Programm des Workshops

Training neural networks requires significant memory and specialized hardware, directly impacting the accessibility and carbon footprint of acquiring such models. Dynamic sparse training, in which the model maintains high sparsity throughout training, provides one potential remedy. In this talk we focus on Linearized Bregman Iterations (LinBreg) which minimizes the training loss while implicitly minimizing a sparsity-promoting regularizer. We consider a multilevel version of LinBreg which periodically freezes the sparsity pattern and also consider adaptive regularization parameter strategies to ensure a target sparsity level is achieved.

Dynamical systems evolving on non-uniform time domains arise naturally in many contexts where continuous and discrete dynamics interact. The calculus on time scales, introduced by Stefan Hilger, provides a unifying framework to study such systems within a single mathematical theory. In this talk, we explore stability questions in this hybrid setting, with a particular focus on robustness. After a concise introduction to time scale calculus, we turn to input- to-state stability (ISS). The main part of the presentation highlights recent advances in the characterization of ISS for both linear and nonlinear systems on time scales. We discuss various generalizations of classical results from continuous and discrete systems.

In the final part, I will address when and if stability properties are preserved under small changes of the underlying time scale. To this end I present results on the robustness of ISS with respect to distortions of the time scale and identify conditions under which stability is preserved.

We are interested in sparse optimization problems with convex objective where sparsity is achieved by an explicit L⁰--constraint. This non-convex constraint can be equivalently reformulated by the difference of two convex functions, the L¹-norm and the so-called largest-K-norm. A penalty approach renders the resulting problem to be of difference-of- convex (DC) type, which can be adressed using the well-known. DC algorithm. In this talk we present theoretical and numerical results on this approach and its application in optimal control and inverse problems. Moreover, we show that this approach can be generalized to problems with an L⁰-constraint on the gradient of the optimization variable, i.e., where piecewise constant solutions are the target.