简单神经网络的可达性
Reachability In Simple Neural Networks
AI总结：
研究简单神经网络可达性问题的复杂性，证明其NP难性，探讨单隐层和单输出维度的神经网络的NP难性，并讨论神经网络验证的扩展方向。
摘要：
我们研究了深度神经网络的可达性问题的复杂性：给定有效输入，是否能计算有效输出？最近有人声称，对于一般神经网络和由线性不等式连结给出的输入/输出维度规范，该问题是NP完全的。我们回顾了证明并修复了原始上界和下界证明中的缺陷。受一般结果启发，我们证明NP难性在受限的简单规范和神经网络类别中也成立。允许单个隐藏层和单输出维度，以及仅含一个负权、零权和一个正权或偏置的神经网络就足以保证NP难性。此外，我们还详细讨论了该神经网络验证方向的可能扩展。
英文摘要：
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 specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.
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