#DNN-Verification 问题：深度神经网络的不安全输入计数
The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks
AI总结：
本文提出#DNN-Verification问题，旨在精确或近似计算导致深度神经网络违反安全属性的输入数量，并给出复杂度分析及一种带概率界限的随机近似方法。
摘要：
深度神经网络越来越多地被应用于需要高度安全性的关键任务中，例如自动驾驶。虽然最先进的验证器可以用来检查深度神经网络相对于某些给定属性是否不安全（即是否存在至少一个不安全输入配置），但它们的二元输出对于其他目的（如屏蔽、模型选择或训练改进）而言信息量不足。在本文中，我们引入了#DNN-Verification问题，该问题涉及计算深度神经网络中导致特定安全属性被违反的输入配置的数量。我们分析了该问题的复杂性，并提出了一种能够返回违规精确数量的新颖方法。由于该问题是#P完全的，我们还提出了一种随机近似方法，该方法在显著降低计算需求的同时，提供了正确计数的可证明的概率界限。我们在一些安全关键基准上展示了实验结果，证明了我们近似方法的有效性，并评估了该界限的紧致性。
英文摘要：
Deep Neural Networks are increasingly adopted in critical tasks that require a high level of safety, e.g., autonomous driving. While state-of-the-art verifiers can be employed to check whether a DNN is unsafe w.r.t. some given property (i.e., whether there is at least one unsafe input configuration), their yes/no output is not informative enough for other purposes, such as shielding, model selection, or training improvements. In this paper, we introduce the #DNN-Verification problem, which involves counting the number of input configurations of a DNN that result in a violation of a particular safety property. We analyze the complexity of this problem and propose a novel approach that returns the exact count of violations. Due to the #P-completeness of the problem, we also propose a randomized, approximate method that provides a provable probabilistic bound of the correct count while significantly reducing computational requirements. We present experimental results on a set of safety-critical benchmarks that demonstrate the effectiveness of our approximate method and evaluate the tightness of the bound.
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