Sophie Langer

Email: s.langer(at)rub.de

Ruhr University Bochum

Universitätsstraße 150

44801 Bochum

Germany

I am a Professor in Mathematical Statistics at Ruhr University Bochum. Prior to this, I worked as an Associate professor in the Statistics group at University of Twente.

In 2020, I completed my PhD at the Technical University of Darmstadt under the supervision of Michael Kohler.

After graduating, I worked as a postdoctoral researcher with Johannes Schmidt-Hieber at University of Twente and with Lorenzo Rosasco at Universita' di Genova, before joining University of Twente as an Assistant professor in October 2022.

My research mainly focus on the mathematical understanding of deep learning, combining statistical and computational-related aspects, with particular focus on deep learning in image classification. Recently, I got also interested in analysing different optimisation schemes and regularisation methods used in deep learning's training like accelerated gradient descent, dropout and SAM.

News and Upcoming Events

In March 2025, we started the initiative Kindness and Excellence in Academia, promoting a supportive, empathetic and inclusive academic environment. In case you are interested in joining our initiative or sharing your story related to this topic, feel free to contact me or email kindnessandexcellence[at]proton[dot]me.

Since January 2025, I am part of the strategic research initiative 'Real-World-Inspired Sequential Decision-Making' within 4TU.AMI

Keynote speaker at the Early Career Event on Uncertainty Quantification and AI for Science, Cambridge, UK (08/2025)

Invited talk at ENUMATH, Heidelberg, Germany (09/2025)

Invited talk at the European Conference on Computational Optimization, Klagenfurt, Austria (09/2025)

Seminar talk, University of Vienna, Austria (10/2025)

Organization of the Oberwolfach Mini-Workshop "Probabilistic Perspectives in Neural Network-based Machine Learning" (jointly with Sebastian Kassing, Steffen Dereich and Aymeric Dieuleveut), Oberwolfach, Germany (10/2025)

Invited talk at the Workshop "New challenges in high-dimensional statistics", CIRM, France (12/2025)

Seminar talk at TU Darmstadt, Germany (02/2026)

Oberwolfach Workshop "Mathematical Foundation of Digital Twins, Oberwolfach, Germany (06/2026)

Preprints

[1] On the expressivity of deep Heaviside networks (with I. Kong, J. Chen and J. Schmidit-Hieber)

[2] Training diagonal linear networks with stochastic sharpness aware minimization. (with G. Clara and J. Schmidt-Hieber). Preprint (2025).

[3] A novel statistical approach to analyze image classification (with J. Chen and J. Schmidt-Hieber). Preprint (2024).

[4] On the VC dimension of deep group convolutional neural networks (with A. Sepliarskaia and J. Schmidt-Hieber). Preprint (2024).

[5] Accelerated Mirror Descent for Non-Euclidean Star-convex Functions (with C. Lezane and W. Koolen). Preprint (2024).

Publications

[1] Dropout Regularization Versus l2-Penalization in the Linear Model (with G.Clara and J. Schmidt-Hieber). Journal of Machine Learning Research, to appear (2024).

[2] Convergence rates for shallow neural networks learned by gradient descent (with A. Braun, M. Kohler and H. Walk). Bernoulli, 30(1): 475-502 (2024).

[3] Statistical theory for image classification using deep neural networks with cross entropy loss (with M. Kohler). Journal of Statistical Planning and Inference, to appear (2024).

[4] Learning green’s function efficiently using low-rank (with K. Wimalawarne and T. Suzuki). ICML2023

[5] Estimation of a regression function on a manifold by fully connected deep neural networks (with M. Kohler and U. Reif). Journal of Statistical Planning and Inference, 222: 160-181 (2023).

[6] Estimation of a function of low local dimensionality by deep neural networks (with M. Kohler and A. Krzyzak). IEEE Transactions on Information Theory, 68(6): 4032-4042 (2022)

[7] Analysis of the rate of convergence of fully connected deep neural network regression estimates with smooth activation function. Journal of Multivariate Analysis, 182(C) (2021)

[8] Approximating smooth functions by neural networks with sigmoid activation function. Journal of Multivariate Analysis, 182(C) (2021)

[9] On the rate of convergence of fully connected deep very deep neural network estimates (with M. Kohler). Annals of Statistics, 49(4): 2231-2249 (2021)

[10] Discussion of "Nonparametric regression using deep neural networks with ReLU activation function" (with M. Kohler). Annals of Statistics, 48(4):1906-1910 (2020)

[11] Ein Beitrag zur statistischen Theorie des Deep Learnings. Verlag Dr. Hut (2020).

[A] The Smoking Gun: Statistical theory improves neural network estimates (joint with Michael Kohler), Oberwolfach Report 2021

[B] The Role of Statistical Theory in Understanding Deep Learning, Oberwolfach Report 2023

Selected Keynotes/Invited Talks

Keynotes:

Workshop "Understanding generalization in deep learning", Raitenhaslach (02/2025)

"Workshop for Junior Female Researchers in Probability" at TU Berlin (2024/07)

International Conference of Maths4DL, London (2023/07)

Invited Talks:

Workshop on "Mathematical Foundations of Data Science", Centre de Recherches Mathématiques (CRM), Montréal, Canada (06/2025)

Oberwolfach Workshop "Frontiers of Statistics and Machine Learning" (03/2025)

WIAS research seminar, Berlin (02/2025)

Workshop "Statistical Theory of Deep Neural Network Models" , Brin Mathematics center, University of Maryland, USA (2024/11)

Workshop "Probabilistic and statistical analysis of random networks, stochastic processes and deep neural networks", Nice, France (2024/09)

Oberwolfach Workshop "Applied Harmonic Analysis and Data Science" (2024/04)

