Mathematics of Generative AI

Welcome to the seminar "Mathematics of Generative AI"
by Prof. Dr. Gitta Kutyniok.

Content

Generative artificial intelligence has rapidly become one of the most influential areas of modern AI. Large language models underlying systems such as ChatGPT and Claude, as well as diffusion models, generative flow models and other foundation models, have achieved remarkable capabilities across text, images, scientific data and increasingly complex reasoning tasks. Despite their impressive empirical success, many fundamental questions concerning their mathematical foundations remain open.

From a mathematical perspective, generative AI brings together ideas from probability theory, optimization, high-dimensional geometry, dynamical systems, approximation theory, information theory and statistical learning. Current research aims, for instance, to understand how generative models represent complex probability distributions, why large pretrained models exhibit surprising generalization and in-context learning capabilities, how diffusion and flow-based models generate samples, and how reliability, uncertainty and robustness can be quantified.

In this seminar, we will study selected mathematical aspects of generative AI based on current research articles. Possible topics include the mathematical foundations of transformers and large language models, including models underlying systems such as ChatGPT and Claude, diffusion and flow-based generative models, in-context learning, foundation models, generative models for scientific applications, as well as questions of reliability, uncertainty and robustness.

Each presentation will be based on a scientific article, allowing the topics to be prepared largely independently of each other. The choice of topic will take into account the mathematical background and interests of each participant. By the end of the seminar, participants will have developed a deep understanding of their own topic as well as a broader perspective on the mathematical foundations of generative AI.

Since communicating scientific ideas clearly is an essential part of academic and professional development, we will also conduct a short presentation and rhetoric training at the beginning of the seminar.

Registration

Students who are interested in participating are asked to register in advance. To do so, please register for the corresponding Moodle Course, enrollment key: MGAI2026. 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 Wed 16:00 to 18:00 in Akademiestraße 7, Room 504. The exact timetable will be discussed in the first meeting on 14.10., presumably 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.