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.

翻译：本文评估了在分类任务中确定神经网络保证稳定性和准确性的理论局限性。我们考虑经典的分布无关框架以及最小化经验风险且可能带有权重正则化的算法。研究表明，存在一大类任务，在这些任务设定下，即使给定神经网络架构类别中存在理想解，计算和验证理想的稳定且准确的神经网络也极其困难（甚至可能无法实现）。