Fredholm integral equations for function approximation and the training of neural networks

Patrick Gelß, Aizhan Issagali, Ralf Kornhuber

Published 2023-03-09, updated 2023-04-17Version 2

We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods.