Propagation of~Interval Belief Structures and~Imprecise Copulas for~Neural Network Verification
It addresses the problem of verifying neural network safety under realistic uncertainty in input distributions and dependence, offering a more reliable alternative to precise probabilistic models.
The paper proposes a sound framework for quantitative verification of neural networks under imprecise probabilistic information, combining interval belief structures and imprecise copulas to provide guaranteed bounds on safety properties.
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.