
Workshop DonauIsarInn
WDI²  Approximation Theory and Applications
in honor of Prof. Dr. Rupert Lasser  
Program Registration Directions
Program
(preliminary) Schedule


1pm 
Welcome Address 
1:05pm 
Frames and dynamical samplingFrames and dynamical sampling The talk will give a short survey on frame theory in Hilbert spaces, followed by a more detailed discussion of the recent recearch topic "dynamical sampling." Formulated in purely mathematical terms, the key question is when and how a frame a frame can be represented via iterations of a certain bounded operator, acting on a fixed vector in the underlying Hilbert space. The talk presents joint work with Marzieh Hasannasab. Ole Christensen ^{} DTU  Technical University of Denmark 
1:50pm 
Break 
2:00pm 
Approximation theoretic properties of deep ReLU neural networks Approximation theoretic properties of deep ReLU neural networks Studying the approximation theoretic properties of neural networks with smooth activation function is a classical topic. The networks that are used in practice, however, most often use the nonsmooth ReLU activation function. Despite the recent incredible performance of such networks in many classification tasks, a solid theoretical explanation of this success story is still missing. In this talk, we will present recent results concerning the approximation theoretic properties of deep ReLU neural networks which help to explain some of the characteristics of such networks; in particular we will see that deeper networks can approximate certain classification functions much more efficiently than shallow networks, which is not the case for most smooth activation functions. We emphasize though that these approximation theoretic properties do not explain why simple algorithms like stochastic gradient descent work so well in practice, or why deep neural networks tend to generalize so well; we purely focus on the expressive power of such networks. As a model class for classifier functions we consider the class of (possibly discontinuous) piecewise smooth functions for which the different "smooth regions" are separated by smooth hyper surfaces. Given such a function, and a desired approximation accuracy, we construct a neural network which achieves the desired approximation accuracy, where the erroris measured in L^2. We give precise bounds on the required size (in terms of the number of weights) and depth of the network, depending on the approximation accuracy, on the smoothness parameters of the given function, and on the dimension of its domain of definition. Finally, we show that this size of the networks is optimal, and that networks of smaller depth would need significantly more weights than the deep networks that we construct, in order to achieve the desired approximation accuracy. Felix Voigtländer ^{} Catholic University of EichstättIngolstadt 
2:30pm 
A Deterministic Sparse FFT for Functions with Structured Fourier Sparsity A Deterministic Sparse FFT for Functions with Structured Fourier Sparsity Abstract here. Sina Bittens ^{} University of Göttingen 
3:00pm 
Coffee and Cake 
3:45pm 
Von der Abstrakten zur Anwendungsorientierten Harmonischen AnalyseVon der Abstrakten zur Anwendungsorientierten Harmonischen Analyse In diesem kurzen Beitrag möchte ich ausgehend von einer kurzen historischen Betrachtung des Gebietes der Harmonischen Analyse, über die Tagungen zur Harmonischen Analyse in der abstraktesten Form, bei denen wir einaner erstmals begegnet sind, auf die Entwicklungen der letzten 40 Jahre eingehen. Diese Zeit ist geprägt von einer Reaktivierung und starken Verbreiterung der Forschungsaktivitäten, vor allem aber auch des Anwendungsbezuges sowie der Verwendung von Numerischen Methoden. Die Entwicklung der Wavelets, aber ebenso der Gabor Analysis oder neuerdings der Shearlets, aber genauso Einsichten im Bereich der orthogonalen Polynome und Hypergruppen haben dazu beigetragen. Ich werde an die junge Generation appellieren, weiter Anstrengungen in diese Richtung zu machen, auch um die Bedeutung der Harmonischen Analyse im Gesamtkontext der Angewandten Mathematik hochzuhalten. Hans Georg Feichtinger ^{} University of Vienna 
4:05pm 
Break 
4:10pm 
Sampling in shiftinvariant spaces with totally positive generatorsSampling in shiftinvariant spaces with totally positive generators We will present new results on nonuniform sampling in shiftinvariant spaces whose generator is a totally positive function. For a subclass of such generators the sampling theorems can be formulated in analogy to the theorems of Beurling and Landau for bandlimited functions. In contrast to the cardinal series, the reconstruction procedures for sampling in a shiftinvariant space with a totally positive generator are local and thus accessible to numerical linear algebra. Karlheinz Gröchenig ^{} University of Vienna 
4:55pm 
Break 
5:05pm 
Subsampled random convolutions in sparse recoverySubsampled random convolutions in sparse recovery I will discuss recovery of (approximately) sparse vectors from its subsampled convolution with a random vector and, in particular, provide bounds on the number of samples required for successful recovery. Apart from this standard linear compressive sensing setup, we will present new results for onebit compressed where only the sign of each entry of the subsampled convolution is retained. Finally, we generalize to certain nonlinear functions replacing the sign function. Holger Rauhut ^{} RTWH Aachen 
5:50pm 
End of Scientific Program 
7:00pm 
Dinner Location: Scheidegger ^{} 
Workshop dinner
We invite the participants to join us for dinner at 7 PM at restaurant Scheidegger ^{}.
Registration
If you are interested in our workshop, please register until June 15, 2018 and indicate whether you plan to attend the conference dinner. This will facilitate the organization of the event. Registration is free.
For registration, please contact Frau Silvia TothPinter (tothpinterma.tum.de). If you have further questions, please contact the organizers (wdiima.tum.de).
Directions
The venue of the workshop is the building of the Mathematics and Informatics departments of TU München (Boltzmannstr. 3, 85747 Garching) on the Garching campus, Room MI 00.06.011 (Lecture Hall MI HS 3), located straight through the hall when entering through the main entrance.
The Garching campus can easily be reached by subway (UBahn Linie U6, station GarchingForschungszentrum) from Munich city center. There are many parking lots free of charge in LudwigPrandtlStraße at the back of the building. Further details can be found here.
Organizers
Frank Filbir ^{}
Sara KrauseSolberg
Nada Sissouno
Contact: wdiima.tum.de
