# Chair for Mathematics of Information Processing

Our group's research interests revolve
around the broad areas of Information Processing and Data Science.
We work on the mathematical foundations of these areas in both deterministic and stochastic settings and
investigate the modelling of real world high-dimensional systems and the efficiency of their related numerical approaches in several subfields:

1.) Compressive Sensing is concerned with the recovery of objects (signals, functions, matrices etc.) from incomplete measurements.
We focus in particular on the analysis of structured random matrices arising in this context, on quantization in measurement schemes,
on phase retrieval and on the use of compressive sensing in numerical analysis (uncertainty quantification).

2.) Mathematical understanding of Machine Learning techniques: We are interested in several aspects of deep learning (deep neural networks):
convergence theory for (stochastic) gradient descent algorithms for learning neural networks, implicit bias, understanding overparametrization
and recurrent neural networks. Moreover, we investigate the use of the theory of rough paths and signature methods for machine learning.

3.) We work on various aspects of optimisation, robust optimisation, parametric optimisation, analysis of gradient descent and optimisation
algorithms related to compressive sensing.

Our work combines aspects from several mathematical areas: high-dimensional probability theory (random matrices), analysis (harmonic analysis, geometric functional analysis, convex analysis) and optimisation.

## Professors and Lecturers

Prof. Dr. Holger Rauhut
QI

Prof. Dr. Yubao Guo
QI

PD Dr. Harald Guenzel
QI

## Organisation

## Postal Address

RWTH Aachen University

Chair for Mathematics of Information Processing

Pontdriesch 12-14

52062 Aachen

Germany