7 papers
Characterization of the reproducing structure of the Bessel potential spaces beyond
Tjeerd Jan Heeringa
Reproducing kernel Hilbert spaces are uniquely characterized by their kernel, but reproducing kernel Banach spaces (RKBS) are not. However, a characterization of which RKBS admit a…
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Sven Dummer, Tjeerd Jan Heeringa, José A. Iglesias
Recently, there has been growing interest in characterizing the function spaces underlying neural networks. While shallow and deep scalar-valued neural networks have been linked to…
Deep Networks are Reproducing Kernel Chains
Tjeerd Jan Heeringa, Len Spek, Christoph Brune
Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banac…
Sparsifying dimensionality reduction of PDE solution data with Bregman learning
Tjeerd Jan Heeringa, Christoph Brune, Mengwu Guo
Classical model reduction techniques project the governing equations onto a linear subspace of the original state space. More recent data-driven techniques use neural networks to e…
Learning a Sparse Representation of Barron Functions with the Inverse Scale Space Flow
Tjeerd Jan Heeringa, Tim Roith, Christoph Brune +1
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an function , the inverse scale space flow is used to find a spar…
Embeddings between Barron spaces with higher order activation functions
Tjeerd Jan Heeringa, Len Spek, Felix Schwenninger +1
The approximation properties of infinitely wide shallow neural networks heavily depend on the choice of the activation function. To understand this influence, we study embeddings b…
Duality for Neural Networks through Reproducing Kernel Banach Spaces
Len Spek, Tjeerd Jan Heeringa, Felix Schwenninger +1
Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various areas of machine learning. Recently, Barron spaces have been used to prove bounds on the genera…