sets for this course, which will help you better understand the lectures and prepare you for the exam. All the problem sets will be discussed in the exercise session, and the solutions will be uploaded afterwards.

Problems Solutions
Set 1 Solutions to Set 1
Set 2 Solutions to Set 2
Set 3 Solutions to Set 3
Set 4 Solutions to Set 4
Set 5 Solutions to Set 5
Set 6 Solutions to Set 6
Set 7 Solutions to Set 7
Set 8 Solutions to Set 8
Set 9 Solutions to Set 9
Set 10 Solutions to Set 10
Set 11 Solutions to Set 11

Parts of the notes relevant for the exam:

Note that you are not required to learn proofs by heart or to recite key steps in proofs. You are, however, expected to understand the main ideas/techniques/concepts used in the proofs in the relevant material listed above, but only applying to those proofs that were taught in class. To see which proofs were taught in class, please consult the handwritten notes of the class posted on the course web page.

Previous years' exams and solutions

Winter Exam 2020: Problems Solutions
Summer Exam 2020: Problems Solutions
Winter Exam 2021: Problems Solutions
Summer Exam 2021: Problems Solutions
Winter Exam 2022: Problems Solutions