Seminar Supervisor

Prof. Dr. Evgeny Spodarev

Date and Place

Talks (90 min each) will be made in one or two day blocks in the middle or at the end of the summer term.

Prerequisites

Good working knowledge of elementary probability and statistics is a must. Advanced courses in stochastic processes (like Markov Chains) and statistics are recommended but not necessary. 

Intended Audience

Bachelor and Master students in any mathematical programme of studies. 

Content

Diffusion neural networks (DNN) are a state-of-the art technology in modern artificial intelligence (AI) applications to imaging and computer vision. Many of you have already some experience with commercial AI image generators such as BING of Microsoft, Stable Diffusion 2.1 of Stable AI, DALL-E 3 of Open AI, etc. which revolutionize modern arts. The number of computer science and engineering research papers  only on DNNs within the last three years is huge which indicates the vast growth potential of this technology and its eligibility to numerous applications. 

In this seminar, we will learn mathematics behind DNN as well as a range of its applications to imaging, vision, time series analysis, NLP, to name just a few.  At the same time,  students get an opportunity to apply their new expertise in a context of a bachelor/master theses on subjects which range from e.g. the use of various probability metrics to train neural networks to their applications in anomaly detection within brain EEGs or prediction of financial time series. 

The seminar will be organized with the following subjects:

1. SDEs; Ito integral; solutions, existence and uniqueness [1, Chapter 5/6].
2. Diffusions as Markov processes; Forward and backward Kolmogorov equations; ergodicity and stable regime [1, Chapter 8/9/11].
3. Transformer models [2, Chapter 12].
4. Autoencoders [2, Chapter 19].
5. Diffusion models [2, Chapter 20].
6. Applications to time series analysis [3].
7. Applications to imaging [4,5,6,7].
8. Application to NLP [8].

Registration

To enroll yourself, please write an email to tran-1.nguyen(at)uni-ulm.de till 30th April 2024 and enroll to the Moodle course. 
Please indicate your name, matriculation number, and your studies programme (Bachelor, Master)  as well as courses you have already attended in the area of Probability & Statistics. 

Maximal number of participants: 14.  

Criteria to pass the seminar

Each student is supposed to give a talk. Those who give a (good) talk together with written summary will pass the seminar. Talks will be held in English. A preliminary version of the Slides need to be submitted two weeks before each talk.

Literature

[1] Gopinath Kallianpur and P. Sundar. Stochastic Analysis and Diffusion Processes. Oxford Graduate Texts in Mathematics, volume 24. Oxford University Press, Oxford, 2014. xii+352. ISBN 978-0-19-965707-0. MR 3156223. Peter E. Kloeden.
[2] Christopher M. Bishop and Hugh Bishop. Deep Learning: Foundations and Concepts. Springer Cham, 2023. ISBN 978-3-031-45467-7 (Hardcover), 978-3-031-45468-4 (eBook). DOI 10.1007/978-3-031-45468-4.
[3] Lequan Lin, Zhengkun Li, Ruikun Li, Xuliang Li, and Junbin Gao. Diffusion Models for Time Series Applications: A Survey. 2023. arXiv:2305.00624.
[4] Zhen Xing, Qijun Feng, Haoran Chen, Qi Dai, Han Hu, Hang Xu, Zuxuan Wu, and Yu-Gang Jiang. A Survey on Video Diffusion Models. 2023. arXiv:2310.10647.
[5] Ryan Po, Wang Yifan, Vladislav Golyanik, Kfir Aberman, Jonathan T. Barron, Amit H. Bermano, Eric Ryan Chan, Tali Dekel, Aleksander Holynski, Angjoo Kanazawa, C. Karen Liu, Lingjie Liu, Ben Mildenhall, Matthias Nießner, Björn Ommer, Christian Theobalt, Peter Wonka, and Gordon Wetzstein. State of the Art on Diffusion Models for Visual Computing. 2023. arXiv:2310.07204.
[6] Tianyi Zhang, Zheng Wang, Jing Huang, Mohiuddin Muhammad Tasnim, and Wei Shi. A Survey of Diffusion Based Image Generation Models: Issues and Their Solutions. 2023. arXiv:2308.13142.
[7] Xin Li, Yulin Ren, Xin Jin, Cuiling Lan, Xingrui Wang, Wenjun Zeng, Xinchao Wang, and Zhibo Chen. Diffusion Models for Image Restoration and Enhancement -- A Comprehensive Survey. 2023. arXiv:2308.09388.
[8] Hao Zou, Zae Myung Kim, and Dongyeop Kang. A Survey of Diffusion Models in Natural Language Processing. 2023. arXiv:2305.14671.