BIMSA > Seminar on Control Theory and Nonlinear Filtering The Kolmogorov Superposition Theorem and High Dimensional Function Approximation
The Kolmogorov Superposition Theorem and High Dimensional Function Approximation
Organizer
Shing Toung Yau
Speaker
Zeju Sun
Time
Tuesday, January 10, 2023 9:00 PM - 9:30 PM
Venue
Online
Abstract
In this talk, we will discuss the paper entitled "The Kolmogorov Superposition Theorem can Break the Curse of Dimension When Approximating High Dimensional Functions" by M.-J. Lai and Z. Shen. In this paper, the authors explain how to use Kolmogorov Superposition Theorem to break the curse of dimension when approximating continuous multivariate functions. Using the so-called LKB-splines to approximate high dimensional functions, the authors show that it is not necessary to use a lot of basis functions or a lot of data locations when approximating high dimensional continuous functions which is not very oscillated.