Learning a Sparse Representation of Barron Functions with the Inverse Scale Space Flow

Description

In this talk, we will discuss several results about Barron spaces. These spaces are the natural function spaces for neural networks and are instances of integral-type Reproducing Kernel Banach spaces (RKBS), which in turn are generalizations of Reproducing Kernel Hilbert spaces (RKHS). Integral-type RKBS are unions over RKHSs. Some of the results we know for RKHSs carry over to the RKBSs. We will briefly discuss properties like approximation rates, embeddings and a representer theorem. The representer theorem tells us that a sparse solution exists, but not how to find it. We present a method for finding that using the inverse scale space. The convergence properties of this method are analysed in an ideal setting and in the cases of measurement noise and sampling bias.

Period	15 May 2024
Held at	Centre for Analysis, Scientific computing and Applications (CASA), Netherlands
Degree of Recognition	Local