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math.OC2024
On the mean field limit of consensus based methods
Marvin Koß, Simon Weissmann, Jakob Zech
Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivativ…
cs.LG2024★ 1 cited
Mathematical theory of deep learning
Philipp Petersen, Jakob Zech
This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learni…
math.NA2024
On the mean-field limit for Stein variational gradient descent: stability and multilevel approximation
Simon Weissmann, Jakob Zech
In this paper we propose and analyze a novel multilevel version of Stein variational gradient descent (SVGD). SVGD is a recent particle based variational inference method. For Baye…