Umberto Hryniewicz (RWTH Aachen University)

Title: Classical Morse theory and deep learning
Abstract: The goal of this talk is to bring ideas from classical Morse theory closer to some problems arising in deep learning. We would like to discuss possible implications that certain statements about gradient flows of proper real-analytic functions might have in the analysis of “linear” deep learning schemes. An example of such a statement would be that a “typical” anti-gradient trajectory of a proper real-analytic function which is bounded from below converges necessary to a local minimum. The analogous version of this statement holds for a generic smooth function.