Kolloquium Wilhelm Killing

New postdocs of Mathematics Münster will introduce themselves at the MM Postdoc Colloquium. In short lectures they will give an insight into their fields of research and outlined the research questions they will be dealing with in Münster.

• Gayrat Toshpulatov -- Long time behavior of kinetic equations
• Dario Reggiani -- Gamma-convergence and stochastic homogenisation of degenerate functionals
• Francesco Deangelis -- Homogenization on randomly perforated domains
• Floris Vermeulen -- Definable sets in valued fields
• Ioannis Zachos -- On semi-stable integral models for some Shimura varieties
• Sam Shepherd -- Quasi-isometric rigidity of groups

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The mathematical core of deep learning is function approximation by neural networks trained on data using stochastic gradient descent.

I will present a collection of results on training dynamics for the deep linear network (DLN). The DLN is a phenomenological model of deep learning for linear functions that was introduced by computer scientists. It allows a comprehensive analysis that reveals interesting ties with several areas of mathematics and several lessons for 'true' deep learning.

This is joint work with several co-authors: Nadav Cohen (Tel Aviv), Kathryn Lindsey (Boston College), Alan Chen, Zsolt Veraszto and Tianmin Yu (Brown).

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