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Corpus ID: 231662111

Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem

@article{Antun2021CanSA,
title={Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem},
author={Vegard Antun and Matthew J. Colbrook and A. Hansen},
journal={ArXiv},
year={2021},
volume={abs/2101.08286}
}

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, DL suffers from a universal phenomenon: instability, despite universal approximating properties that often guarantee the existence of stable neural networks (NNs). We show the following paradox. There are basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm… CONTINUE READING