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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
Stephen S-T. 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.