Noon Seminar of C3S , Frankfurt, Germany (2024/04)

EURANDOM 25th anniversary , Eindhoven, Netherlands (2024/04)

SMSA, Delft, Netherlands (2024/03)

SIAM Conference on Uncertainity Quantification ,Trieste, Italy (2024/02)

Google Research Workshop on Deep Learning Down Under in Lorne, Australia (2024/01)

IMS-APRM , Melbourne, Australia (2024/01)

Selected Seminar Talks: TU Eindhoven (2025/06), Sorbonne Université (2025/05), LMU Munich (2025/01), Heinrich Heine University Düsseldorf (2024/09), Karlsruher Institut für Technologie (2024/02), Ruhr-Universität Bochum (2023/12), Universität Heidelberg (2023/07), Eindhoven University of Technology (2023/01)

Invited Talks (2021-2023)

Oberwolfach Workshop "Nonlinear approximation of high-dimensional functions in scientific computing" (2023/10)

Latin American congress of probability and mathematical statistics, São Paulo (2023/07, link to program)

Seminar++ - Machine Learning Theory, Amsterdam (2023/05, link to program)

Workshop on Functional Inference and Machine Intelligence, Tokyo (2023/03, link to program)

Meeting in Mathematical Statistics, CIRM, Luminy (2022/12, link to program)

One World Seminar Series on the Mathematics of Machine Learning (2022/10, link to program, video of my talk)

Non-linear and High Dimensional Inference, IHP, Paris (2022/10, link to program and video)

IMS Annual Meeting, London (2022/06, link to program)

Curve and Surfaces, Arcachon (2022/06, link to program)

ESI Workshop on Computational Uncertainty Quantification: Statistical estimation and deep learning in UQ for PDEs, Vienna (2022/05, link to program, video of my talk)

CMStatstics, London (2021/12)

Oberwolfach Workshop: "Mathematical Foundations of Machine Learning" (2021/03)

Awards and Grants

Veni grant, NWO Talent Programme, 2024-2027

Incentive grant (together with Moritz Hahn and Janusz Meylahn), University of Twente, 2024 - 2028

Ruth Moufang Price - Best female PhD-student in Mathematics, TU Darmstadt, 2020

Ruth Moufang Price - Best female Postdoc in Mathematics, TU Darmstadt, 2020

Editorial activities

Electronic Journal of Statistics (2025 - )

Journal of Statistical Planning and Inference (2024 - )

Guest editor for a special volume on "Deep learning: Statistical perspectives", Journal of Statistical Planning and Inference (with Johannes Schmidt-Hieber and Taiji Suzuki), 2023/24

Short Courses and Invited Lectures

Invited short course about Statistical theory of deep learning, Universidade de Aveiro, Portugal (2024/07)

Invited short course at the Latin American congress of probability and mathematical statistics, Sao Pãulo (2023/07)

Invited Lecture on Statistical Learning Theory and Applications at the Centre of Brains, Minds and Machines (link to course description), MIT, Boston (2022/11)

Research school (part 1): High-dimensional approximation and Deep Learning (link to program), Nantes (2022/05)

Online short course on (deep) statistical learning, UCLouvain (2021/12)

Online short course on Statistical Theory of Deep Learning, International Statistical Institute (2022/12)

Conference and Seminar Organizations

Workshop "Statistical Theory of Neural Networks" (with Johannes Schmidt-Hieber and Gabriel Clara), Egmond aan Zee, Netherlands (05/2025)

Seminar series on the Mathematics of Data Science (with Marcello Carioni), University of Twente (since 2023/01- 2025/03)

Invited session organization at 6th International Symposium on Nonparametric Statistics in Braga, Portugal (2024/06)

Session organization (with Tim van Erwen), Second workshop on AI and Mathematics, University of Twente (2023/06)

Machine Learning Session (with Michael Kohler), German Probability and Statistic Days 2023, Essen (2023/03)

Workshop on the statistical analysis of deep learning (with Stefan Richter and Johannes Schmidt-Hieber), Sommerakadamie der Studienstiftung, Hattingen (2022/08)

Minisymposium on "The Role of Learning Theory in Machine Learning" (with Nicole Mücke), EWM General Meeting, Helsinki (2022/08)

Teaching

Statistics I, Ruhr University Bochum (summer semester 2025)

Mathematical Statistics II, University of Twente (fall semester 2023/2024 & 2024/2025)

Capita Selecta Statistics on Theory of Reinforcement Learning, University of Twente (summer semester 2024)

Statistics for Industrial Engineering and Management, University of Twente (summer semester 2024)

Capita Selecta Statistics on the Theory of Deep Learning (link to course description), University of Twente (summer semester 2023)

Lecture on Statistical Foundations of Deep Learning, TU Darmstadt (summer semester 2021)

Miscellaneous

I have three great PhD students: Clement Lezane (joint supervision with Wouter Koolen), Gabriel Clara (joint supervision with Johannes Schmidt-Hieber), and Leon Halgryn (joint supervision with Janusz Meylahn and Moritz Hahn)
I was a member of the Young Academy at University of Twente (before leaving the Netherlands)
I want to support women in science as we are still strongly underrepresented. Without having really planned this career paths, I am today incredibly happy to do what I do. If you are thinking about a career in academia and are unsure, feel free to contact me and I will share my experiences.
Recently, I shared my academic journey with WAZ, see article
I have a weakness for Pizza. In my opinion, this is the place with the best.
I dance ballet and am a gifted yogi. Painting and writing helps me to switch off from everyday life.
I love quotes. One of my favorite is written below.

The invariable mark of wisdom is to see the miraculous in the common.

Ralph Waldo Emerson

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