Gelß, P. and Issagali, A. and Kornhuber, R.
(2023)
*Fredholm integral equations for function approximation and the training of neural networks.*
arXiv
.
(Submitted)

PDF
547kB |

Official URL: arXiv:2303.05262v2

## 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. Patrick , Aizhan , Ralf

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

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Computational PDEs Group |

ID Code: | 2966 |

Deposited By: | Ulrike Eickers |

Deposited On: | 27 Apr 2023 13:37 |

Last Modified: | 27 Apr 2023 13:37 |

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