Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Sebastian Krapp

In this talk, I will illustrate how the concept of Vapnik–Chervonenkis (VC) dimensions connects the three areas of this seminar: Complexity Theory, Model Theory and Set Theory. While the VC dimension is classically introduced in Statistical Learning Theory as a measure for the complexity of indicator function classes, it can also be applied to first-order formulas within Model Theory. This connection between Statistical Learning and Model Theory opens a fascinating interplay between artificial neural network learning and the study of NIP archimedean ordered fields. I will illustrate this interplay by describing the intuition behind statistical learning as well as by giving explicit examples of VC dimensions of functions classes and first-order formulas.