The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning

Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil Prokhorov +3 more
9/13/2023
cs.LG

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Abstract

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks and potentially subjected to some weights regularisation. We show that there is a large family of tasks for which computing and verifying ideal stable and accurate neural networks in the above settings is extremely challenging, if at all possible, even when such ideal solutions exist within the given class of neural architectures.

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Cite this paper

@article{bastounis2023boundaries,
  title  = {The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning},
  author = {Alexander Bastounis and Alexander N. Gorban and Anders C. Hansen and Desmond J. Higham and Danil Prokhorov and Oliver Sutton and Ivan Y. Tyukin and Qinghua Zhou},
  year   = {2023},
  eprint = {2309.07072},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2309.07072v2}
}

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