Viktor Stein

PhD candidate, Applied Mathematics Group

Technische Universität Berlin

CV

I am a PhD candidate in the Applied Mathematics Group led by Gabriele Steidl at TU Berlin working on Wasserstein gradient flows, regularized f-divergences and regularized optimal transport.

My research develops rigorous analytical foundations and practical algorithms for particle-based sampling methods, aiming to (i) understand properties of gradient flows in probability spaces and (ii) design fast, efficient, and stable algorithms. Developing methods that are both theoretically grounded and practically robust enables safer, faster, and more interpretable inference methods in modern applications.

When I am not doing maths, you can find me visiting the opera or the concert hall or playing badminton and table tennis.

Recent News

• I am very much looking foward talking about our work on accelerated Stein Variational Gradient Descent at the GSI'25 - 7th International Conference on Geometric Science of Information in France at the end of October.
• I am very excited to be giving a talk about our work on Wasserstein gradient flows of regularized f-divergences at the Conference on Mathematics of Machine Learning 2025 in Hamburg at the end of September.
• On the 15.09.2025, I gave a talk about the papers The emergence of clusters in self-attention dynamics and A Unified Perspective on the Dynamics of Deep Transformers in Benjamin Gess' seminar Berlin-Leipzig Hybrid Seminar SS25: Mathematics of Machine Learning.
• This week (05.08.2025) I will present a poster on Accelerated Stein Variational Gradient Flow at the conference Mathematical and Scientific Machine Learning '25 in tuesdays session.
• This Friday (25.4), I have the opportunity to present our work on Wasserstein gradient flows of MMD-regularized f-divergences via zoom in Zaid Harchaoui's Statistics groups at the University of Washington.

Accepted Publications

• R. Duong, V. Stein, R. Beinert, J. Hertrich,, G. Steidl: Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions. Accepted subject to minor modifications by the journal ESAIM: Control, Optimisation and Calculus of Variations [abstract] [pdf] [code]
• V. Stein, S. Neumayer, N. Rux, G. Steidl. Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces Analysis and Applications (World Scientific). [Journal version] [arxiV] [code] [Twitter 🧵] [Mathstodon post]
• R. Duong N. Rux , V. Stein, G. Steidl: Wasserstein Gradient Flows of MMD Functionals with Distance Kernels under Sobolev Regularization. Philosophical Transactions of the Royal Society A, special issue "Partial Differential Equations in Data Science". [abstract] [pdf] [journal version]
• V. Stein, Wuchen Li: Accelerated Stein Variational Gradient Flow. Accepted for publication in the proceedings of GSI'25: Geometric Science of Information, Part II (Springer Lecture Notes in Computer Science 16034) [arXiv] [code] [Slides] [Video]

Preprints under review

• Towards understanding Accelerated Stein Variational Gradient Flow - Analysis of Generalized Bilinear Kernels for Gaussian target distributions (joint work with Wuchen Li) [pdf] [code]
• Interpolating between Optimal Transport and KL regularized Optimal Transport using Rényi Divergences (joint work with Jonas Bresch, TU Berlin) Submitted to the journal "Results in Mathematics" in April 2024. [abstract] [pdf] [code] [Twitter 🧵] [Slides]

Talks and posters

• Accelerated Stein Variational Gradient Flow Stan Osher's Level Set Seminar, UCLA.
• Interpolating between Optimal Transport and KL regularized Optimal Transport using Rényi Divergences. University of South Carolina Mathematics Graduate Colloqium, 12.09.2024 [Slides]
• Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions. Joint Applied and Computational Mathematics (Changhui Tan & Siming He) and RTG data science seminar (Wuchen Li), University of South Carolina. 30.08.2024. [Slides]
• Wasserstein gradient flows of Moreau envelopes of f-divergences in reproducing kernel Hilbert spaces. Stan Osher's UCLA level set seminar, 19.08.24. [Slides] [Video]
• Posters at OT-DOM 24: Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces [Pitch] [Poster] (also presented at Learning and Optimization in Luminy 24 and SIGMA'24 ) and Rényi-regularized Optimal Transport (joint work with Jonas Bresch, TU Berlin) [Pitch] [Poster].
• I attended the Chemnitz Summer School on Applied Analysis in September 2023 and presented a poster about ongoing work.

