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.


  • 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.Montufar880G4 11personal
Banerjee, Pradeep KumarPradeep.Banerjee884G4 13 
Nguyen, QuynhQuynh.Nguyen876G4 10 
Wang, YuguangYuguang.Wang850G4 01personal
Bréchet, PierrePierre.Brechet887G4 01 
Müller, JohannesJohannes.Mueller885G4 13external
Tseran, HannaHanna.Tseran881G4 13external

Future group members and visitors

  • An, Jing


    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/collaborateur.

    Outstanding candidates will always be considered. 

    20.04.2021, 01:40