Systematic approaches to the analysis and design of optimization algorithms
Adrien Taylor (INRIA, Paris)
In this talk, I will provide a high-level overview of recent principled approaches for constructively analyzing and designing numerical optimization algorithms. The presentation will be example-based, as the main ingredients necessary for understanding the methodologies are already present in the analysis of base optimization schemes, such as gradient descent. Based on those examples, I will discuss how those techniques can be leveraged for constructing Lyapunov-based analyses and optimal convex optimization algorithms. The methodology can be accessed through easy-to-use open-source packages (including PEPit: https://github.com/PerformanceEstimation/PEPit), allowing the use of the framework without the modelling pain. This talk is based on joint works with great colleagues that I will introduce during the presentation.
Spectral Phases of the Erdős–Rényi graph
Johannes Alt (Bonn University)
We consider the Erdős–Rényi graph on N vertices with expected degree d for each vertex. It is well known that the structure of this graph changes drastically when d is of order log N. Below this threshold it develops inhomogeneities which lead to the emergence of localized eigenvectors, while the majority of eigenvectors remains delocalized. In this talk, I will explain our results in both phases and present the phase diagram depicting them. For a certain regime in d, we establish a mobility edge by showing that the localized phase extends up to the boundary of the delocalized phase. This is based on joint works with Raphael Ducatez and Antti Knowles.
Algebraic machine learning and the problem of finding singularities
Markus Pflaum (University of Colorado)
TBA
TBA
Cordian Riener (UiT The Artic University)
TBA