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arXiv · 2309.07072

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

Alexander Bastounis·Alexander N. Gorban·Anders C. Hansen·Desmond J. Higham·Danil Prokhorov·Oliver Sutton·Ivan Y. Tyukin·Qinghua Zhou
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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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Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen, Desmond J. Higham, Danil Prokhorov, Oliver Sutton, Ivan Y. Tyukin, Qinghua Zhou. 2023-09-13. The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning. https://doi.org/10.1007/978-3-031-44207-0_44

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