Colloquium Mathematics - Dr. J. Schulte

Title: High-dimensional random tessellations, deep neural networks and image classification in a security relevant setting

Abstract:

Random tessellations as hyperplane and Voronoi tessellations are probabilistic models studied in stochastic geometry. In the talk a recent line of research concerning asymptotic properties of random tessellations for growing dimension of the Euclidean space is presented. Random tessellations have applications in data science and multivariate statistics since each classification problem corresponds to the search for a tessellation. Here, in particular deep neural networks are a recent controversial approach with great successes in machine learning challenges on the one hand but the lack of mathematical understanding and robustness on the other hand. For illustration we present the results of a feasibility study concerning the application of deep neural networks in a security relevant setting. Improving the mathematical understanding of deep neural networks is thus a topic of high interest. The talk will be concluded with some open mathematical questions.

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