We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive input/output specifications. We repair some flaws in the original upper and lower bound proofs. We then show that NP-hardness already holds for restricted classes of simple specifications and neural networks with just one layer, as well as neural networks with minimal requirements on the occurring parameters.

中文翻译：

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即使对于最简单的神经网络，可达性也是 NP 完备的

我们研究了（深度）神经网络可达性问题的复杂性：在给定一些有效输入的情况下，它是否计算有效输出？最近有人声称该问题对于一般神经网络和联合输入/输出规范是 NP 完全的。我们修复了原始上下界证明中的一些缺陷。然后，我们证明 NP-hardness 已经适用于仅具有一层的简单规范和神经网络的受限类别，以及对出现参数的要求最低的神经网络。