Date/Time
Date(s) - 15/09/2023
12:30 pm - 1:30 pm

Location: HH 312

Speaker: Lothar Sebastian Krapp (University of Konstanz)

Title: NIP Archimedean Fields and Learning in Neural Networks

Abstract: In 1971, the related notions VC dimension and “not the independence property” (NIP) were established independently of each other. The former was introduced by Vapnik and Chervonenkis in the context of linear learning theory, the latter by Shelah in the study of stable theories — a highly abstract concept from model theory. It took 21 years until a connection between VC dimensions and NIP was noticed, describing how the two notions give different descriptions of the same idea. This connection resulted in an interesting application of a purely model theoretical and combinatorial concept to neural network learning.

In my talk, I will firstly outline the mathematical idea behind artificial neural networks over the ordered field of real numbers and in this regard describe the formal learning process for such a network. I will then highlight the theorem which links neural network learning to the model theoretic concept of NIP theories. Finally, I will present our recent progress in the study of NIP archimedean ordered fields.