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In this work, we assess the theoretical limitations of determining guaranteedstability and accuracy of neural networks in classification tasks. We considerclassical distribution-agnostic framework and algorithms minimising empiricalrisks and potentially subjected to some weights regularisation. We show thatthere is a large family of tasks for which computing and verifying ideal stableand accurate neural networks in the above settings is extremely challenging, ifat all possible, even when such ideal solutions exist within the given class ofneural architectures.

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