用区间信念与模糊耦合建模不确定性，保障神经网络概率安全验证的可靠性。
Propagation of~Interval Belief Structures and~Imprecise Copulas for~Neural Network Verification
- 用区间信念结构和模糊耦合表示输入分布与依赖关系的不完全信息
- 通过前向传播推导出输出的概率下界与上界，覆盖所有兼容模型
- 适用于对安全性要求高、输入信息不精确的场景，如自动驾驶
神经网络的定量验证需要在输入分布及其依赖结构存在大量不确定性的情况下进行概率推理。在现实场景中，这些信息往往仅部分已知，若假设精确的概率模型可能导致不可靠结果。本文提出一个在不精确概率信息下进行定量验证的可靠框架，结合区间信念结构表示边际不确定性，使用模糊耦合建模依赖关系的不确定性。我们开发了通过前馈神经网络传播不精确耦合的区间信念结构的方法。利用混合模糊耦合体积，推导出仿射变换和激活函数下的可靠前向构造。所得输出可提供针对所有与指定不精确输入相容的概率安全性质的保证下界和上界。
原文摘要 · Abstract (English)
Quantitative verification of neural networks requires reasoning about probabilities under substantial uncertainty in both input distributions and their dependence structure. In realistic settings, this information is often only partially specified, and assuming precise probabilistic models can lead to unreliable results. We propose a sound framework for quantitative verification under imprecise probabilistic information, combining interval belief structures to represent marginal uncertainty with imprecise copulas to model uncertain dependence. We develop a propagation method for imprecisely coupled interval belief structures through feed-forward neural networks. Using mixed imprecise copula volumes, we derive sound push-forward constructions through affine transformations and activation functions. The resulting output can provide guaranteed lower and upper bounds on probabilistic safety properties, valid for all probability models compatible with the specified imprecise inputs.
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