# Mathematics of Deep Neural Networks

## Welcome to the seminar "Mathematics of Deep Neural Networks"

by Prof. Dr. Gitta Kutyniok.

## Content

Artificial intelligence (AI) is currently changing public life and science in an unprecedented way. Deep artificial neural networks, which mimic the human brain, are one of the central methods here; these are usually summarized under the term "deep learning". If you take a closer look, the class of neural networks is nothing more than a parameterized structured function class, i.e. a highly mathematical object.

Intensive research is currently being carried out, particularly on the mathematical side, to develop a mathematical basis for deep learning, for example to analyze phenomena such as a lack of robustness, to understand the behaviour of training algorithms or to explain the decisions of an AI algorithm. Depending on the problem at hand, a wide variety of mathematical methods are used, from algebraic geometry, functional analysis and stochastics to discrete mathematics such as graph theory and even mathematical logic.

In this seminar we will get to know various of these topics. Each presentation will be based on a scientific article, so that the presentations can also be prepared independently of each other. Of course, great attention will be paid to the previous knowledge and interests of the respective participant. At the end of the seminar, each participant will have gained a deep understanding of their own topic as well as a very good overview of this exciting and highly topical field of research. In order to further improve the quality of the presentations and since giving presentations is of central importance for any professional development, we will conduct a short rhetoric training at the beginning.

## Registration

All students who are interested in participating are asked to register in advance (by 14.04.). To do so, please register for the corresponding Moodle course Mathematics of Deep Neural Networks (Kutyniok, Fono) with the registration key MDNNs24. If there are too many interested students, it is possible that not all of them can be accepted. If you are unable to attend the seminar after registering, please let us know so that other interested students have the opportunity to register.

## Dates

The seminar takes place on Wednesdays 10-12 in B 251. The exact timetable will be discussed on the first date, possibly the presentations of the participants will be held in blocks at the end of the semester.

## Organizational details

The seminar can be credited as a pro-seminar and also as a main seminar in the mathematics and business/financial mathematics degree programs. If interested, students of computer science and statistics are also welcome. For crediting as a main seminar, a draft is required in addition to the presentation. Details will be discussed at the first meeting.

All participants who would like to receive credit for their work are requested to write an email to Prof. Dr. Kutyniok kutyniok@math.lmu.de with the following information: Name, matriculation number, title and date of the presentation, credits for (module), any attachments (e.g. a draft).