Mathematical Machine Learning

Guido Montúfar (Email)

+49 (0) 341 - 9959 - 880

+49 (0) 341 - 9959 - 658

Inselstr. 22
04103 Leipzig

Research group Guido Montúfar

Our group (started July 2018) is supported by the ERC StG project. It is located at the Max Planck Institute for Mathematics in the Sciences in Leipzig. The head of the group, Guido Montúfar, also holds a position at UCLA.

Research topics

Deep Learning Theory:
Geometric Analysis of Capacity, Optimization, and Generalization for Improving Learning in Deep Neural Networks.

Deep Learning is one of the most vibrant areas of contemporary machine learning and one of the most promising approaches to Artificial Intelligence. Deep Learning drives the latest systems for image, text, and audio processing, as well as an increasing number of new technologies. The goal of this project is to advance on key open problems in Deep Learning, specifically regarding the capacity, optimization, and regularization of these algorithms. The idea is to consolidate a theoretical basis that allows us to pin down the inner workings of the present success of Deep Learning and make it more widely applicable, in particular in situations with limited data and challenging problems in reinforcement learning. The approach is based on the geometry of neural networks and exploits innovative mathematics, drawing on information geometry and algebraic statistics. This is a quite timely and unique proposal which holds promise to vastly streamline the progress of Deep Learning into new frontiers.


  • Workshop on Algebraic Geometry, Combinatorics, and Machine Learning (online on August 08, 2022)
  • Geometry & Learning from Data (Online) (21w5239) (October 24 - 29, 2021, Banff International Research Station for Mathematical Innovation and Discovery)
    In this workshop we will bring together experts from academia, government stakeholders, applied researchers from industry, as well as graduate students and early career scientist to interact and develop novel solutions that apply abstract tools from high dimensional geometry to contribute to the solution of these problems.
  • Conference on Mathematics of Machine Learning (August 04 - 07, 2021, Center for Interdisciplinary Research (ZiF), Bielefeld University)
    The conference is aimed as a contribution to the field of Mathematics of Machine Learning, by bringing together experts from various mathematical areas with shared interest in applications to machine learning and experts from fields such as computer science and biology.
  • Deep Learning Theory Kickoff Meeting (March 27 - 29, 2019, MPI MiS Leipzig)
    This meeting aims to discuss mathematical topics in machine learning and deep learning and to kickoff the ERC project Deep Learning Theory at MPI MIS.

Group Members

Nachname, VornameEmailTelefonRaumHomepage
Montúfar, GuidoGuido.Montufar731E2 05personal
Banerjee, Pradeep KumarPradeep.Banerjee733E2 06 
Brandenburg, Marie-CharlotteMarie.Brandenburg810G3 04external
Bréchet, PierrePierre.Brechet726E2 04 
Tseran, HannaHanna.Tseran666----external

Future group members


Postdoc positions, PhD positions, and Research internships available:
Please see the general MPI MiS application form and for PhD scholarships the IMPRS application form. Select Guido Montúfar as mentor/collaborator.

Outstanding candidates will always be considered.

27.09.2023, 01:41