Propagation of~Interval Belief Structures and~Imprecise Copulas for~Neural Network Verification

2026-06-29

AI Summary

This work addresses the challenge of verifying probabilistic safety guarantees for neural networks when the input distribution and its dependency structure are only partially known. The authors propose a novel framework that integrates interval-valued belief structures with imprecise copulas—a combination not previously explored—to construct forward propagation operators tailored for affine transformations and activation functions. By employing a hybrid imprecise copula volume method, the approach enables end-to-end propagation of uncertainty and efficiently computes tight lower and upper bounds on the probability of output safety properties. These bounds are guaranteed to hold universally across all probability models consistent with the specified imprecise input information, thereby significantly enhancing the robustness and reliability of the verification results.

Abstract

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.

Problem

• neural network verification
• imprecise probabilities
• interval belief structures
• copulas
• uncertainty propagation

Innovation

• interval belief structures
• imprecise copulas
• neural network verification
• uncertainty propagation
• probabilistic safety bounds