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arXiv · 2303.05262

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

Patrick Gelß·Aizhan Issagali·Ralf Kornhuber
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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.

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Patrick Gelß, Aizhan Issagali, Ralf Kornhuber. 2023-03-09. Fredholm integral equations for function approximation and the training of neural networks. https://arxiv.org/abs/2303.05262

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