Expository Talks

• Mode collapse and metastability in transformers, an overview of the papers The emergence of clusters in self-attention dynamics and A Unified Perspective on the Dynamics of Deep Transformers, held in Benjamin Gess' seminar Berlin-Leipzig Hybrid Seminar SS25: Mathematics of Machine Learning.
• "Zoom and enhance" geht wirklich - mit Atomic Norm Minimization A talk (in German) about my bachelor's thesis entitled "Atomic Norm Minimisation for Superresolution". Won one of the the "Best Talk (Bachelor)"-Prizes at the 17. Dies Mathematicus, 25.11.2022 at TU Berlin. [Slides] [Video] [MATLAB code for creating the figures in the talk]
• 3 minute talk about the Kullback-Leibler Divergence (Seminar Optimal Transport, Prof. Gabriele Steidl, summer semester 2021).
• Adversarial Regularisation in Inverse Problems (about a NeurIPS-2018 paper by Sebastian Lunz et al. by the same name in the seminar "Neural Networks for Inverse Problems" with Prof. Gabriele Steidl, winter semester 2021/2022).
• Compactly supported shearlets are optimally sparse (about a paper by Gitta Kutyniok and Wang-Q. Lim in J. Approx. Theory by the same name, Seminar Applied Functional Analysis, Prof. Kutyniok, summer semester 2019).
• Atomic Norm Minimisation for Superresolution (the topic of my bachelor's thesis, Seminar Optimal Transport, Prof. Gabriele Steidl, summer semester 2021).

Teaching at Technische Universität Berlin

• Summer semester 25: Mathematical Physics II - Statistical mechanics (lecturer: Prof. Dr. Yuri B. Suris) and Probability Theory I (lecturer: Prof. Wolfgang König)
• Winter semester 2024 / 2025: Harmonic Analysis (lecturer: Dr. Oleh Melnyk) and Analysis II (lecturer: Prof. Gabriele Steidl)
• Summer semester 2024: Convex Analysis (lecturer: Dr. Oleh Melnyk)
• From January to March 2024, I was an assistant for the Course "Numerische Mathematik I" (Numerical Mathematics I).
• I tutored the courses Linear Algebra for Engineers (in German, winter semester 2019/2020, Prof. Reinhard Nabben), Functional Analysis I (summer semester 2020, Prof. Dr. Nicole Mücke) and Differential equations I (in German, winter semester 2020/2021, Dr. Hans-Christian Kreusler).

Unofficial lecture notes & flashcards

Below you can find some lecture notes I wrote for courses I attended at TU Berlin in descending order by quality. I am satisfied with the top eight, read the rest at your own risk. If you find any errors or are perhaps an instructor discontented with the material shared here, please contact me at lastname at math.tu-berlin.de.

To help me study for the exams, I have created texed flashcards: [Approximation theory], [Functional Analysis II], [Topology I]. Beware that they might be incomplete and will probably contain errors. You can contact me at the above email adress if you want the corresponding .tex files.

• Discrete and Computational Topology, Dr. Frank Lutz, summer semester 2022.
• Statistik, Prof. Michael Scheutzow, summer semester 2022.
• Differential equations III: Initial-boundary value problems, Dr. Robert Lasarzik, summer semester 2021 [Flashcards].
• Differential equations IIA: Weak solutions for stationary PDEs, Dr. Hans-Christian Kreusler, summer semester 2019 and 2020 [Flashcards].
• Differentialgleichungen IIB: Stationäre nichtlineare partielle Differentialgleichungen und die Theorie monotoner Operator, Dr. Hans-Christian Kreusler, winter semester 2019/2020 [Flashcards].
• Lineare Algebra II, Prof. Boris Springborn, summer 2018.
• Complex Analysis, Prof. Boris Springborn, summer semester 2021 [Flashcards].
• Differentialgleichungen I: Gewöhnliche Anfangswertproblem und Randwertprobleme zweiter Ordnung , Dr. Hans-Christian Kreusler, winter semester 2018/19 and 2020/21.
• Nonlinear optimization, Prof. Dietmar Hömberg, summer semester 2020 (mostly in English, partially in German) [Flashcards].
• Wahrscheinlichkeitstheorie, Prof. Wilhelm Stannat, summer semester 2019.
• Machine Learning II, Dr. Grégoire Montavon, summer semester 2020.
• Complex Analysis, Prof. Yuri Suris, summer semester 2020.
• Computerorientiere Mathematik, Prof. Michael Joswig, summer semester 2020 [Flashcards].
• Machine Learning I, Prof. Klaus-Robert Müller, winter semester 2019/2020.
• Mathematics of Deep Learning, Prof. Gitta Kutyniok, winter semester 2019/2020.