Kornhuber, Ralf
*Fredholm integral equations for function approximation and the training of neural networks.*
(Submitted)

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## Abstract

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.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Numerical Analysis |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3153 |

Deposited By: | Prof. Dr. Ralf Kornhuber |

Deposited On: | 09 Aug 2024 10:00 |

Last Modified: | 09 Aug 2024 10:00 |

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